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Resource 2: Looking at properties of solids Teacher resource for planning or adapting to use with pupils Many objects are made from solids. Solids come in many different types, each with their own properties. The properties of the solid must be suitable for the object it is being used to make. One activity for your pupils is to brainstorm all the different properties materials can have. Put out a display of objects around the classroom. Make a label for each object with some questions (see below for examples). Pupils, working in pairs, should spend 20 minutes looking at the objects and answering the questions about the materials to help them describe their properties. Here are some suggestions for objects and labels for your display: |Piece of copper wire||Pick up the wire. Can you bend it? Where have you seen it being used? What is able to pass through it?| |Woven basket||How does the basket feel? Can you easily pull it apart?| |Metal spoon||Pick up the spoon and think of three words to describe how it feels. What happens to the spoon if you put one end in a cup of very hot water?| |Pottery cup||Can you change the shape of the pottery? Would it break if you dropped it? (DO NOT TRY THIS.)| |Piece of glass||Can you see through the glass? What would happen if you dropped it? (DO NOT TRY THIS.)| |Plastic bag||What happens if you drop water onto the plastic bag? Does it go through into the bag? Can you easily fold up the bag?| |Wooden spoon||Can you bend the spoon? What happens to the spoon if you put one end in a cup of very hot water?| |Piece of cotton fabric||Hold the material up to your face. Can you see through it? What does it feel like?| |Small magnet and pins||Move the magnet over the pins. What happens? Where have you seen a magnet being used?| As your pupils look at the objects you should move around the class talking to pupils about what they observe. At the end of the time, gather your pupils back together and ask different pupils to tell you what they observed about one of the objects. Build up a list of properties on your chalkboard or class wall. If your pupils aren’t familiar with these property words in English, let them use them in their own language. You could put the English words on a display in your classroom to help pupils learn them. This is an example list: Melting point (high/low) Insulator (heat and electricity) Conductor (heat and electricity) Easy to cut Make sure that your pupils can explain what each property means and ask them to draw a table in their books to show each property and an example of a material with that property e.g. |Property||What it means||Example| |Insulator||Does not let heat go through it||Wood| Now set your pupils some problems around choosing materials. Here are some examples: A: Isanga grows vegetables close to her house but she needs some way of protecting her young plants from birds. What sort of structure might she build? What materials should she use? Why should she choose these materials? B: Gagwala wants to put a new top on the table in his kitchen; the old one is very uneven and covered in burn marks. What sort of material should he use for the new table top? C: Samuel needs a bag to carry his books to school. What sort of material should he choose for the bag? For each problem, pupils should think about what the object needs to do, and choose, from their list, the properties it must have. Then they can choose which material would be best in each case.
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Respect Teacher Resources Find Respect educational ideas and activities Showing 1 - 20 of 750 resources Digital citzenship is explored as your class discusses how to show respect in social situations, in-person, and online by recognizing the importance of "tone" in both face-to-face and online communications. Using a hand-out, learners edit an e-mail message and follow rules given for writing clear and respectful e-mails. Students identify different ways to demonstrate respect towards others. They discuss ways to show respect using their eyes, ears, mouth, and hands, identify how they like to be treated by others, and draw a picture of ways to show respect. First graders identify behaviors and attitudes that demonstrate respect versus disrespect toward others. They discuss examples of how to respect others, describe pictures of examples of respectful behavior, and role-play scenarios of various ways to demonstrate respect. Third graders identify the main ideas illustrated in the story "Dancing Rainbows." They identify details from the story that show respect toward self and others. Students write a paragraph to illustrate how the Tewa Indians show respect. Students participate in a service project to show respect for their school or community. Fourth graders explore how to hold conversations and respect the privacy of others. They discuss why it is important to ask those in authority for help and to respect others' belongings. They review signs they have observed in public and discuss the meanings of them. They simulate scenarios where they need to ask others for things and show respect for the privacy of others. First graders discuss the term "respect beliefs and unique" their definitions and ways that we can show respect to others. They brainstorm ways that people are unique and their different beliefs and complete the handout, "My family and I." Young scholars discuss how to respect other's privacy online. In this personal information lesson plan, students discuss the reputation of themselves and others if privacy information is leaked out. Eleventh graders explore, analyze and study how to make decisions and act as responsible members of society. They role-play several scenarios of enactments of individuals making choices for resolving conflict while respecting others. Learners get together in small groups to create a set of rules, such as how to respectfully express one's opinion, and how to respect other people's opinions, even if they differ from you own. Everyone role-plays, and attempts to use the rules they came up with. Students participate in meaningful discussion about respecting others. In this character education lesson, students respond to a poem on respect and work in small groups to create a way to present the respect message to an audience (poem, short play, poster, news article, web page, debate, documentary) Learners discuss ways to help and respect others. They create skits that demonstrates cooperation, sportsmanship, and kindness. They video skits and share the information with other grades. Students write an essay on respectfulness. Students identify persons whom they respect and who have influenced them to remain drug free. They define "influence" and "respect," list individuals who influence them in a positive way, complete an activity sheet, and discuss the results of the activity sheet. Students apply research skills, open-ended discussions, and cooperative learning experiences to investigate the meaning of respect. Practicing good manners means showing respect for yourself, for others, for property, and for the world at large. First graders explore the topics of fair play, good sportsmanship, showing respect for others, and treating others the way you want to be treated. They listen to stories, draw pictures, and participate in games that support the topic of fair play and respect for others. Third graders explore respect. For this lesson about respecting others and their property, 3rd graders learn hoe to be nice to other people. Students discuss different situations and whether or not it is being respectful. Students write a story about a person they respect and then role-play the situations discussed earlier. Students discuss proper ways to work in a group. In this character education lesson, students identify the vocabulary words "inclusion" and "exclusion" and create a list of ways to respect others in a group setting. Students increase listening comphrehension and use critical thinking skills. They take turns and show respect for the work of others. They cooperatively build a block structure. Students illustrate an event from an ants point of view. They predict the outcome of a story they are reading as a class and express ways on how to show respect for others. They role play cooperative behaviors to end the lesson. Students interpret facts and paraphrase information regarding respect. They assess the importance of showing respect for themselves, for others, for property, and for the world at large. They integrate The Golden Rule into their daily lives.
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CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. I created this little fraction compare worksheet and chose fractions that I thought would elicit some of the different strategies suggested by the Common Core The first one is 3/16 and 3/15This questions is obviously written to illicit ideas about common numerators. We spend so much time on common denominators that sometimes common numerators get completely ignored! The majority of my students used unit fraction reasoning on this one. They reasoned that we had 3 pieces for each one and since fifteenths are larger than sixteenths, 3/15 would be larger than 3/16. A few of my students tried drawing a model for this. Because these fractions are really close, it was hard to tell from their models which was larger because of the inherent margin of error with drawing models. Model drawing is an important first step for kids who are still working on developing conceptual understandings of fractions. It is not where I want to leave students at the end of grade 5, but it is an important first step! Let's look at 5/9 and 3/7The strategy I was trying to elicit with this one was comparing to the benchmark of 1/2. Here are the four strategies used by my group to compare these fractions |Here was the strategy I was thinking of when I wrote the problem. This student compared both fractions to the benchmark of 1/2. Since one fraction is just below 1/2 and the other just above it, this is a great strategy for this problem.| |This student drew a model. As far as model drawing goes, this is fairly good. This can not be the only strategy kids use to compare fractions but it is a great place to start and really helps build conceptual understanding of fractions.| |This student surprised me by using a common numerator strategy. It is actually very efficient for this problem. I didn't write the problem purposely to illicit this strategy but it works quite well.| How about 5/6 and 7/8? |This student used reasoning about how far away from 1 these fractions are. They used what they know about unit fractions to help them with this comparison.| The Last One |I chose this problem because it was really easy to create a common numerator for these numbers. That is what this student did and it was very effective and efficient!| |This student used a common denominator strategy to compare these two fractions. You can see that in this case it is much less efficient than finding a common numerator.| This took an entire class period but I got such great ideas and strategies out of the students. I love days like this when kids have a lot of time to share strategies! A GREAT resource if you want to really help your kids excel with fractions is this book A Focus on Fractions. Reading it completely changed the way I thought about teaching fractions in grades 1-6. What strategies do your students have for comparing fractions?
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Today in class we went over some rules for naming compounds--then we named some. The notes from today's class are below: Tell me (in your notebook) as much as possible about the following chemical formula. Ba(NO3)2 (how many atoms of each element, how do you think it bonds, could you draw the structure?) Follow-up question. If the formula breaks up into its ions, what are the charges of the Ba and the NO3? Naming Covalent compounds. Copy the prefixes on page 31(mono, di, tri, etc) Put the element symbols in the order they are in the periodic table -but- Hydrogen would fit between nitrogen and oxygen. Use the prefixes to name them - but you usually don't use a prefix for the first element in the formula. The prefixes tell you how many atoms of each there are. drop the 'a' and 'o' from the prefix when attaching the prefix to oxide. Ex CO is carbon monoxide Naming Ionic Compounds • The positive element (the metal) goes first. • The positive one gets to keep its name. • The negative one gets ide attached to the root of the name. • (think sodium chloride) To find out how many of each ion to use, first figure out the charge of each ion (see chapter one) Then criss-cross the charge numbers. Example: figure out the formula for a substance made from magnesium and chlorine Mg, the charge is +2, Cl the charge is -1 Flip flop the charges and the formula is MgCl2 Determine if ionic or covalent, then write the formula for these compounds.
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Commas can be confusing to students. When they first learn about comma use, students often understand the concept of how to use commas, but the knowledge doesn't always stick. Finding ways to help the knowledge stick is the key to helping students understand exactly how to use commas. After you teach students how to use commas, reinforce the lesson with an activity that gets them involved in comma use. Cereal Serial Commas Commas that combine lists are called serial commas. You can play with the idea of serial-cereal by using cereal boxes to create a list that needs commas. Cover cereal boxes with white butcher paper. Come up with a list of items and write each word on one cereal box. Make large commas out of black butcher paper. Arrange the cereal boxes in a row and have the students tell you where to put the serial commas to connect the cereal boxes. Commas are used to join phrases into compound sentences. You can help students understand how to use commas by teaching them that the phrases are like building blocks and commas are what holds them together. Use foam blocks with phrases written on them and self-adhesive Velcro to illustrate how to use commas to create compound sentences. The Velcro represents commas. Have the students tell you how to connect the blocks with the Velcro. Daily Oral Language Daily Oral Language is an exercise that gives students the opportunity to identify and correct spelling, grammar and punctuation errors in sentences written on the board. You can use Daily Oral Language to help teach comma use. Write a few sentences on the board that require commas. You can leave commas out, add extra commas or put them in the wrong places. Have the students write the sentences correctly. Commas Out Loud Something as simple as having students tell you where a comma belongs can help reinforce what you've taught them about comma use. Write two or three sentences on the board. The sentences should need commas but not include them. Read the sentences aloud, have the students shout “comma” at the appropriate times in the sentences and add the commas when they indicate them. Afterward, go through the sentence again to make sure the commas are placed properly. This can be done with lists to teach serial commas, as well. - Comstock Images/Comstock/Getty Images
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Strings in Python Strings are a fundamental data type in Python, representing text and characters. As one of the most versatile and frequently used data types, understanding how to work with strings is essential for any Python programmer. In this, we will explore strings in Python, covering their creation, manipulation, and various operations. A string in Python is a sequence of characters enclosed within single (‘ ‘), double (” “), or triple (”’ ”’ or “”” “””) quotes. It can contain letters, numbers, symbols, spaces, and even special characters. In the below PDF we discuss about Strings in Python in detail in simple language, Hope this will help in better understanding. Creating Strings : Let’s start by creating some strings in Python: string_single = 'This is a single-quoted string.' string_double = "This is a double-quoted string." string_triple = '''This is a triple-quoted string.''' Python allows you to use single, double, or triple quotes to define strings, providing flexibility when working with different types of text. String Operations : You can concatenate (combine) strings using the + operator: first_name = "Topper" last_name = "World" full_name = first_name + " " + last_name full_name now contains “TopperWorld.” - String Length To find the length of a string, use the len() function: message = "Hello, World!" length = len(message) length will be 13, as there are 13 characters in the string. String Methods : Python provides numerous built-in string methods for manipulation, such as: - upper(): Converts the string to uppercase. - lower(): Converts the string to lowercase. - strip(): Removes leading and trailing whitespace. - replace(): Replaces a substring with another. - split(): Splits the string into a list of substrings based on a delimiter. In Python, a string is a sequence of characters enclosed within single (‘ ‘), double (” “), or triple (”’ ”’ or “”” “””) quotes. It can contain letters, numbers, symbols, spaces, and special characters. You can create a string in Python by enclosing text within single, double, or triple quotes. For example: name = ‘John’, sentence = “Hello, World!”, and paragraph = ”’This is a paragraph.”’. String concatenation is the process of combining two or more strings into a single string. It is achieved using the + operator. For example, “Hello” + ” ” + “World!” results in “Hello World!”. You can find the length of a string in Python using the len() function. For instance, len(“Hello, World!”) returns 13 because there are 13 characters in the string. String indexing is the process of accessing individual characters within a string. Slicing allows you to extract a portion (substring) of a string. Strings are zero-indexed, meaning the first character is at index 0. Python provides various built-in string methods for manipulation, including upper(), lower(), strip(), replace(), and split(), among others. These methods enable you to modify and transform strings.
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KS2 Maths is an important core subject in the National Curriculum and this area of the website covers all the major aspects of the curriculum including numbers, calculations, problems and measures. Each subject area is designed to help children develop their knowledge, whether they are learning in a classroom or home schooling environment. At Key Stage 2 children are encouraged to engage in mental and oral work for their mathematics so this KS2 Maths area includes a collection of interactive activities to help develop both mental and oral skills. A key requirement of KS2 Maths is the understanding of the Number and the Number System which includes counting, estimating & rounding, fractions, decimals & percentages, number patterns & sequences and place value & ordering. Within the Number and the Number System section children are able to practice their calculations in addition, subtraction, multiplication and division. The interactive activities help children to practice using a variety of calculation methods by encouraging the use of written calculation methods, mental calculations and using a calculator. The KS2 Maths section also has a problem solving area to help children further develop their problem solving skills using numbers, money, measures and shape and space. There are many activities to help children test their knowledge, including a variety of problems using money in ‘real life´ situations. The Measures area of the KS2 Maths section helps children to enhance their knowledge of length, mass & capacity, time, area and perimeter. The Shape and Space area includes useful information and activities relating to position and movement, 2D shapes, 3D shapes, symmetry, angles, co-ordinates and sorting. Children are also able to learn about handling data through a number of activities based on interpreting and organising data as well as a section on probability. The resources and activities in the KS2 Maths section are in an interactive, online, or printable format that brings a differing dynamic to the subject for children studying at Key Stage 2. How many lines of Symmetry? - How many lines of symmetry are there for each shape? Reflective Symmetry - Interactive activities about symmetry Rotational Symmetry - Interactive activity where you can build up a pattern of rotational symmetry - Excellent. Rotational Symmetry - Interactive activity about rotational symmetry Shape Criteria - Compare different shapes to see whether they are symmetrical or have right angles with this activity Symmetrical Lines - Interactive activity where you have to count the number of symmetrical lines for each shape. Symmetrical Patterns - Printable activity to complete the symmetrical patterns Symmetrical Puzzle - Print and do activity where you have to complete the symmetrical picture. Symmetry Clown - Print out this page and complete the picture of a clown - symmetry activity. Symmetry Sort - Whiteboard activity for symmetry
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Recursion is the process of defining something in terms of itself. A physical world example would be to place two parallel mirrors facing each other. Any object in between them would be reflected recursively. Python Recursive Function We know that in Python, a function can call other functions. It is even possible for the function to call itself. These type of construct are termed as recursive functions. Following is an example of recursive function to find the factorial of an integer. Factorial of a number is the product of all the integers from 1 to that number. For example, the factorial of 6 (denoted as 6!) is 1*2*3*4*5*6 = 720. Example of recursive function # An example of a recursive function to # find the factorial of a number def recur_fact(x): """This is a recursive function to find the factorial of an integer""" if x == 1: return 1 else: return (x * recur_fact(x-1)) num = int(input("Enter a number: ")) if num >= 1: print("The factorial of", num, "is", recur_fact(num)) Enter a number: 4 The factorial of 4 is 24 In the above example, recur_fact() is a recursive functions as it calls itself. When we call this function with a positive integer, it will recursively call itself by decreasing the number. Each function call multiples the number with the factorial of number-1 until the number is equal to one. This recursive call can be explained in the following steps. recur_fact(4) # 1st call with 4 4 * recur_fact(3) # 2nd call with 3 4 * 3 * recur_fact(2) # 3rd call with 2 4 * 3 * 2 * recur_fact(1) # 4th call with 1 4 * 3 * 2 * 1 # retrun from 4th call as number=1 4 * 3 * 2 # return from 3rd call 4 * 6 # return from 2nd call 24 # return from 1st call Our recursion ends when the number reduces to 1. This is called the base condition. Every recursive function must have a base condition that stops the recursion or else the function calls itself infinitely. We must avoid infinite recursion. Advantages of recursion - Recursive functions make the code look clean and elegant. - A complex task can be broken down into simpler sub-problems using recursion. - Sequence generation is easier with recursion than using some nested iteration. Disadvantages of recursion - Sometimes the logic behind recursion is hard to follow through. - Recursive calls are expensive (inefficient) as they take up a lot of memory and time. - Recursive functions are hard to debug.
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The Cambrian period, part of the Paleozoic era, produced the most intense burst of evolution ever known. The Cambrian Explosion saw an incredible diversity of life emerge, including many major animal groups alive today. Among them were the chordates, to which vertebrates (animals with backbones) such as humans belong. What sparked this biological bonanza isn't clear. It may be that oxygen in the atmosphere, thanks to emissions from photosynthesizing cyanobacteria and algae, were at levels needed to fuel the growth of more complex body structures and ways of living. The environment also became more hospitable, with a warming climate and rising sea levels flooding low-lying landmasses to create shallow, marine habitats ideal for spawning new life-forms. Nevertheless, the scale of the Cambrian Explosion is likely exaggerated due to the proliferation of hard-bodied animals that fossilized much more readily than their soft-bodied precursors. These included brachiopods, which lived in shells resembling those of clams or cockles, and animals with jointed, external skeletons known as arthropods—the ancestors of insects, spiders, and crustaceans. These toughened-up creatures represented a crucial innovation: hard bodies offering animals both a defense against enemies and a framework for supporting bigger body sizes. The iconic arthropods of the Cambrian were the trilobites, which left a huge number of fossils. Trilobites had flattened, segmented, plated bodies that helped to protect them in seas that were increasingly filled with predators. With many varieties and sizes—they ranged from a millimeter to more than 2 feet (0.6 meters) in length—trilobites proved among the most successful and enduring of all prehistoric animals. More than 17,000 species are known to have survived until the mega-extinction that ended the Permian period 251 million years ago. A predator of the Cambrian was the giant, shrimplike Anomalocaris, which trapped its prey in fearsome mouthparts lined with hooks. Even stranger was the five-eyed Opabinia, which caught its victims using a flexible clawed arm attached to its head. These animals hunted along the seabed, where colonies of archaic sponges grew on organic, mineral structures formed by the activity of cyanobacteria. The sponges added to these reef habitats by building supporting skeletons from calcium carbonate, which they collected from the water. The earliest known primitive chordate is Pikaia gracilens, a wormlike creature that swam in middle Cambrian seas. Fossils found in the Burgess Shale of British Columbia show traces of a notochord (a rodlike primitive backbone), a significant step in the evolution of vertebrates. Cambrian sediments found in Canada, Greenland, and China have yielded rarely fossilized soft-bodied creatures such as marine worms buried during undersea mud avalanches. Representing the oldest known backboned animals with living relatives, the fossils showed that our vertebrate ancestors entered the evolutionary story some 50 million years earlier than previously thought. The end of the Cambrian saw a series of mass extinctions during which many shell-dwelling brachiopods and other animals went extinct. The trilobites also suffered heavy losses.
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Changing Up The Y Students will be able to make the plural forms of nouns that end with “y.” - Show students a book. Ask, “What’s the word for more than one book?” - Write the word “books” on the board. Say, “When there is more than one of a noun we call it a plural noun. For most nouns you can form the plural by adding an -s.” Explicit Instruction/Teacher modeling(5 minutes) - Write the word “baby” on the board. Say, “There are some nouns that have irregular plural forms. Some of these are nouns that end with ‘y.’” - There are two rules for making the plural form of nouns that end with y: - If a vowel comes before the Y, add an S. - If a consonant comes before the Y, you drop the Y and add an "ies." - In the word “baby,” the letter before the y is “b,” a consonant. That means to make the plural form you drop the y and add “ies.” - Show how to form the word “babies” by writing it on the board. Guided Practice(10 minutes) - Hand out index cards to each student. Write the following nouns on the board, one at a time: Monkey, daisy, story, and key. - After you write each word, have the students write the plural form on their index cards. Ask them to hold up their card after writing each word. Independent working time(15 minutes) - Pass out the Plural Nouns: Changing Up the Y worksheets. Have students work independently to complete the worksheet. Enrichment: Have students write sentences featuring the plural forms of nouns ending with “y.” - Support: Highlight the letters before the “y” to make it clear whether they are consonants or vowels. - Assess students’ understanding by observing how they are making plural nouns. Are they following the two rules for nouns that end with “y?” Pay special attention to how they complete the worksheet. Review and closing(5 minutes) Have students come up to the board to write some of the answers they came up with on their worksheet.
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The 6th graders are learning about different properties of matter and how to measure them. Properties like mass and volume were straightforward for them to understand while density remained abstract. So we chose to do a couple of activities to get a better understanding. First, they were given similar sized cubes made of different metals and a list of densities of standard metals. Their task is to identify the metal by finding the density of the cube and comparing it with the given list to find the closest match. This helped them to understand that density is a characteristic property that is unique to every material. They extended the inquiry by investigating whether the size of an object affects its density. They found the density of a ball of play dough and compared it with the density after halving the size of the ball. This helped them to understand that the density of a material remains the same irrespective of its size or shape. This activity also gave them an opportunity to try out the water displacement to find the volume of irregularly shaped objects.
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This resource helps students answer questions by picturing the concepts behind them. Highly-visual content bridges the gap between concrete and abstract language. - Communicate with less frustration - Answer questions about feelings and comprehend these question forms: why/because, going to, what if, what happened, what do you need, what do you do when, and what should Click here for more information on Digital Downloads. Simple illustrations help students understand the logic behind the question and respond appropriately. Students look at the picture, read the question or statement at the top of the page, and respond. The complexity of response can range from single-word answers to complex utterances. Visual prompts can be faded and question forms intermixed to facilitate generalization of the question concepts. Eight chapters include: - Describing Feelings: Students answer the question, "How does he/she feel?" and identify emotions of hurt, mad, sad, happy, and scared. - What Happened: Students answer the question, "What happened?" and explain situations like spilling a drink or breaking an object. - What Do You Do When: Students draw from personal experiences or the experiences of others to answer the question, "What do you do when . . . ?" This section gives practice in answering questions in novel, yet logical ways. - Why/Because: Students give logical reasons for questions such as "Why is she taking her medicine?" and "Why is she mad?" - Going To: Students learn to make and express predictions and draw conclusions as they answer questions that pertain to related objects (e.g., "He has a drum and drumsticks. What is he going to do?" ) . - What Do You Need: Students name two items needed to complete tasks like washing hands or drawing a picture (e.g., "Name two things you need to make toast"). Simple organizational skills like verbal sequencing and basic storytelling are developed. - What Should: Students demonstrate beginning logic and problem-solving skills by stating solutions to simple problems like what to do if a glass breaks ("John broke a glass. What should he do?"). - What If: Students hypothesize about events they may not have experienced themselves ("What happens if you let go of a balloon?"). You may purchase Autism & PDD Answering Questions Level 1 individually or in a 2-book set, which consists of: Copyright © 2001 - Many children with autism spectrum disorders learn more readily through the visual modality (Taylor-Goh, 2005). - Asking wh- questions is a common method of teaching. Difficulty answering wh- questions affects a child academically, linguistically, and socially (Parnell, Amerman, & Hartin, 1986). - Explicitly teaching and reinforcing inference-making leads to better outcomes in overall text comprehension, text engagement, and metacognitive thinking (Borné et al., 2005). - Reasoning skills encourage critical thinking and meta-awareness of internal thought processes. Reasoning skills support students' logical judgments based on conscious reflection and sensitivity to multiple viewpoints (Little, 2002). - Reasoning and critical thinking are necessary skills for competence across the curriculum. They require students to examine, relate, and analyze all aspects of a problem or situation. Students engaged in critical thinking must make associations that connect problems with their prior knowledge (Pellgrini, 1995). Autism & PDD Answering Questions Level 1 incorporates these principles and is also based on expert professional practice. Borné, L., Cox, J., Hartgering, M., & Pratt, E. (2005). Making inferences from text [Overview]. Dorchester, MA: Project for School Innovation. Little, C. (2002). Reasoning as a key component of language arts curricula. The Journal of Secondary Gifted Education, 13(2), 52-59. Parnell, M.M., Amerman, J.D., & Hartin, R.D. (1986). Responses of language-disordered children to wh- questions. Language, Speech, and Hearing Services in Schools, 17, 95-106. Pellegrini, J. (1995). Developing thinking and reasoning skills in primary learners using detective fiction. Yale-New Haven Teachers Institute, 1. Retrieved March 11, 2009 from http://www.yale.edu/ynhti/curriculum/units/1995/1/95.01.05.x.html Taylor-Goh, S. (2005). Royal college of speech & language therapists: Clinical guidelines. United Kingdom: Speechmark.
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CC-MAIN-2014-41
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If we execute these assignment statements: a = 'banana'b = 'banana' We know that a and b both refer to a string, but we don’t know whether they refer to the same string. There are two possible states: In one case, a and b refer to two different objects that have the same value. In the second case, they refer to the same object. To check whether two variables refer to the same object, you can use the is operator. >>> a = 'banana'>>> b = 'banana'>>> a is bTrue In this example, Python only created one string object, and both a and b refer to it. But when you create two lists, you get two objects: >>> a = [1, 2, 3]>>> b = [1, 2, 3]>>> a is bFalse In this case we would say that the two lists are equivalent, because they have the same elements, but not identical, because they are not the same object. If two objects are identical, they are also equivalent, but if they are equivalent, they are not necessarily identical. Until now, we have been using “object” and “value” interchangeably, but it is more precise to say that an object has a value. If you execute a = [1,2,3], a refers to a list object whose value is a particular sequence of elements. If another list has the same elements, we would say it has the same value.
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CC-MAIN-2020-40
http://www.opentextbooks.org.hk/zh-hant/ditatopic/6748
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Here's a quick, easy number sense activity you can do in the classroom or at home. All you need is a deck of cards. Deal out 16 cards face up. Arrange them in a 4x4 box. This square is kind of a "number bank," which will be drawn from in the same way you would pick vocabulary from a word bank. Ask your student to create as many correct equations using the numbers in the "box" to fill boxes or spaces. You create a framework like this (this would be a great early elementary version): __ + __ = __ __ - __ = __ __ + __ + __ = __ __ - __ - __ = __ Your student might not be able to fill the entire framework because the cards are drawn randomly, but that's the nature of the activity. Encourage them to use as many cards as possible. You can repeat this as long as your student is willing to do it. Even better, you can adjust both the equations and the rules to practice different types of problems. For example, you have to decide what to do about the ace and face cards. I would suggest making the ace a one and the face cards all equal to 10. You can have all of the cards be positive, or make black cards positive and red cards negative. You can increase or decrease both the amount of cards and equations you ask them to fill in. You can also change the type of problem (add multiplication or division). Here's a much more challenging version of this activity: Increase the square to 25 cards, but create a framework of three addition equations with fractions. Your student has to use the cards to fill in both the numerator and denominator, and while they might take the easy road and use a common denominator, some students will take the challenge of making correct equations without them.
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CC-MAIN-2014-42
http://www.teachforever.com/2009/11/use-playing-cards-for-unlimited-number.html?showComment=1257828516064
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The First Amendment: Free Speech Lesson Overview Overview Students will be asked to critically think about what the right to free speech means and why we have limitations to free speech. Students will examine several U.S. Supreme Court cases to explore the benefits and limits of free speech. Students will be able to: - Identify benefits of freedom of speech and identify limits to freedom of speech. - Define the term libel and how it applies to the First Amendment. - Copy of Free Speech Student Handout 1 - Copy of Free Speech Student Handout 2: Court Case Decisions Warm-up Introduction (5 minutes) Strategy: Walk the Line This strategy can be used as an introduction to a topic to gage student opinions and spark interest for what will be covered during the session. Procedure: Ask students to stand at the front of the room in a single horizontal line, all facing forward. Explain to students that they will be presented with several statements. If they agree with the statement they should step forward. If they disagree they should step back. After each statement a mentor or facilitator should have all students get back in line. Read the following statements The right to free speech protected in the First Amendment means: - You have the right to say whatever you want without consequence. - You have the right to write, print, and publish whatever you want without consequence. After students have made their decisions on each question ask: - Why or why not? Small Group Activity: Learning the limits to free speech (30 minutes) - Students break into smaller groups to review three Supreme Court cases and to learn about the limits to free speech. Student Handout 1 - Review the definition of libel with students before reading the court cases. - Ask students the following questions after each of the court cases. - After each court case small groups should share their discussion answers with the larger group. Case 1 Discussion Questions: Does the police commissioner have a valid libel case against the New York Times? Why or why not? What would be the difference between you taking space in a magazine to say derogatory things about a classmate or neighbor and criticizing the mayor of a city for neglecting his duties? When the police commissioner in this case assumed office did he relinquish his rights to some degree? Is it necessary to prove that every statement in a signed editorial or ad be true before a paper prints it? What would be the effect of such a policy on freedom of the press? What are the advantages of a totally free press? What are the disadvantages? Case 2 Discussion Questions Was the burning of the flag a form of expression? Or was burning the flag an action which the state had a right to regulate? What is the distinction between expression and action? What values are protected by the law against defiling the flag? What values are asserted by the act of burning the flag as a political protest? Which set of values should win in this case? Case 3 Discussion Questions Why would a school have the right to censor students? How does this limit students’ free speech? Do you think this is fair? Possible Questions for Further Discussion - Do you think that schools should have the right to censor what students say or wear in schools? Why or why not? - When should schools limit free speech? - Do you think it is harder to prove that someone is libel in the age of so many forms of digital communication like the internet and Twitter? Why or Why not?
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CC-MAIN-2014-42
http://www.americanbar.org/groups/public_education/initiatives_awards/constitution_day/lessons/lessons_3/the-first-amendment--free-speech-.html
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When, where, and how life first appeared are among science's biggest questions. A new model attributes life's formation to bombardment by meteorites. It also suggests there was only a short period during which life could have begun. Natural selection provides a powerful force for life to grow and develop, but getting started required the bringing together of nucleobases to form what became RNA. The most popular suggestions for the location of this event are hydrothermal vents at the bottom of the ocean and what Darwin called a warm little pond (WLP). A nuclear reactor has recently been proposed as well, but it is yet to be properly reviewed. According to McMaster University graduate student Ben Pearce, WLPs have several advantages: “Their wet and dry cycles have been shown to promote the polymerization of nucleotides into chains possibly greater than 300 links,” Pearce writes in Proceedings of the National Academy of Sciences. “Furthermore, clay minerals in the walls and bases of WLPs promote the linking of chains up to 55 nucleotides long.” Attempts to replicate the conditions around hydrothermal vents have produced RNA chains too short to be likely starter kits for life. However, WLPs still need nucleobases to join together in the first place, and the atmosphere back then is not thought to have been something well-suited to their formation. Moreover, three sorts of nucleobases have been found in meteorites. How likely then was it that nucleobases could reach Earth aboard a meteorite, survive passage through the atmosphere, and splashdown in a suitable pond where wet-dry cycles could cause them to join together to become life's first RNA? We know the early Earth was peppered by meteorites, although the record of the exact rate has been lost to erosion and geologic forces. Pearce and his co-authors use the rate of cratering on the Moon to calculate the number of impacts the Earth experienced in its first few hundred million years and factored in that only carbonaceous meteorites are likely to be suitable carriers. In addition, only a few of those traveled slowly enough to not burn up in the atmosphere. These estimates were compared with likely numbers of lakes and ponds on the Earth's very limited continental crust at the time. The authors conclude that prior to 4.17 billion years ago, there were sufficient cases of suitable meteorites touching down in WLPs to make seeding credible. RNA formation needed to occur before the nucleobases seeped out of the pond, which required temperatures of 50-80ºC (122-176ºF), but that is considered likely at the time. The paper concludes that life could have begun within just a few cycles of rainfall and drought after a meteorite strike, particularly if sedimentation protected the nucleobases from UV radiation.
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This resource helps ELs make strong connections with a simple fiction text. After reading a short story, students will think about how they can connect with the text and use sentence frames to explain their thinking. After independent reading, check in to see how students are understanding what they read. Having students make character paper dolls is a fun way to assess their comprehension and bring the story to life! Main characters would be lost without their supporting characters! Use this reading comprehension worksheet to compare and contrast characters from classic novels using a graphic organizer and paragraph excerpts. One way to bring books to life for students is to have them empathize with one of the characters. This fun worksheet engages students in analyzing how a character’s feelings change over the course of the beginning, middle, and end of the book. It's important for students to understand how characters and the storyline are interconnected. Help your students break down individual character responses to major story events with this graphic organizer. Let your students show you the way through a story of their choice using this fun road map! Your students will get to flex their reading comprehension muscles as they write about various story elements, including main characters, setting, and plot.
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CC-MAIN-2020-40
https://nz.education.com/worksheets/analyzing-story-structure/CCSS/?page=5
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When presenting the target language, the teacher has several methods. No one method proves more ably suited than another for the class. However, the teacher will almost always use several methods to clarify the information, as all the following methods work in tandem. What follows are four methods, namely: Method One: Explanations If a teacher were introducing zero conditionals, for example, the explanation would likely explain that the grammar structure is used to talk about always or almost always true statements. It consists of an if-clause or a when-clause which states the condition, followed by the action taken under that condition. Zero conditionals usually use the present tense, but can sometimes be used in the past tense too. Method Two: Visual Aids Timelines, pictures, and diagrams all fall into the category of visual aids. The teacher can draw a diagram or timeline on the board to highlight how to use the target language. This works especially well when introducing new grammar structures. Pictures work equally well, as they can show the meaning of the word. For example, flashcards can be used to introduce new vocabulary, or videos can be used to show gestures and facial expressions. In short, a visual aid may be anything in which the students can visually link the key language of the lesson with the explanation. Method Three: Examples For the class on zero conditionals, the teacher might provide two or three examples on the board: If it looks like rain, I bring an umbrella. I almost always bring an umbrella on dark, cloudy days. For a class on adverbs of frequency, the teacher might write the following on the board: I always eat breakfast in the morning. Students can more readily see and understand the target language because of the examples. They further can see how the target language fits into sentences and other structures. Method Four: Elicitation The teacher may think to provide more examples, in order to provide a lot of sentences for reference and models. However, too many examples from the teacher tend to establish a teacher-centered classroom. Students will look to the teacher for examples as a means for added clarity. They won't attempt to generate their own examples, which then places too much reliance on the teacher. In addition, when practicing the language, students may very well be less likely to deviate from what the teacher has given, in fear of being wrong. In addition, elicited examples allow the teacher to effectively asses if the students understand both the form and the function of the newly presented material. If the examples fail to use the language correctly, or stick far too closely to the examples provided by the teacher, then this serves as a signal for the teacher to further clarify the target language. Students don't yet fully understand the form and/or meaning. Let's look at two examples. In the first example class on conditionals, the teacher calls on the students for some sentences using the target language. He writes the following on the board after making some minor grammar corrections for articles and singular/plural. If I'm hungry, I go to restaurants. All of the sentences elicited from the class demonstrate that the structure is sound, but the meaning isn't quite correct. Does the student always go to restaurants when hungry, no matter that it's breakfast, lunch, dinner, or a snack? Does the second student always play tennis during his free time? In other words, he does nothing else? The teacher realizes that additional examples and a clearer explanation are required on his part. He returns to the presentation before allowing the students to practice. After all, if he simply stated that the examples weren't zero conditionals, made corrections, and then began a practice activity, then the students would still likely be unable to correctly use the structure. The other example on adverbs of frequency sees the teacher elicit the following: I always study for my tests. His class obviously understands the structure, and so should move on to practice it. Although the teacher may opt to use only one of the above methods, improved comprehension and use of the language in the initial stages of the lesson results when a combination of methods are used. Each reinforces another method. In addition, it also taps into select learning styles, giving consideration to auditory learners, visual learners, and others. Lastly, with elicitation, the teacher can gauge comprehension among the class in general, and choose to move on to the practice portion of the lesson or to provide additional explanation.
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CC-MAIN-2014-49
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A virus is a submicroscopic agent that acts as a parasite. It consists of a segment of DNA or RNA enclosed in a protein coat. Because they do not reproduce without a host cell, viruses are not considered to be living organisms by conventional taxonomy. However, once a virus has been shown to replicate and cause disease, it is classified as a living organism. Here are some facts about viruses. Viruses are composed of multiple copies of the same genetic material. The genes and RNA are contained within a virus particle. To replicate a virus, several copies of a protein must self-assemble. This process follows two basic patterns. One pattern is called helical symmetry, and involves the arrangement of the protein subunits and the nucleic acid in a helix. The second pattern is icosahedral symmetry, in which the protein subunits form a symmetric shell over the nucleic acid. Viruses contain nucleic acids. The nucleic acids are either RNA or DNA. They are both single-stranded or double-stranded. The nucleic acids are surrounded by a protective coat of protein in the form of a capsid, which is a set of microunits. Some viruses also have an envelope, which makes it difficult for the virus to survive outside of a living cell. In a minimal virus, multiple copies of the virus’s protein subunits need to self-assemble in order to produce a continuous three-dimensional capsid. The process of self-assembly follows two basic patterns. In the helical symmetry, the protein subunits and nucleic acid are arranged in a helix. In the icosahedral symmetry, the protein subunits assemble into a symmetric shell covering the nucleic acid. The virion is a specialized component that protects the viral nucleic acid. It contains proteins that bind to receptors on the surface of host cells. These proteins allow the virion to enter the host cell and inject the infectious nucleic acid inside. The virion has two types of capsids. Each one has a unique structure. They differ in both their size and their shapes. This type of virus can infect different types of cells. In humans, viruses are pathogenic because they are small enough to be carried in the body. They can cause diseases in humans and animals. In the past, they were thought to be caused by bacteria, but it is now clear that viruses can also infect other organisms. This is why some virus-producing species have an unusually low immune response. The immune system must respond to a specific virus to prevent the infection. A vaccine is an ideal way to combat this type of infection. The structure of a virus is relatively simple. It consists of genetic material in a capsule and a membrane. It has a membrane that contains its genetic material. The capsid is surrounded by a lipid envelope, which contains the host cell’s genetic material. These particles, called capsids, are made by the virus. Once a virus enters the host cell, it replicates its genome and copies its genetic material.
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Have you ever told a student she "dropped the ball" on an assignment? Do you encourage your students by telling them to "reach for the stars" or "go for the gold"? Your native English-speaking students likely understand what you mean when you use such figurative language, but the English Language Learners (ELLs) in your classrooms may be confused. Figurative language is an element of the Common Core State Standards and many middle grades teachers will incorporate figures of speech and idioms into the curriculum. If you have ELL students in your classroom, it's important to go that extra mile to ensure they understand language elements such as idioms and how to use them appropriately. The following suggestions may help teach about idioms—phrases that have a different meaning from the dictionary definition of the individual words. - Introduce idioms in context. Don’t provide the idiom and the “definition.” Use idioms in sentences and help students determine the meaning based on the context. - Have students demonstrate correct use of idioms. Pair students and ask them to have a conversation that incorporates idioms. Ask them to “present” their conversation to the class so everyone can learn from each other. - Practice with games and activities. Worksheets and games can reinforce student comprehension of figurative language (see websites below). Use real-life, authentic material students can relate to. Share examples of how idioms are used in movies, magazine articles, songs, and advertisements. These websites can extend classroom lessons on idioms. - Using English: www.usingenglish.com/reference/idioms. This database is rich with examples of idioms commonly used in English. The idioms are organized categorically so students and teachers can easily find idioms in areas such as animals, crime, food, politics, time, and character. ESL Mania: www.eslmania.com. This website provides opportunities for students to learn new idioms and to practice grammar skills. Students can even see how idioms are used in the news and in the business world. Download an iPhone app there. When students understand and can use figurative speech such as idioms correctly, they are better able to enhance their oral and written language skills. Melanie W. Greene is a professor in the middle grades program at Appalachian State University in Boone, North Carolina. firstname.lastname@example.org.
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CC-MAIN-2018-05
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Teaching our children about their personal values is a valuable and important lesson. Learning about these core beliefs and principles can equip students with the knowledge to make wise choices for themselves. By exploring their values, kids gain greater insight into themselves, why they do what they do and how their decisions may affect themselves and those around them. Let's go through a lesson you could do on personal values with a whole class, small group, or individual student. Step By Step Personal Values Lesson Define Personal Values First, start by defining what personal values are. How have students already seen these displayed by themselves and others? Personal values are the core beliefs and principles that shape our daily lives. They encompass how we think, how we act, and what we ultimately care about. Personal values help us determine what is essential and decide based on those priorities. Personal values include kindness, honesty, respect, integrity, and fairness. You could ask students to define what they think personal values are in their own words. Discuss Influences on Our Personal Values Various factors, such as our personalities, friends and family members, cultural beliefs, and experiences, shape our values. Our perspectives on life can be molded by the people we surround ourselves with, the books we read or movies we watch, and even the conversations that occur in our daily lives. Culture also impacts how personal values develop; different cultures have different ideas about what is important to prioritize in life. Religious beliefs or political ideologies can also determine individual values. Ultimately, it’s up to each person to decide which influencing factors will shape their value system. Have students draw themselves at the center of a paper or write their names. They can write down the different people, places, and circumstances influencing them. Brainstorm Possible Values When teaching students about personal values, provide a space for them to brainstorm and discuss what they know. For example, as a group, teachers can have their third-grade students explore current events or characters in books as sources of inspiration for understanding different values. This can be done by looking at characters' actions in stories and asking questions such as “What value does this character demonstrate?” Or, when discussing current events, teachers can ask their class, “What value do you think is most important here?” Work with students to generate a list of values they have observed in others and themselves. Use Personal Values Scenarios to Explore Once you have identified various personal values, give them scenarios to predict their decision if they have a particular value. For example, if the class discusses honesty, you can provide a hypothetical situation such as, "You find a wallet with money in it." Another option would be to give them a scenario and the decision someone made. They then have to decide what value guided that decision. Circle - Star - Slash Personal Values Activity Use the list of personal values that you brainstormed as a group. Give each student a copy of the list. Tell them to review the list and circle the values that are important to them. You can limit this to 7-10 values. Next, tell them to slash the values that aren't important to them. Lastly, they should look at the circled values and put a star next to the three values that are most important to them. After identifying their three values, discuss how they influence their thoughts, feelings, actions, and decisions. Then, you can use the previous scenarios to discuss how their values impact decisions. Personal Values Worksheets Students will learn what values they find important and how their values affect how they act, think, and feel. Personal values are an essential part of understanding and informing our decisions. Teaching children about personal values can help them become more self-aware and confident decision-makers. Through activities such as brainstorming possible values, exploring scenarios to demonstrate how those values influence us, and the Circle-Star-Slash activity to identify their most important three values, you can give students with a better sense of who they are and what matters most to them. In This Post Personal Values Lesson Five no prep 15-minute SEL lessons you can use to teach students about their personal values - what is important to them. These print-and-go worksheets will help students learn what they value and how that affects how they feel and act. Daily SEL Lessons This bundle of 35 social emotional learning topics. These simple daily worksheets introduce social emotional learning to the whole class, small groups, or individual students.
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Scaffolding is a teaching strategy that focuses on raising students' abilities one step at a time and removing support as the student progresses. This encourages independence and enables the students to be active learners. Scaffolding begins with lessons that are just a step beyond what the learners are able to accomplish unassisted; the teacher builds on the students' previous knowledge and then removes himself as the support, allowing students to master and internalize the content. Key to success with this teaching strategy is assessing accurately the students' current abilities; it is also important to decrease support from the teacher at an appropriate time, neither too quickly, nor too slowly. The method can be employed in any subject matter for any grade level. Identify the concept you wish to teach using scaffolding. It can be a single skill, such as "borrowing" when doing subtraction problems, or a larger skill set, such as persuasive writing. To begin, it might be simpler to plan one trial lesson before trying to use scaffolding for an entire unit. Assess the students' prior knowledge of the skill or concept. This can be done informally through class discussion and brainstorming or with a formal pretest assessment. A "K/W/L" chart is a tool that can be used with some subjects and all grade levels. With this tool, the class would collaboratively record what they currently know about the topic in one column and what they would like to know about the topic in another, and, finally, after the unit or lesson, they record what they learned. Identify the next step beyond what the students are currently capable of doing and set this as a learning goal for the lesson or unit. Goals must be obtainable, but not already within the students' capabilities. This step may need some differentiation, as not all students will be capable of reaching the same level of mastery over a skill. Create an activity introducing the new skill. This should be one that can be repeated several times -- first modeled by the teacher, then completed as an entire class, then completed in small groups of students and lastly completed individually. For instance, a teacher might prepare a number of sentences that need to be edited to correct grammatical errors. She would edit a couple of the sentences, thinking aloud as an example, then would ask the students to give her ideas for completing the next couple of sentences and then assign students to complete the remainder in pairs or alone. Assess the students individually after the lesson or unit to determine whether they have mastered the concept.
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Similes, Metaphors, and Idioms of Figurative Language Students will be able to identify and create similes, metaphors, and idioms. - Write these terms on the board: simile, metaphor, and idiom. - Distribute a blank piece of paper to partners or table groups and have students divide the paper into three columns. Have them title each column with one of the literary devices. - With a partner or table group, call on students’ prior knowledge by having them discuss and write what they know about each of these literary devices on their sheets under each column. Have them add examples of each, if possible. - Ask table groups to report to the class what their group thinks each one is. Explicit Instruction/Teacher modeling(15 minutes) - Distribute the Idioms: Tell Us What You Think! activity. Go over the definition and examples. - Craft an answer for the first exercise together. - Distribute the worksheet Metaphors and Similes. Go over the definitions on the top, read the story together, and find the similes and metaphors in the first two sentences. Guided Practice(10 minutes) - Instruct students to finish both activities with a partner or table group. - Distribute the worksheet Review: Metaphors and Similes. - Go over the examples at the top together and then read the first few lines identifying the similes and metaphors as a class. Independent working time(15 minutes) - Instruct students to finish Review: Metaphors and Similes, using the Similes and Metaphors worksheet as a resource. - Finish the worksheet Review: Metaphors and Similes together as a class, discussing examples and addressing questions. - Have students make another three-column table and title the columns "Simile," "Metaphor," and "Idiom." Instruct them to find examples of each in the book they are reading independently. They might also look for examples in other books or shorts stories that are available in the classroom or think of some on their own. - Have students write a pretend postcard or friendly letter of their own and include two similes, two metaphors, and two idioms. You might have them circle or underline each for ease of checking for understanding. Review and closing(5 minutes) - How do these figures of speech make reading and writing more interesting?
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Before the Apollo missions we knew almost nothing about the interior of the Moon. The Apollo missions left seismometers on the lunar surface that have allowed us to deduce the general features of the Lunar interior by studying the seismic waves generated by "moonquakes" and occasional meteor impacts. The Structure of the Interior Our present picture of the Moon's interior is that it has a crust about 65 km thick, a mantle about 1000 km thick, and a core that is about 500 km in radius. A limited amount of seismic data suggests that the outer core may be molten. There does appear to be some amount of differentiation, but not on the scale of that of the Earth. It has no magnetic field to speak of, but magnetization of Lunar rocks suggests that it may have had a larger one earlier in its history. Although there is a small amount of geological activity on the Moon, it is largely dead geologically (the energy associated with the Earth's seismic activity is about 10^14 times larger than that of the Moon). Most Lunar seismic activity appears to be triggered by tidal forces induced in the Moon by Geological History of the Moon The weight of the evidence is that the Moon was active geologically in its early history, but the general evidence suggests that the Moon has been essentially dead for more than 3 billion years. Based on that evidence, we believe the chronology of Lunar geology was as follows: Thus, Lunar surface features, particularly in the Highlands, tend to be older than those of the Earth, which remains to this day a geologically active body. - The Moon was formed about 4.6 billion years ago; maybe hot or maybe cold. The surface was subjected continuously to an intense meteor bombardment associated with debris left over from the formation of the Solar System. By about 4.4 billion years ago the top 100 km was molten, from original heat of formation and from heat generated by the meteor bombardment. By 4.2 billion years ago the surface was solid again. - As the intense meteor bombardment associated with debris left over from the formation of the Solar System continued, most of the craters that we now see on the surface of the Moon were formed by meteor impact. The fracturing and heating of the surface and subsurface by the meteor bombardment led to a period of intense volcanic activity in the period 3.8-3.1 billion years ago. Meanwhile, the meteor bombardment had tapered off because by this time much of the debris of the early Solar System had already been captured by the planets. The lava flows associated with the volcanism filled the low areas and many craters. These flows solidified to become the flat and dark maria, which have little cratering because most of the original craters were covered by lava flows and only a few meteors of significant size have struck the surface since the period of volcanic activity. The regions that were not covered by the lava flows are the present Highlands; thus, they are heavily cratered, and formed from different rocks than the seas. The volcanism stopped about 3.1 billion years ago: the Moon has been largely dead geologically since then except for the occasional meteor impact or small moonquake, and micro-meteorite erosion of the surface.
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Worksheets dealing with the scientific method should include all the questions answered while going through a scientific procedure. These questions include everything from describing the problem to reaching a final conclusion.Continue Reading Instructors should begin any worksheet by asking students to describe the problem and what they are testing. The next step should include outside research, which asks if others researchers have also done work on this or a similar problem. This worksheet should then ask students to formulate a hypothesis using a simple if/then formula. Afterward, a student should be asked to design the experiment itself. This step needs to include materials and the proper steps to be taken during experimentation. Worksheets should remember to ask students to collect data as they are going through the experimentation step. With that data in hand, students should then be asked to begin reaching conclusions based on their observations. Data should be summarized in written form and also presented in graphical form. This allows the student to communicate their ideas both in detailed verbal descriptions, as well as with graphical aids that allow for a quick summarization of the data. Finally, the worksheet should ask students to make conclusions based on their observations. Was the hypothesis confirmed? Was it proven wrong? What lessons could be made and how might they apply to other experiments? Students can then be asked to review all the steps they took during this initial experiment and apply them to a second experiment.Learn more about K-12
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In this unit, students will learn about using indices and standard form to represent numbers. They will begin by understanding the laws for multiplying indices, dividing indices and raising a power to another power. They will then look at some of the applications of standard form and learn how to convert ordinary numbers into standard form and vice versa. Finally, they will learn how to perform calculations in standard form, both with and without a calculator. This pack is designed to provide teachers with complete lesson plans and classroom resources to teach excellent lessons. It is designed to both teach the mathematical content and draw students into deeper consideration of its implications, including the mathematical reasoning and problem solving skills required for the new Maths GCSE. The pack contains: 6 Lesson Plans: Full lesson plans for you to use in your classroom on the following topics: Lesson Resources: A variety of additional resources to accompany the lesson plans, including student worksheets and aids for students needing extra support. 2 Homework Activities: Further activities to give students to complete at home. Assessment: A series of questions to enable you to assess the progress of students in this unit of work. This pack is designed for GCSE foundation tier students. It could also be used with mid or low ability Key Stage 3 students.
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|Nelson EducationSchoolMathematics 2| Surf for More Math Lesson 1 - Likely or Unlikely? To encourage students to have fun on the Web while learning about Likely or Unlikely?, here are some games and interactive activities they can do on their own or in pairs. Demonstrate an understanding of probability in everyday situations. Use likely and unlikely to describe probability. Instructions for Use Likely or Unlikely? Practice Page lets students understand probability in everyday situations. To use Likely or Unlikely? Practice Page, read each sentence and choose, likely, unlikely, or equally likely as unlikely. Calendar prompts students to fill in events they may do in a month and create their own calendar.To use Calendar, type in a title for the calendar. Add information to each day of the month. Click "Make my Calendar" button. Print off the calendar.
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Some chemical reactions release energy by heat. In other words, they transfer heat to their surroundings. These are known as exothermic reactions -- "exo" means releases and "thermic" means heat. Some examples of exothermic reactions include combustion (burning), oxidation reactions like burning and neutralization reactions between acids and alkalis. Many everyday items like hand warmers and self-heating cans for coffee and other hot beverages undergo exothermic reactions. TL;DR (Too Long; Didn't Read) To calculate the amount of heat released in a chemical reaction, use the equation Q = mc ΔT, where Q is the heat energy transferred (in joules), m is the mass of the liquid being heated (in grams), c is the specific heat capacity of the liquid (joule per gram degrees Celsius) and ΔT is the change in temperature of the liquid (degrees Celsius). Difference Between Heat and Temperature It's important to remember that temperature and heat are not the same thing. Temperature is a measure of how hot something is -- measured in degrees Celsius or degrees Fahrenheit -- while heat is a measure of the thermal energy contained in an object measured in joules. When heat energy transfers to an object, its temperature increase depends on the mass of the object, the substance the object is made from and the amount of energy transferred to the object. The more heat energy transferred to an object, the greater its temperature increase. Specific Heat Capacity The specific heat capacity of a substance is the amount of energy needed to change the temperature of 1 kg of the substance by 1 degree Celsius. Different substances have different specific heat capacities, for example, liquid has a specific heat capacity of 4181 joules/kg degrees C, oxygen has a specific heat capacity of 918 joules/kg degrees C and lead has a specific heat capacity of 128 joules/kg degrees C. To calculate the energy required to raise the temperature of a known mass of a substance, you use the equation E = m × c × θ, where E is the energy transferred in joules, m is the mass of the substances in kg, c is the specific heat capacity in J/kg degrees C and θ is the temperature change in degrees C. For example, to work out how much energy must be transferred to raise the temperature of 3 kg of water from 40 degrees C to 30 degrees C, the calculation is E = 3 × 4181 × (40 - 30), which gives the answer 125,430 J (125.43 kJ). Calculating Heat Released Imagine 100 cm3 of an acid was mixed with 100 cm3 of an alkali, then the temperature was increased from 24 degrees C to 32 degrees C. To calculate the amount of heat released in joules, the first thing you do is calculate the temperature change, ΔT (32 - 24 = 8). Next, you use Q = mc ∆T, i.e. Q = (100 + 100) x 4.18 x 8. Dividing the specific heat capacity of water, 4181 joules/kg degrees Celsius by 1000 to get the figure for joules/g degrees C. The answer is 6,688, which means 6688 joules of heat is released.
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There are 3 worksheets for each letter of the alphabet. Students will print uppercase and lowercase letters, identify lower and uppercase letters, and identify pictures beginning with the focus letter sound. *Letter X has pictures with ending sounds. Letter Worksheet 1 – Uppercase Letter Formation and letter-sound correspondence. Students will recognize all uppercase letters of the alphabet. RF.K.1.d Students will print uppercase letters. L.K.1.a Students will identify the letter sound and words that begin with that letter sound. Letter Worksheet 2 – Lowercase Letter Formation & upper and lowercase letter identification. Students will recognize all lowercase letters of the alphabet. RF.K.1.d Students will print lowercase letters. L.K.1.a Letter Worksheet 3 – Upper and lowercase letter identification and sort. Beginning sound identification. Students will demonstrate basic knowledge of letter-sound correspondences by producing the primary sound for each letter. Students will also discriminate between uppercase and lowercase letters and identify the focus letter among other letters. RF.K.3.a Letters C and G – For letters, c and g both the hard and soft sounds are included. Long and short vowel sounds are included as well. This resource is also great for substitutes – a sub pack, student teachers, classroom helpers, homeschool, homework, or groups!
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The Cambrian period, part of the Paleozoic era, produced the most intense burst of evolution ever known. The Cambrian Explosion saw an incredible diversity of life emerge, including many major animal groups alive today. Among them were the chordates, to which vertebrates (animals with backbones) such as humans belong. What sparked this biological bonanza isn't clear. It may be that oxygen in the atmosphere, thanks to emissions from photosynthesizing cyanobacteria and algae, were at levels needed to fuel the growth of more complex body structures and ways of living. The environment also became more hospitable, with a warming climate and rising sea levels flooding low-lying landmasses to create shallow, marine habitats ideal for spawning new life-forms. Nevertheless, the scale of the Cambrian Explosion is likely exaggerated due to the proliferation of hard-bodied animals that fossilized much more readily than their soft-bodied precursors. These included brachiopods, which lived in shells resembling those of clams or cockles, and animals with jointed, external skeletons known as arthropods—the ancestors of insects, spiders, and crustaceans. These toughened-up creatures represented a crucial innovation: hard bodies offering animals both a defense against enemies and a framework for supporting bigger body sizes. The iconic arthropods of the Cambrian were the trilobites, which left a huge number of fossils. Trilobites had flattened, segmented, plated bodies that helped to protect them in seas that were increasingly filled with predators. With many varieties and sizes—they ranged from a millimeter to more than 2 feet (0.6 meters) in length—trilobites proved among the most successful and enduring of all prehistoric animals. More than 17,000 species are known to have survived until the mega-extinction that ended the Permian period 251 million years ago. A predator of the Cambrian was the giant, shrimplike Anomalocaris, which trapped its prey in fearsome mouthparts lined with hooks. Even stranger was the five-eyed Opabinia, which caught its victims using a flexible clawed arm attached to its head. These animals hunted along the seabed, where colonies of archaic sponges grew on organic, mineral structures formed by the activity of cyanobacteria. The sponges added to these reef habitats by building supporting skeletons from calcium carbonate, which they collected from the water. The earliest known primitive chordate is Pikaia gracilens, a wormlike creature that swam in middle Cambrian seas. Fossils found in the Burgess Shale of British Columbia show traces of a notochord (a rodlike primitive backbone), a significant step in the evolution of vertebrates. Cambrian sediments found in Canada, Greenland, and China have yielded rarely fossilized soft-bodied creatures such as marine worms buried during undersea mud avalanches. Among the most surprising discoveries, announced in 1999, came from the 530-million-year-old Chengjiang fossil bed in China, where scientists found the remains of two different types of tiny, jawless fish. Representing the oldest known backboned animals with living relatives, the fossils showed that our vertebrate ancestors entered the evolutionary story some 50 million years earlier than previously thought. The end of the Cambrian saw a series of mass extinctions during which many shell-dwelling brachiopods and other animals went extinct. The trilobites also suffered heavy losses. Volunteers risk their lives to vaccinate children in Islamic State-controlled territory in Syria. Video.
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In introductory physics courses we often assume the force of gravity near the Earth is constant. That isn’t really true, since the farther you get from the Earth’s surface, the weaker its gravitational force becomes, but this change is very small. If you could stand on a platform 5 kilometers above the Earth, the gravitational force you feel would only be about 0.2% less than on the surface. The rate at which the gravitational force varies with height is known as the gradient. By measuring the force of gravity at two different heights, we can determine the variation of the gravitational field. It is similar to the way you can measure the speed of a car by measuring its position at two different times. We’ve been able to measure gravitational gradients for some time, but a bigger challenge is measuring how the gradient changes with height, which is known as the curvature. Despite its name, “curvature” in this sense is not the same as the relativistic curvature of space. Now a team has successfully measured this curvature, and the results are published in Physical Review Letters.1 To achieve this, the team used very cold clouds of atoms and tossed them in a vertical chamber. They then flashed the clouds with laser light from above and below. The first flash from above caused some of the atoms to absorb the light and become excited. These excited atoms also get a slight push from the laser pulse, so they shift relative to unexcited atoms in the cloud. The second pulse from below remixes the excited and unexcited atoms, which then interfere with each other quantum mechanically. The amount of interference depends upon how widely the two groups were separated, which depends upon the strength of the gravitational field around them. So by measuring the interference, the team could measure the acceleration of gravity to within a few millionths of a percent. The team did this measurement at three different heights, from which they could determine not only the gradient of gravity in this region, but also the curvature. You might wonder why this is a big deal. After all, we know that gravity is an inverse square force, so a bit of math should tell us what the gradient and curvature is. While that’s true, it’s only true for “point” masses, or spherical masses of uniform density. The Earth is neither, so there are fluctuations of gravitational strength, gradient and curvature depending on where you are on Earth. Since these fluctuations depend upon the shape and density of Earth at different regions, this type of measurement useful for determine what lies underneath the Earth’s surface. The experiment could also be useful in better determining the universal constant of gravity. In this particular work the team really performed a proof of concept. Rather than measuring the curvature of Earth’s gravity directly, they placed large weights around their device in order to give the region a stronger gravitational curvature. But with this experiment under their belt, the team can now work to increase the sensitivity to be useful for real-world applications. Rosi, G., et al. “Measurement of the gravity-field curvature by atom interferometry.” Physical Review Letters 114.1 (2015): 013001. ↩︎
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As teachers, we have to provide care for our students. We must consider thinking about their abilities and background and how they can freely interact inside the classroom. For those who are teaching students with disabilities, we must impose a respectful and friendly environment for them that will help them cope up with particular challenges in their life where they need assistance and considerations. Our primary goal is to make them realize that they can learn things that can allow them to make their own decisions. There are tons of effective teaching strategies. However, it may vary on the type of disability the children have. We have to learn the proper development of designing a course or intervention practices that will help the students adapt efficiently. Direct Instruction – The process of direct instruction focuses on content knowledge acquisition. It will allow teachers to focus on the underlying learning needs of the child such as introduction, development, guided practice, closure, independent practice, and evaluation. They can access their cognitive domains by providing clear examples and explanations and bring the lesson to a conclusion that is applicable for monitoring and assessment. Learning Strategy Instruction – The integration of tools and techniques is a process where teachers give specific operations and procedures to the students that provide multiple opportunities for feedback and practice. This will also allow students with disabilities to have full responsibility for their tasks. Inclusive Design – Though teachers may find it hard to incorporate their teaching strategies due to the condition of the children, they can always make an inclusive design that will determine the purpose of the course. They can use precise methods and instructions and know the required outcomes from the students’ tasks. This strategy also involves assessing ways on how the students can use these methods and determining student performance levels. It will be convenient for both teachers and students to have equal access to learning. TEACHING PROCEDURES – There are teaching procedures that teachers can also apply to be able to know if the strategy is working. It may offer some compelling intervention that can make a real difference in the student’s performances. Some of the mediation follows: - Provide prompt strategies that apply to all students with disabilities. - Use photos, diagrams, audios and videos that can help augment the said words. - Engage students in an environment that processes and answers typical questions. - Provide well-designed psychomotor activities that all students can participate in. - Present model instructions and practices that students can quickly follow. - Engage in a learning conversation that can boost student’s confidence. - Make regular quality assessment and feedback. Though procedures and types of teaching methodology are present in the classroom, we must also consider that not all the students are able to adapt quickly. Students’ disabilities may differ from one another. It could be a low vision, chronic health disorders, PTSD, dyslexia, hearing loss, and the list go on. We have to understand the need for considering our audience before using instructional materials.
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Inclusive education happens when children with and without disabilities participate and learn together in the same classes. Inclusion itself refers that equal opportunities are provided to all the students for their personal growth and enhancement. Inclusive education takes place when diversity and unique contribution of each student brought to the same classroom is equally valued. It is more effective for students with special needs to experience social interactions with all the peers in the school. Inclusive schools are the one which welcomes all the students to attend age-appropriate, regular classes and support them to learn, contribute and participate in all aspects of the life of the school. Such schools are essential for a quality inclusive education system. Inclusive education is about how to develop and design schools, classrooms, programs and activities so that all students learn and participate together. Inclusion does not simply mean the placement of students with disabilities in general education classes. This process must inculcate fundamental change in the way a school community supports and addresses the individual needs of each child. In such a manner inclusive education not only benefit students with disabilities but also create an environment in which every student, including those who do not have disabilities, has the opportunity to flourish. A school will be referred as inclusive when it adapts the models of inclusive education and has certain characteristics, such as: The school environment supports teachers in working collaboratively and taking responsibility for each student. Curriculum instruction and assessment Students with special learning needs receive differentiated and specific instruction in the general education classroom and are helped to participate in extracurricular activities with necessary support. The staff develops a school behaviour plan and implements it. All students participate in state and district assessments with needed or approved adaptations and modifications. Clinical and other support staff are available in the school community. For instance, shadow teachers are made available for children who have adjustment problem at school. School personnel actively involve parents, including those of students with disabilities and those from diverse backgrounds, in all school activities. School personnel make a concerted effort to reach out to all community members, leaders and organizations. Resources are available throughout the school, not just in specialized settings or classrooms. Comprehensive education plan School’s planning documents and processes address the needs of all students in all areas. All children benefit from inclusive education. It allows them to develop individual strengths and gifts, with high and appropriate expectations for each child. It helps them to work on individual goals while participating in the life of the classroom with other students of their age. Inclusive education provides opportunities to learn about and accept individual differences, lessening the impact of harassment and bullying. It helps students develop friendships with a wide variety of other children, each with their own individual needs and abilities. Inclusive approach increases the opportunities for participation and growth in various areas of a child who has a disability, within the educational system of a mainstream school. It helps students in understanding and accepting individual differences while providing personal growth opportunities. List of Inclusive Schools in Mumbai: Tridha School: Andheri The Aditya Birla Integrated School: Fort. Udayachal High School: Vikhroli east. S.M.Shetty International School: Powai. Nahar International School. Poddar International School: Powai and Santacruz Beacon High School, Khar. Gokuldham group of schools: Goregaon. Orchid International School. Vibgyor School. Malad, Goregaon and Borivali Universal School: Ghatkopar, Dahisar and Malad Billabong International school: Santacruz, Malad New Horizon Scholars School: Thane Hiranandani Foundation School: Powai Besant Montessori School Bombay Cambridge Gurukul Group of Schools: Andheri, Malad, Borivali
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Teaching about human rights and the values underlying them helps to create a culture within a school where everyone's rights are respected. What are human rights? “Human rights are about treating all people with the equal dignity that they are entitled to as human beings. Every person in the world, including children, must be recognised as having the same worth and dignity without regard to such differences as ethnic origin, colour of skin, sex or beliefs. Working out what this principle means in terms of individual entitlements and needs has arguably been the most important advance of recent history.” Why teach about human rights? The description above, taken from Amnesty International UK’s Human Rights in the Curriculumdemonstrates exactly how wide ranging and also how essential human rights are. Teaching about human rights from a very young age helps children to understand that they matter. From here they can progress to see how human rights are universal. They can also then learn that with rights, as you get older, come responsibilities. It can introduce thoughtful discussions about many key Citizenship and Humanities themes such as the rights and freedoms underpinning communities and society as a whole, as well as linking to work on race equality. Children often have a strong sense of justice and what is ‘fair’ - and the United Nations Convention on the Rights of the Child (and later the Universal Declaration of Human Rights) can provide a language with which they can discuss the idea of fairness. A deeper understanding of the concept of human rights is as much about respecting others’ rights as knowing your own. There is not only a legal entitlement for every individual to have their rights respected, but also an entitlement for everyone to learn what those rights are. The UK government signed up to the United Nations Convention on the Rights of the Child, and this includes a commitment to teach children and young people what their rights are. » For more details, read Unicef’s guide to the Convention Read about how other schools have covered human rights » Learning about rights in Year 2 This 8-minute video clip provides a useful overview. Browse through teaching resources relating to Human Rights or Child Rights. Sign up to the monthly Global Dimension newsletter containing resources, news, events and other exciting updates from Global Dimension.
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- Read, write and order whole numbers to at least 1000; know what each digit represents Examples of what pupils should know and be able to do - Primary mathematics exemplification: Ordering (whole numbers) - Mathematics ITP: Number grid (SWF-60 KB) Attachments - Which numbers are easiest to write down? Which do you have to think about? - When ordering a set of numbers, what do you look for first? - How do you find the smallest number/the largest number? What clues do you use? - What do you do when the numbers you are ordering have the same hundreds digit/tens digit? - Can you explain to me what you would do to order 384, 356 and 401? What if pupils find this a barrier? Place value cards are useful to practise the concepts with pupils: - Use digit cards to show me 364. What does the three represent? Remove the four. What number have you got now? What does the three represent now? Why is it different from before? - Use digit cards in pairs or threes (then you can have numbers with repeated digits) to make different numbers. Use a guessing game to guess mystery numbers between one and 1000, using 'higher' and 'lower'. Give pupils a matching activity with common misconceptions, e.g.: - three hundred and five - three hundred and fifty - 3005, 305, 350, 30 050.
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The students will learn the characteristics and locations of the subatomic particles of an atom. The students will utilize PBS Learning Media resources and teacher-created learning activities to study protons, neutrons, electrons, and nuclei. The student will create their own atomic model to illustrate the components of elements. How can you develop and use simple atomic models to illustrate the components of elements (including the relative position and charge of protons, neutrons, and electrons)? Other Instructional Materials or Notes: Digital Device for students (PC, Laptop, Chromebook, tablet, or iPad, etc.) Cloud File Storage (Google Drive, iCloud, One Drive, or Dropbox, etc.) Digital Productivity Software (Google Suite, Microsoft Office, etc.) If digital services are not available, then the following can be used in their place: Art Supplies for the model - 7.P.2 The student will demonstrate an understanding of the structure and properties of matter and that matter is conserved as it undergoes changes. - 7.P.2A All substances are composed of one or more elements. Elements are pure substances which contain only one kind of atom. The periodic table organizes these elements based on similar properties. Compounds are substances composed of two or more elem... Lesson Created By: MattieShuler
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Geography Oceanography, and Weather How was seafloor spreading discovered? In the 1950s, scientists realized that as igneous rocks cool and solidify (crystallize), magnetic minerals align with the Earth’s magnetic field like tiny compass needles, essentially locking the magnetic field into the rock. In other words, rocks with magnetic minerals act like fossils of the magnetic field, allowing scientists to “read” the rock and determine the magnetic field from the geologic past. This is called paleomagnetism. The idea was proposed by Harry Hess (1906–1969), a Princeton University geologist and U.S. Naval Reserve rear admiral, and independently by Robert Deitz, a scientist with the U.S. Coast and Geodetic Survey, both of whom published similar theories that became known as seafloor spreading. In 1962, Hess proposed the idea of seafloor spreading, but had no proof. As Hess formulated his hypothesis, Dietz independently proposed a similar model, which differed by noting the sliding surface was at the base of the lithosphere, not at the base of the crust. Support for Hess’s and Dietz’s theories came only one year later: British geologists Frederick Vine and Drummond Matthews discovered the periodic magnetic reversals in the Earth’s crust. Taking data from around mid-ocean ridges (seafloor spreading areas), Vine noted the magnetic fields of magnetic minerals showed reversed polarity. (The Earth’s magnetic field has reversed its polarity around 170 times in the last 80 million years.) From the spreading center outward, there was a pattern of alternating magnetic polarity on the ocean floor—swaths of opposing polarity on each side of the ridge. As the spreading center continues to grow, new swaths develop, pushing away material on either side of the ridge. Thus, these strips of magnetism were used as evidence of lithospheric plate movement and of seafloor spreading.
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General Topics: Physics, Engineering, Simple Machines, Kinetic Energy, Architecture, Design, Geometry Grade Level: 6-8 In this activity we built marble ramps. This exercise teaches students how to plan a design and how to build it, and how gravity, acceleration and momentum affect objects. This is an exercise designed around creativity and problem solving. The students are given a cardboard base to start, extra cardboard to build their towers to give the ramp its height, scissors to cut the cardboard, stencils to base curves from, construction paper to make their ramps, and tape and hot glue to hold it all together. Because there is no one way to build these ramps, the students have to get creative: do they want a zig-zag slide, do they want a loop-de-loop? Each group gets to choose what they want each of their ramps to look like. Also, here is how we divided the activity into digestible components in order for the students to grasp each piece of the whole instead of getting lost and losing interest: - Creating simple ramp - Measuring momentum based on angle of descent - cutting out & assembling stencils for spiral ramp - Designing and creating loop - Assembling final marble ramp What did we learn? - Observe how gravity, force, counter force, speed, and mass play a role in the making of our marble ramps. - Show that the project can be done with the tools the have. - Students learn what works for their ramp and are able to think about what went wrong, and then fix it. - Try complex things. Things to keep in mind for future activities: - Facilitate the process of what it means to work together, for example: each person has a specific job or task, part of a whole. - The fun is where the problem is. Allow students who have trouble visualizing, to explore their ideas by making.
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Calculating How Far an Object Will Slide Down an Inclined Surface You can use physics to calculate how far an object will slide down an inclined surface, such as a ramp. For example, say you and your friends are pushing a refrigerator up a ramp onto a moving van, when suddenly your combined strength gives out and the refrigerator begins to plummet back down the 3.0-meter ramp. As you watch with dismay, it picks up speed. A car is parked behind the ramp, only 7.2 meters away. Will the errant refrigerator smash it? Assuming that the ramp and the ground both have the same kinetic coefficient of friction and that the refrigerator starts to slide from the top of the ramp, you need to calculate how far the refrigerator will slide. You quickly pull out a pencil and paper and draw a figure showing the refrigerator as it slides down the 3.0-meter ramp. When an object slides downward, the forces acting on it are different from the forces used to push it up the ramp (see the figure). With the fridge, there’s no Fpush force to push it up the ramp. Instead, the component of the refrigerator’s weight acting along the ramp pulls the refrigerator downward. And while the fridge slides down, friction opposes that force. You also need to know the coefficient of kinetic friction, For this example, the coefficient of kinetic friction is 0.15. So what force accelerates the refrigerator downward? The weight acting along the ramp is and the normal force is which means that the force of kinetic friction is The net force accelerating the refrigerator down the ramp, Facceleration, is the difference between the component of the refrigerator’s weight along the ramp and the frictional force opposing it: Note that you subtract FF, the force due to friction, because that force always acts to oppose the force causing the object to move. Plugging in the numbers gives you The net force pulling the refrigerator down the ramp is 360 newtons. Because the refrigerator is 100 kilograms, you have an acceleration of 360 N/100 kg = 3.6 m/s2, which acts along the entire 3.0-meter ramp. You can calculate the final speed of the refrigerator at the bottom of the ramp this way: Plugging in the numbers, you get The final speed of the refrigerator when it starts traveling along the street toward the parked car is about 4.6 meters per second. Now you need to calculate how far the refrigerator is going to go. Because it’s traveling along the pavement now, you need to factor in the force due to friction. Gravity will no longer accelerate the object because the street is flat. Sooner or later, the refrigerator will come to a stop. But how close will it come to a car that’s parked in the street 7.2 meters away? As usual, your first calculation is the force acting on the object. In this case, you figure the magnitude of the force due to friction: Because the refrigerator is moving along a horizontal surface, the normal force, FN, is simply the weight of the refrigerator, mg, which means the force of friction is Plugging in the data gives you A force of 150 newtons acts to stop the sliding refrigerator that’s now terrorizing the neighborhood. So how far will it travel before it comes to rest? If you take the refrigerator to be moving horizontally in the positive direction, then because the force is acting in the opposite direction, its horizontal component is negative. Because of Newton’s second law, the acceleration is also negative and is given by You can find the distance through the equation The distance the refrigerator slides is In this case, you want the final velocity, vf, to be zero, because you need to know where the refrigerator will stop. Therefore, this equation breaks down to Whew! The refrigerator slides only 7.1 meters, and the car is 7.2 meters away. With the pressure off, you watch the show as your panic-stricken friends hurtle after the refrigerator, only to see it come to a stop right before hitting the car — just as you expected.
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To describe a specific position on the surface of the Earth, we must rely on the geographic coordinate system. The geographic coordinate system is a method used to give every possible location on Earth to be specified by a set of numbers or letters. A common choice of coordinates is latitude and longitude. With this information we can calculate a distance between two points along a surface. For simplicity’s sake, we will suppose that the Earth is a perfect sphere with a radius of 6,371 kilometers (it gives a mistake no more than 0.3%). You are given two point coordinates and you must find the shortest distance between these points on the surface of the Earth, measured along the surface of the Earth. Coordinates are given as a string with the latitude and longitude separated by comma and/or whitespace. Latitude and longitude are represented in the follow format: In this example, "d" is degrees, "m" is minutes, "s" is seconds as integers, while "X" is "N" (north) or "S" (south) for a latitude and "W" (west) or "E" (east) for a longitude. The result should be given as a number in kilometers with a precision of ±0.1 (100 metres). Input: Two arguments. Coordinates as strings (unicode). Output: The distance as a number (int or float). distance(u"51°28′48″N 0°0′0″E", u"46°12′0″N, 6°9′0″E") == 739.2 distance(u"90°0′0″N 0°0′0″E", u"90°0′0″S, 0°0′0″W") == 20015.1 How it is used: The concepts presented in this mission are the exact sorts of concepts used in navigational software, enabling a ship or plane to understand where it is, where it must go and how far it has gone. Along the same vein, Global Positioning Satellites use similar principles to provide pinpoint accurate locations to GPS receivers for use in navigation. Precondition: Correct Coordinates.
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Here's a quick, easy number sense activity you can do in the classroom or at home. All you need is a deck of cards. Deal out 16 cards face up. Arrange them in a 4x4 box. This square is kind of a "number bank," which will be drawn from in the same way you would pick vocabulary from a word bank. Ask your student to create as many correct equations using the numbers in the "box" to fill boxes or spaces. You create a framework like this (this would be a great early elementary version): __ + __ = __ __ - __ = __ __ + __ + __ = __ __ - __ - __ = __ Your student might not be able to fill the entire framework because the cards are drawn randomly, but that's the nature of the activity. Encourage them to use as many cards as possible. You can repeat this as long as your student is willing to do it. Even better, you can adjust both the equations and the rules to practice different types of problems. For example, you have to decide what to do about the ace and face cards. I would suggest making the ace a one and the face cards all equal to 10. You can have all of the cards be positive, or make black cards positive and red cards negative. You can increase or decrease both the amount of cards and equations you ask them to fill in. You can also change the type of problem (add multiplication or division). Here's a much more challenging version of this activity: Increase the square to 25 cards, but create a framework of three addition equations with fractions. Your student has to use the cards to fill in both the numerator and denominator, and while they might take the easy road and use a common denominator, some students will take the challenge of making correct equations without them.
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Comparing and ordering numbers up to ten thousands Comparing and ordering numbers can be further extended to ten thousands for 3rd grade kids. As explained in ICS-Grade3math under Standard 1: Number and Operations, under Objective 1, "When comparing numbers between 1,000 and 9,999, numbers will differ in only hundreds and thousands places. When comparing, the symbols for greater than and less than will not be used. When ordering, no more than four values are used. Numbers may be ordered least to greatest or greatest to least." Place value skills can assist the kids to compare and order numbers. When we compare two numbers, we compare their digits from left to right. The rule of thumb to compare numbers is that 4 digit number is greater than a 3 digit number and a 3 digit number is greater than a 2 digit number. If two numbers have the same number of digits then we need to compare each and every digit stating from left to right side of the number. Print the following lesson plan on comparing numbers: |Comparing Numbers to Ten Thousands Lesson| Following is the second lesson plan on comparing and ordering numbers: There is the following lesson found on www.nsa.gov site is very helpful to learn and teach comparing and ordering two digit numbers: More or Less Worksheets: Please feel free to print following very basic worksheets on finding 1 big or 1 less numbers than a given numbers. These worksheets proved to be key skill developers among third grade kids. More worksheets on comparing and ordering numbers: Print the following worksheets on ordering and comparing numbers so that kids get more exposure to this concept of number sense. Comparing two numbers fill in the blanks worksheet Comparing and ordering 3 numbers worksheet Comparing and ordering 4 numbers worksheet Finding greater numbers compared to a given number worksheet Finding the smaller numbers compared to a given number worksheet That's all about ordering and comparing numbers for 3rd grade math. Students need real appreciation after doing all the above worksheets.
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This quiz addresses the requirements of the National Curriculum KS1 Maths and Numeracy for children aged 6 and 7 in year 2. Specifically this quiz is aimed at the section dealing with using mental methods for division. Understanding the process of division can be quite a tricky challenge for some children. Children may be initially introduced to the idea of 'sharing' equally before they are shown how to use mental methods to solve problems. This starts when they begin to understand the division facts related to the multiplication facts they are learning (for example, if they know that 2 x 5 = 10, than they could recognise that 10 ÷ 5 = 2). They will learn that division is, in fact, the same as repeated subtraction and also understand that whilst the multiplication of two numbers can be done in any order (commutative), the division of one number by another cannot. This quiz will help your child to solve division problems using the mental methods they have learnt.
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Students will be able to identify prepositions and prepositional phrases. - Explain to the class that a preposition is a word that specifies location. Some examples of prepositions are "near," "above," and "before." Note that prepositions can also indicate location in time. A prepositional phrase is the combination of a preposition and its object. In the sentence "The dog is sitting near the tree," the prepositional phrase is "near the tree." - On the board, write three sentences that include prepositions. - Ask students to copy the sentences down, circle the prepositions, underline the prepositional phrases, and draw an arrow from the preposition to its object. - Give students 5-10 minutes to complete this warm-up. - Go over the answers. - Explain that this lesson will involve finding prepositional phrases in a multi-paragraph written sample. Explicit Instruction/Teacher modeling(10 minutes) - Hand out copies of the Reading Comprehension: The Secret Garden worksheet to students. - Model the process of reading the text on the worksheet using your own copy and a document camera. - Read up to the first semicolon. - Underline the following prepositional phrases: "for Mary Lennox," "like the others," "in her tapestried room," and "upon the hearth." - Slowly circle the prepositions. Then, draw arrows from the prepositions to their objects. Make sure to explain your actions as you go. Guided Practice(15 minutes) - Have students go through the passage and mark up the prepositional phrases that they find. - As they work, highlight the phrases on your own copy. Pace yourself so that you finish highlighting after 15 minutes. - Have students stop working once you're done. - Mark up all the sentences you highlighted to reveal the answers for the exercise, and have students correct their own passages. Independent working time(15 minutes) - Have students re-read the excerpt and answer the questions on the worksheet. - Enrichment: Students who complete their worksheet early can be given the challenge of using the four vocabulary words (tapestried, hearth, moor, and heather) in sentences on the backs of their worksheets. Remind them to make sure that the sentences contain context clues for understanding the word. - Support: Have struggling students focus on circling the prepositions in the passage. They can underline and draw arrows if there's enough time remaining, but their goal should just be to find the prepositions before time is up. - Circulate the room during Independent Working Students to identify and help struggling students. Keep an eye out for students who seem to need an extra challenge. - Return to your worksheet and camera. Ask students to share their answers as you reveal the correct answer for each question. Review and closing(5 minutes) - Go over the definitions of "preposition" and "prepositional" phrase once again. - Allow students to ask questions and give comments about the lesson content.
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A function accepts values, performs particular operations on these values and generates an output. The inverse function accepts the resultant, performs an operation and reaches back to the original function. If you consider f and g are inverse functions, f(g(x)) = g(f(x)) = x. A function that consists of its inverse functions fetches the original value. How to find the inverse of a function? Generally, the method of calculating an inverse is swapping of coordinates x and y. This newly created inverse is a relation but not necessarily a function. The inverse of a function – The relation that is developed when the independent variable is interchanged with the variable that is dependent in a specified equation and this inverse may or may not be a function. Inverse function – If the inverse of a function is a function by itself, then it is known as inverse function, denoted by f-1(x). The original function has to be a one-to-one function to assure that its inverse will be also a function. A function is said to be a one-to-one function only if every second element corresponds to first value. (values of x and y are used only once) You can apply on the horizontal line test to verify whether a function is one-to-one function. If a horizontal line intersects the original function in a single region, the function is a one-to-one function and inverse is also a function. To solve for an equation: f(x) = 2x + 3, at x = 4 f(4) = 2 x 4 + 3 f(4) = 11 Now, lets apply for reverse on 11. f-1(11) = (11 – 3) / 2 f-1(11) = 4 Magically we get 4 again Therefore, f-1(f(4)) = f(4) So, when we apply function f and its reverse f-1 gives the original value back again, i.e, f-1(f(x)) = x An example illustrating inverse functions using Algebra. Put “y” for “f(x)” and solve for x: |Put “y” for “f(x)”:||y||=||2x+3| |Subtract 3 from both sides:||y-3||=||2x| |Divide both sides by 2:||(y-3)/2||=||x| |Solution (put “f-1(y)” for “x”) :||f-1(y)||=||(y-3)/2| To refer more on Inverse functions formula, Calculator and solved examples, you can visit www.byjus.com Practise This Question
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Following on from the lesson on how to use grouping symbols and the lesson on the rest of the rules for the order of operations work, this lesson will give you the opportunity to write some simple expressions. By the end of this lesson, your children will be able to use the order of operations rules to write simple expressions, which includes recording numbers, grouping symbols, and operation signs correctly. They will also be able to understand some basic relationships between numbers and operations in expressions. Parent Tip: Encourage your children to use a pencil or erasable pen so they can keep their notes and calculations neat without having to start over again every time they want to change the order of part of the expression. The lesson on order of operations rules explains how the location of each number, operation sign, and grouping symbol in an expression can make a big difference in how the expression is evaluated. In this lesson, you will practice writing simple expressions. Not only are the rules for the order of operations important, but you will also need to remember your basic math vocabulary. Review these terms: |Sum||The answer to an addition problem.| |Difference||The answer to a subtraction problem.| |Product||The answer to a multiplication problem.| |Quotient||The answer to a division problem.| Make sure to use grouping symbols in the correct order (parentheses, brackets, then braces) to enclose steps that need to be done first. Remember that multiplication and division will be done before any addition and subtraction, so you must enclose addition and subtraction with grouping symbols if you need them to be done first. Have your children take the Pre-Test that follows to make sure you are able to identify which operation comes first in each expression, and why it is first. If they get 7 or less correct, review the introduction with them or go back to the lessons on grouping symbols and order of operations before continuing on to the lesson. |Writing Simple Expressions| If you want an expression that accurately shows 7 multiplied by the sum of 4 and 2, you need to think carefully about what you must include, and the order in which you should write it. For the example above, "7 multiplied by the sum of 4 and 2," make a list of the things you know you must include: Based on the notes listed above, we are ready to write a simple expression for the verbal problem: “seven multiplied by the sum of four and two.” 7 x (4 + 2) 4 + 2 is in parentheses to make sure this addition is done first. Without the parentheses, the operation of multiplication would have to be done first, based on the order of operation rules. Another way you could write it is just: 7(4 + 2) A number right next to a parentheses mark, with no operation sign in between, infers the operation of multiplication. Let's try writing a couple more expressions. Write down each of the expressions, then click on the Show/ Hide Answer link to check your work. Remember to think carefully about what to include, and the order you need to write it. |The product of five and two, added to seven.| |The sum of twelve and twenty, divided by eight.| Besides being able to write simple expressions, you should be able to look at an expression without solving the whole thing and realize some basic things about it. Look at the two examples below. |3 x (4 + 1)|| When you see this expression, you should be able to understand that having "3 x" in front of the parentheses means that the value of the expression will be three times as big as 4 +1 would be by itself. |35 - (2 x 4)|| When you see this expression, you should be able to understand that having x 4 after the 2 means that you will be subtracting four times as much as you would for 2 by itself. Review the above recap points with your children and then print out the Post Test that follows. At least 7 out of 10 correct will show that your children are ready to go on to move on.
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Circle Area Formula The primary aim of this activity is to explain the formula for the area of a circle. Instead of presenting the formula as is, students can explore the limiting process of slicing a circle up into progressively more and more sectors. Physically cutting up a circle with scissors into sectors and then rearranging these pieces has long been a traditional approach in the classroom, but often students only saw one example, and then had to generalise from that. This activity gives them access to all the other examples required to better appreciate and understand the extension of this idea. Whilst it is easier - and often only necessary - for students to know how to process the formula πr², this activity applies knowledge of areas of rectangles, parallelograms and trapeziums to working out the area of a new shape, the circle. The idea of a limit tending towards an exact answer will be required later in their mathematical careers, primarily in the topics of geometric series and calculus. This activity serves as an early introduction to this important mathematical technique.
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The growth of tobacco, rice, and indigo and the plantation economy created a tremendous need for labor in Southern English America. Without the aid of modern machinery, human sweat and blood was necessary for the planting, cultivation, and harvesting of these cash crops. While slaves existed in the English colonies throughout the 1600s, indentured servitude was the method of choice employed by many planters before the 1680s. This system provided incentives for both the master and servant to increase the working population of the Chesapeake colonies. Virginia and Maryland operated under what was known as the "headright system." The leaders of each colony knew that labor was essential for economic survival, so they provided incentives for planters to import workers. For each laborer brought across the Atlantic, the master was rewarded with 50 acres of land. This system was used by wealthy plantation aristocrats to increase their land holdings dramatically. In addition, of course, they received the services of the workers for the duration of the indenture. This system seemed to benefit the servant as well. Each indentured servant would have their fare across the Atlantic paid in full by their master. A contract was written that stipulated the length of service — typically five years. The servant would be supplied room and board while working in the master's fields. Upon completion of the contract, the servant would receive "freedom dues," a pre-arranged termination bonus. This might include land, money, a gun, clothes or food. On the surface it seemed like a terrific way for the luckless English poor to make their way to prosperity in a new land. Beneath the surface, this was not often the case. Only about 40 percent of indentured servants lived to complete the terms of their contracts. Female servants were often the subject of harassment from their masters. A woman who became pregnant while a servant often had years tacked on to the end of her service time. Early in the century, some servants were able to gain their own land as free men. But by 1660, much of the best land was claimed by the large land owners. The former servants were pushed westward, where the mountainous land was less arable and the threat from Indians constant. A class of angry, impoverished pioneer farmers began to emerge as the 1600s grew old. After Bacon's Rebellion in 1676, planters began to prefer permanent African slavery to the headright system that had previously enabled them to prosper.
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Here is a range of short activity ideas for the topic Changing Perceptions. Work with students to generate class woking definitions of the words ‘stereotype’, ‘prejudice’ and ‘discrimination’. These words are often used interchangeably although they have very distinct definitions. They have a clear progressive link, and so by understanding the meanings of the words, students can come to better understand the concepts. Our suggested definitions: Stereotypes – these are beliefs held about a group of people or type of person. A stereotype states that all people who belong to a certain group are the same, they think, dress, act, and talk the same way. Prejudice – this is the action of ‘pre-judging’ someone; forming an opinion about someone or a group of people that is not based on reason or actual experience Discrimination – treating someone differently, usually worse, because of who they are Discrimination or a Fair Decision?: In 2005, a shopping centre in England made a bold move which caused outrage from many people who said it was a form of discrimination. Ask students to read the newspaper article below and ask them to discuss if they think if their decision was discrimination or a fair decision? (n.b. a ‘hoodie’ is a large jumper with a hood) Shopping Mall bans ‘Hoodies’ Hoodies and baseball caps have been banned at a shopping centre in Kent, in an attempt to tackle anti-social behaviour. The move was supported by local police who said that it would reduce intimidating conduct in the shopping area.Action was taken by the shopping mall after a series of anti-social incidents involving youths, occurring primarily in the evenings and weekends. The centre management claims that youths who wear baseball caps and hoodies create an intimidating environment in the shopping centre, which is driving customers away. As these items of clothing obscure the perpetrators faces, other guests at the retail centre feel uncomfortable. The shopping centre also stated that by wearing hoodies and baseball caps, CCTV networks were rendered ineffective as faces could not be registered. Image courtesy of cjc4454/Flickr People who have Changed Perceptions: Over time, as human rights and equality have become increasingly important, people have challenged the stereotypes which they have encountered. Give students fact files on a few prominent people who have done this. When they have read through the information below, choose one of the people to research in more detail, or someone else who has challenged perceptions. It might be someone who is very famous in your country. Make an in-depth profile about them to present to the class. Why not do it in the style of a newspaper article or comic strip? Which other people do you know of who have challenged perceptions? Who: Martin Luther King Jr When: 1950s and 1960s What: Campaigned for racial equality in the USA Who: Germaine Greer When: 1970s- present What: Key role in modern feminism to change the perception of women in modern society Who: Daniel Witthaus What: Challenges homophobia and changes perceptions of homosexuality Challenging Perceptions in Films: Ask students to think about which films support stereotypes and which portray characters which do not follow stereotypes and therefore try to work against them. Are we influenced by what we see in films? Perceptions on Young People: Show this video to your class. It has been said that in some countries in recent generations the relationship between the younger and older generations is deteriorating and young people are seen principally as a nusiance. “Young people are like planes, you only hear about them once they crash” Members of the UK Youth Parliament made a video to challenge the negative stereotypes of young people which feature in the media. Watch the video and share your opinions with the class. (Made by UNICEF uniceftagd/YouTube)
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In 1701, William Penn created a Charter of Privileges for the residents of his colony. Penn envisioned a colony that permitted religious freedom, the consent and participation of the governed, as well as other laws pertaining to property rights. The Charter of Privileges recognized the authority of the King and Parliament over the colony, while creating a local governing body that would propose and execute the laws. Penn clearly states the responsibilities the citizens have in selecting virtuous men to lead and govern. - Students will be able to analyze the interaction of cultural, economic, political, and social relationships at the time of the creation of the Charter of Privileges. - Students will be able to construct a biography of a William Penn and generate conclusions regarding his qualities and limitations. - Students will be able to summarize the privileges and responsibilities granted to the citizens of Pennsylvania. The unit and lesson plan are a part of Preserving American Freedom, which presents and interprets fifty of the treasured documents within the vast catalog of the Historical Society of Pennsylvania. The documents read online will contain annotations that define and explain key terms, figures, and organizations. - Introduce William Penn and the founding of Philadelphia. Review the role that the Quaker faith played in Penn drafting his Charter of Privileges (include major names, events, and vocabulary words). - Have the students take notes on the author, year, title, and possible audience for each document. - Assign the readings either as homework or in class. - Listed below are a few questions / assignments that maybe used as review of the reading. - Have students compare and contrast William Penn's Charter of 1701 with any of the following documents; The Declaration of Independence, The Articles of Confederation, The Constitution, or the Bill of Rights. Most of these documents can be found in either a textbook or through the "Preserving American Freedom" project. - Have students compose a short summary of the Charter of Privileges. When complete answer the question. In your opinion what privilege is the most significant? - To what extent did William Penn create a unique colony based on natural rights? Why is Penn's vision different from other colonies and England? Explain. - In what ways did Penn create a charter that allowed his citizens to enjoy the most freedoms? Explain. - In groups have students create their own questions developed from the document. Students may answer their own questions as an assessment.
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Grades K-8 Worksheets Looking for high-quality Math worksheets aligned to Common Core standards for Grades K-8? Our premium worksheet bundles contain 10 activities and answer key to challenge your students and help them understand each and every topic within their grade level. The best way to show and explain direct proportional relationships is by graphing two sets of related quantities. If the relation is proportional, the graph will form a straight line that passes through the origin. Note: Different countries around the world use different money (or different currencies). People and businesses often need to buy and sell things in a different country so they need to exchange their currency for another. To help with this, each currency has a relationship with each other currency around the world. For currencies this relationship is known as the exchange rate. Graphing Proportional Relationships - Example1 Let us use the relationship between U.S. Dollars and U.K. Pounds to illustrate this. The exchange rate used in this example is 0.69 U.S. Dollars per 1 U.K. Pound. (Note that this, and all currency exchange rates, change all the time). The table of values and their graph show above a straight line that passes through the origin. This indicates that the relationship between the two currencies is in direct proportion. Think about what this means in real terms – if you have ten times more dollars than another person, when you both exchange your money, you will still have ten times more money. Notice also that the graph passes through the origin; this makes sense as if you have no dollars you will get no pounds! We can express these relationships algebraically as well as graphically. U.S. Dollars = 0.69 x U.K. Pounds or, using conventional algebraic terms, where y represents U.S. Dollars and x represents U.K. Pounds, as y = 0.69x All directly proportional relationships can be expressed in the form y = mx m represents the slope (or steepness of the line) when the relationship is graphed. Unit rate as slope In the example above the unit rate is the exchange rate which is 0.69 US Dollars per UK Pound. Note this relationship in algebraic terms, y = 0.69x meaning the slope equals 0.69. The slope of a the line that represents a directly proportional relationship equates to the unit rate. There is more on the slope of a line here. Graphing Proportional Relationships - Example2 Another common example of directly proportional relationships is that between time and distance when travelling at a constant speed. The graph below shows the relationship between distance and time for a vehicle travelling at a constant speed of 30 miles per hour. Note that this means the unit rate is 30 miles per hour. Notice below a similar graph. In this example the vehicle is travelling at a constant speed of 50 miles per hour. The slope of the graph is steeper. The steepness of the slope for directly proportional relationships increases as the value of the constant m (y = mx) increases. In our two speed examples, the change in steepness of slope represents the change in speed or the change in the unit rate. Graphing Other Linear Relationships Directly proportional relationships always pass through the origin (0,0). There are other linear relationships that do not pass through the origin. The example below is for a taxi fare that has a standing charge (a fee payable no matter how far is travelled) and a cost per mile. This relationship is expressed algebraically as follows: y = 4x + 5 Notice where the line intercepts the y-axis in the above example. This point is known as the y-intercept and there is more on this here. Use the worksheet(s) below for practice. - Graphing Proportional Relationships - (2-Pages)
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If you're reading this guide now, you've probably dealt with functions in great detail already, so I'll just include some brief highlights you'll need to get started with calculus. Much of this should be review, so feel free to skip sections you feel comfortable with. A function is a rule that assigns to each element x from a set known as the "domain" a single element y from a set known as the "range". For example, the function y = x 2 + 2 assigns the value y = 3 to x = 1 , y = 6 to x = 2 , and y = 11 to x = 3. Using this function, we can generate a set of ordered pairs of (x, y) including (1, 3),(2, 6), and (3, 11). We can also represent this function graphically, as shown below. Note that in the graph above, each element x is assigned a single value y. If a rule assigned more than one value y to a single element x , that rule could not be considered a function. As you may recall from precalc, we can test for this property using the vertical line test, where we see whether we can draw a vertical line that passes through more than one point on the graph: Because any vertical line would pass through only one point, y = x 2 + 2 must be assigning only one y value to each x value, and it therefore passes the vertical line test. Thus, y = x 2 + 2 can rightfully be considered a function. Although a function can only assign one y value to each element x , it is allowed to assign more than one x value to each y. This is the case with our function y = x 2 + 2. The value x = 4 is mapped to the single value y = 18 , but the value y = 18 is mapped to both x = 4 and x = - 4 . A one-to-one function is a special type of function that maps a unique x value to each element y. So, each element x maps to one and only one element y , and each element y maps to one and only one element x. An example of this is the function x 3 :
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Interval notation is a method of writing down a set of numbers. Usually, this is used to describe a certain span or group of spans of numbers along a axis, such as an x-axis. However, this notation can be used to describe any group of numbers. For example, consider the set of numbers that are all greater than 5. If we were to write an inequality for this set, letting x be any number in the group, we would say: This same set could be described in another type of notation called interval notation. In that notation the group of numbers would be written as: Here is how to interpret this notation: Now consider the group of numbers that are equal to 5 or greater than 5. That group would be described by this inequality: In interval notation this set of numbers would look like this: This interval notation would be interpreted just like the interval above, except: Now, what about numbers greater than 5 but less than 7? Expressed as an inequality this group would look like this: This same group of numbers expressed with interval notation would look like this: And here is an inequality showing a group of numbers equal to or greater than 5 and less than 7: Here is this group of numbers expressed with interval notation: Notice that there is a square, or inclusive, bracket on the left of this interval notation next to the 5. This means that this group of numbers starts at 5 and continues for values greater than 5. The round bracket on the right next to the 7 is, again, an exclusive bracket. This means that the numbers in this group have values up to but not including the 7. Well, by now, hopefully interval notation is clear to you. Let us go through one last simple example. Consider the group of numbers equal to or greater than 5 and less than or equal to 7. An inequality for this set would look like this; Since both the 5 and the 7 are included in the group we will need inclusive, or square, brackets at each end of the interval notation. That notation looks like this: Well, let us get just a bit more complicated. Using interval notation we will show the set of number that includes all real numbers except 5. First, stated as inequalities this group looks like this: The statement using the inequalities above joined by the word or means that x is a number in the set we just described, and that you will find that number somewhere less than 5 or somewhere greater than 5 on the number line. In interval notation a logically equivalent statement does not use the word or, but rather a symbol for what is called the union of two groups of numbers. The symbol for union coincidentally looks like a U, the first letter of union. However, it is really not a letter of the alphabet. Here is what the union symbol looks like: So, the group of numbers that includes all values less than 5 and all values greater than 5, but does not include 5 itself, expressed as interval notation looks like this: Let us consider one last set of numbers. We will consider a group of numbers containing all numbers less than or equal to 5 and also those numbers that are greater than 7 but less than or equal to 12. Using inequalities this group of numbers could be notated like this: And using interval notation as described throughout this material this group would look like this: We would interpret this interval notation as representing the total group of numbers as the union of two other groups. The first would start at negative infinity and proceed toward the right down the number line up to and including 5. The second would start just to the right of 7, but not including 7, and continue to the right down the number line up to and including 12. The total set of numbers would be all those in the first group along with all of those in the second, and this would be the same total group of numbers which we considered in the above inequality where we first introduced this last example. So, we see that interval notation is useful for stating the members of groups of numbers. It is often used to state the set of numbers which make up the domain and range of a function.
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To solve number pattern problems, start by observing the entire pattern from beginning to end. Decide if the numbers are increasing or decreasing. Next, try to figure out if the numbers change by adding, multiplying, subtracting or dividing a static or changing number.Continue Reading Isolate the first three or four numbers in the pattern and try to discover what relationship they have to each other. For example, are the numbers increasing by the same number amount, such as all numbers increasing by seven, or do they increase by a growing number amount such as two, three or four? Take notes on observations of the first four numbers, and then apply the same pattern theories to the rest of the sequence. Another way to test the pattern you have observed is to create a sequence that starts with the first four numbers. If the sequence matches the original pattern, the theory is correct. If not, apply the other theories until you find the right pattern. Finish the problem by writing out the pattern in words. For example, if the number increases by seven each time, write, "each number in the sequence is added to the number seven to produce the next number."Learn more about Homework Help
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In Topic E, students’ engage in counting numbers above 5, namely 6, 7, and 8, in varied configurations. The students use their growing skill and knowledge of counting up to five to reason about larger numbers in the more difficult linear, array, circular, and scattered configurations. As in previous topics the students will count objects and match their count with a digit card to reinforce that the last number said when counting tells the number of objects. Lesson 18 extends the counting of larger numbers by having students count 6 out of a larger set and order numbers 1–6 based on their knowledge that each number represents a quantity of objects. This calls their attention to part and whole concepts. Their 6 Kindergarten Mathematics Module 1, Topic E Resources may contain links to sites external to the EngageNY.org website. These sites may not be within the jurisdiction of NYSED and in such cases NYSED is not responsible for its content. Common Core Learning Standards |K.CC.3||Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0...| |K.CC.4||Understand the relationship between numbers and quantities; connect counting to cardinality.| |K.CC.5||Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular...|
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I’ll begin with some turn-and-talk questions to get students to generate what we have already learned about surface area of a triangular prism. I might ask “How did we find the surface area of a triangular prism in the previous lesson?” I will hold up a model of a triangular prism while asking this question so that students have a good visual. I want to hear a response that says to find the area of each face and add these areas. I want to lead students towards a general formula (Surface area = area of bases + areas of lateral face) for the surface area of a triangular prism (or any prism). So if necessary I will ask students to look at the prism as being composed of the bases and the lateral faces. How could we write a formula in terms of these terms? During this discussion, students are engaged in at least 2 of the mathematical practices. MP6 is evident as students are using precise language regarding prisms –bases & lateral faces. MP7 is evident as students are able to shift perspectives and see that all prisms are made up of bases and lateral faces, yet the specific base shapes may change. This part of the lesson is the “I”, “WE”, and “YOU” of the lesson. In the “I” section I present two examples. Students are to watch my example and then fill in notes when instructed. In the “WE” section, students work together to solve problems that are similar to the examples. They are to show work in a manner similar to the model given in the “I” section. The reason for this is two-fold: 1) It gives students a step-by-step approach that will allow them to be successful; 2) It helps me to diagnose any misconceptions. In the “YOU” section, it is all independent work. I will have identified students who need support at this point. Struggling students will be reminded to follow the steps in the examples, first before asking for help. When nearly all have finished the main independent practice, we’ll go over solutions as needed. I ask for a student to summarize a general formula for the surface area of any prism. We quickly discuss this, and then students take the exit ticket.
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Clouds form whenever and wherever there is more water in a particular volume of the atmosphere than it can hold as vapor. The point at which air holds as much water vapor as it can without liquid water forming (condensation) is called the saturation point. When air cools, the amount of water vapor it can hold decreases. The most effective cooling process in the atmosphere is lifting. As air rises, its presssure decreases, thereby allowing it to expand and cool. With sufficient cooling, the air reaches saturation and small cloud droplets begin to form. The number and size of the droplets depend on the degree to which the atmosphere is oversaturated, and the number and characteristics of tiny particles, called cloud condensation nuclei, on which the water condenses. When enough droplets of at least a few tenths of a micron form, they become visible as a cloud. There are many different types of clouds; which kind forms depends mostly on temperature, the rate of temperature change with height (lapse rate), and processes that generate atmospheric turbulence. Three common cloud types are cumuliform (characterized by vertical development in the form of rising domes or towers), stratiform (characterized by horizontal development in the form of layers that can become many kilometers thick at low- to mid-levels) and cirriform (ice clouds occurring in cold air, usually in relatively thin layers at high altitudes). A common example of cumuliform clouds is fair-weather cumulus that occurs during the day over land. The sun heats the surface, which produces plumes of buoyant rising air. Given sufficient water vapor to reach saturation, clouds can form at the tops of the rising plumes. When condensation occurs, the heat that is given off warms the air and can cause more lifting and more cloud. At the same time, the mixing of cloudy air with the clear air in its environment, and the descent of at least some of the cloudy air, cause cloud droplets to evaporate. Depending on environmental conditions, the cloud may continue to grow for some time and possibly produce rain or become a thunderstorm. More often, however, the cloud will dissipate, owing to mixing or descent. If temperature increases so rapidly with height that clouds cannot grow vertically, stratiform clouds occur. These clouds can persist for longer periods of time (perhaps days) because they are often in regions of general lifting and high humidity. Similarly, cirriform clouds can also be long-lived, since, like stratiform clouds, they are usually layered, and ice crystals vaporize more slowly than water droplets evaporate. Thus, clouds have some similarity with smoke in the air or dye in a glass of water, but significant differences exist, too. In all cases, turbulence in the fluid tends to diffuse, or mix out the tracer. A major difference between smoke and water clouds, however, is that a water cloud can continue to generate more and bigger droplets by condensation if it is rising, and cloud droplets can evaporate if the cloud is sinking. In contrast, if smoke is introduced into the atmosphere above the turbulent layer near the surface, it can persist within a well-defined layer for many days, as exemplified by plumes from forest fires, power plants or volcanoes, which can inject smoke well above the surface. The condensation trails (contrails) that form in the wake of high-flying jets are another interesting example. These cylindrical clouds have variable lifetimes and water concentrations depending on environmental conditions. In some cases the contrails can persist for many minutes. But they do slowly diffuse, much like the smoke plume emitted by an acrobatic aircraft. Since clouds are central to all weather, observing clouds can be useful for predicting weather. A large cloud mass with rising domes or towers directly upwind, for instance, will soon pass overhead as a thunderstorm. But there are more subtle clues, too. Increasing cirriform clouds overhead, especially if they evolve into thickening and lowering cloud layers, indicates air being lifted, often in advance of an approaching front. And increasing vertical development in cumulus clouds can indicate an increasing probability of storms. Conversely, if cumulus clouds become ragged at the edges and show no sharp-edged dome-shaped structures, the likelihood of imminent storms or precipitation is reduced. There are many more examples given in popular books on weather that point out relationships between clouds, their properties and weather systems.
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Without a graph, students will determine some coordinates that would lie on two lines by using the equations. Students should be encouraged to determine points by looking at the structure (MP7) of the equation (for example x + y = 3, what two numbers add up to 3?) Students are asked to list seven points to encourage them to see the pattern extending into the negative values as well as the positive values. Then, by inspection students can determine the solution point (if possible from their values) and verify their findings by graphing the two equations. Students will also look at the three cases for a system of linear equations, namely, no solutions, one solution, and infinite solutions. Again, this can be done both by looking at the structure of the equations (parallel lines, lines that intersect, or the same line) and then students can use a graphing calculator to see how the graphs of each of these cases appears. Lastly, students will be modeling a situation algebraically that involves two constraint equations set in a real world context. As a ticket out the door, students will have a choice of two assessments of learning. Both will give you valuable information about how to structure groups of students for the next days lesson. The target level question requires students to see how the stucture of the system leads to no solution (parallel lines). The more complex question assesses students understanding that lines extend infinitely in both directions and that if two lines do not have the same slope they will eventually intersect.
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- Know and understand the notion of discrete random variables. - Learn how to use discrete random variables to solve probabilities of outcomes. Now, we want to specify the possible values that a discrete random variable can assume. The example below illustrates how. Suppose you simultaneously toss two fair coins. Let be the number of heads observed. Find the probability associated with each value of the random variable . Since there are two coins and each coin can be either heads or tails, there are four possible outcomes each with probability . Since is the number of heads observed, then . The Venn diagram below shows the two-coin experiment. From the Venn diagram, we can identify the probabilities of the simple events associated with each value of : Thus, we have just had a complete description of the values of the random variables and have calculated the associated probabilities that are distributed over these values. We refer to it as the probability distribution. This probability distribution can be represented in different ways, sometimes in a tabular form and sometimes in a graphical one. Both forms are shown below. In tabular form, Figure: The Tabular Form of the Probability Distribution for the Random Variable in the First Example. In a graphical form, We can also describe the probability distribution in a mathematical formula, which we will do later in the chapter. The probability distribution of a discrete random variable is a graph, a table, or a formula that specifies the probability associated with each possible value that the random variable can assume. Two conditions must be satisfied for all probability distributions: Two conditions must be satisfied for the probability distribution: , for all values of The symbol means "add the values of for all values of " What is the probability distribution of the number of yes votes for three voters (see the first example in the first section Introduction) Since each of the outcomes is equally likely, the following table gives the probability of each value of the random variable. Figure: Tabular Representation of the Probability Distribution for the Random Variable in this Example. The table and the graph are two ways to show the probability distribution. Note that the graph of a probability distribution can be either a line graph or a bar graph. 1. The probability distribution of a discrete random variable is a graph, a table, or a formula that specifies the probability associated with each possible value that the random variable can assume. 2. All probability distributions must satisfy: (for all values of ) - Consider the following probability distribution: - What are all the possible values of - What value of is most likely to happen? - What is the probability that is greater than zero? - What is the probability that - A fair die is tossed twice and the up face is recorded. Let be the sum of the up faces. - Give the probability distribution of in tabular form. - What is - What is - What is the probability that is odd? Even? - What is - If a couple has three children, what is the probability that they have at least one boy?
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Use comparison operators to compare two strings in Python. Comparison of strings means wants to know whether both strings are equivalent to each other or not. Another thing can do in Comparison to find greater or smaller than the other string. Here some operators will use:- |Checks two strings are equal| |Checks if two strings are not equal| |Checks if the string on its left is smaller compare to other| |Checks if the string on its left is smaller than or equal to Another| |Check The left side String is greater than that on its right string| |Checks if the string on its left is greater than or equal to that on its right| How to compare two strings in python example code Simple python example code. a = 'A' b = 'A' c = 'B' d = 'BB' print("Are string equal?") print(a == b) print("Are string different?") print(a != c) print("Is a less than or equal to d?") print(a <= d) print("Is c greater than or equal to d?") print(c >= d) print("Is d less than b?") print(d < b) Another simplified example code print("ABC" == "ABC") print("ABC" < "abc") print("ABC" > "abc") print("ABC" != "ABC") True True False False Q: Why does comparing strings using either ‘==’ or ‘is’ sometimes produce a different result? is is identity testing, == is equality testing. what happens in code would be emulated in the interpreter like this: a = 'pub' b = ''.join(['p', 'u', 'b']) print(a == b) print(a is b) In other words: a is b is the equivalent of id(a) == id(b) Do comment if you have any doubts and suggestions on this Python string example code. Note: IDE: PyCharm 2021.1.3 (Community Edition) All Python Examples are in Python 3, so Maybe its different from python 2 or upgraded versions. Degree in Computer Science and Engineer: App Developer and has multiple Programming languages experience. Enthusiasm for technology & like learning technical.
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Probability is simply how likely something is to happen. Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. The best example for understanding probability is flipping a coin: There are two possible outcomes—heads or tails. What’s the probability of the coin landing on Heads? We can find out using the equation P(H) = ?.You might intuitively know that the likelihood is half/half, or 50%. But how do we work that out? Probability = In this case: Probability of an event = (# of ways it can happen) / (total number of outcomes) P(A) = (# of ways A can happen) / (Total number of outcomes) There are six different outcomes. What’s the probability of rolling a one? What’s the probability of rolling a one or a six? Using the formula from above: What’s the probability of rolling an even number (i.e., rolling a two, four or a six)? - The probability of an event can only be between 0 and 1 and can also be written as a percentage. - The probability of event Ais often written as P(A) > P(B), then event Ahas a higher chance of occurring than event P(A) = P(B), then events Bare equally likely to occur. Practice basic probability skills on Khan Academy —try our stack of practice questions with useful hints and answers!
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When presenting the target language, the teacher has several methods. No one method proves more ably suited than another for the class. However, the teacher will almost always use several methods to clarify the information, as all the following methods work in tandem. What follows are four methods, namely: Method One: Explanations If a teacher were introducing zero conditionals, for example, the explanation would likely explain that the grammar structure is used to talk about always or almost always true statements. It consists of an if-clause or a when-clause which states the condition, followed by the action taken under that condition. Zero conditionals usually use the present tense, but can sometimes be used in the past tense too. Method Two: Visual Aids Timelines, pictures, and diagrams all fall into the category of visual aids. The teacher can draw a diagram or timeline on the board to highlight how to use the target language. This works especially well when introducing new grammar structures. Pictures work equally well, as they can show the meaning of the word. For example, flashcards can be used to introduce new vocabulary, or videos can be used to show gestures and facial expressions. In short, a visual aid may be anything in which the students can visually link the key language of the lesson with the explanation. Method Three: Examples For the class on zero conditionals, the teacher might provide two or three examples on the board: If it looks like rain, I bring an umbrella. I almost always bring an umbrella on dark, cloudy days. For a class on adverbs of frequency, the teacher might write the following on the board: I always eat breakfast in the morning. Students can more readily see and understand the target language because of the examples. They further can see how the target language fits into sentences and other structures. Method Four: Elicitation The teacher may think to provide more examples, in order to provide a lot of sentences for reference and models. However, too many examples from the teacher tend to establish a teacher-centered classroom. Students will look to the teacher for examples as a means for added clarity. They won't attempt to generate their own examples, which then places too much reliance on the teacher. In addition, when practicing the language, students may very well be less likely to deviate from what the teacher has given, in fear of being wrong. In addition, elicited examples allow the teacher to effectively asses if the students understand both the form and the function of the newly presented material. If the examples fail to use the language correctly, or stick far too closely to the examples provided by the teacher, then this serves as a signal for the teacher to further clarify the target language. Students don't yet fully understand the form and/or meaning. Let's look at two examples. In the first example class on conditionals, the teacher calls on the students for some sentences using the target language. He writes the following on the board after making some minor grammar corrections for articles and singular/plural. If I'm hungry, I go to restaurants. All of the sentences elicited from the class demonstrate that the structure is sound, but the meaning isn't quite correct. Does the student always go to restaurants when hungry, no matter that it's breakfast, lunch, dinner, or a snack? Does the second student always play tennis during his free time? In other words, he does nothing else? The teacher realizes that additional examples and a clearer explanation are required on his part. He returns to the presentation before allowing the students to practice. After all, if he simply stated that the examples weren't zero conditionals, made corrections, and then began a practice activity, then the students would still likely be unable to correctly use the structure. The other example on adverbs of frequency sees the teacher elicit the following: I always study for my tests. His class obviously understands the structure, and so should move on to practice it. Although the teacher may opt to use only one of the above methods, improved comprehension and use of the language in the initial stages of the lesson results when a combination of methods are used. Each reinforces another method. In addition, it also taps into select learning styles, giving consideration to auditory learners, visual learners, and others. Lastly, with elicitation, the teacher can gauge comprehension among the class in general, and choose to move on to the practice portion of the lesson or to provide additional explanation.
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If humans ever build a permanent base on the Moon, it would likely be located near one of the poles. In particular, the rim of Shackleton crater at the south pole offers perpetual sunlight to power solar panels, while the interior is permanently shadowed and thought to hold water (in the form of ice). A convenient, local source of water would save expensive transportation from Earth. Unfortunately for future lunar colonists, high-resolution observations of the crater reported in Nature show that little, if any, ice is actually located there. Using a laser altimeter onboard the Lunar Reconnaissance Orbiter (LRO), scientists from NASA and multiple universities, led by Maria Zuber at MIT, produced not only detailed topographic maps of the crater but also measurements of its surface roughness and reflectivity. The team produced a 40-kilometer square topographic map—including a stereoscopic projection of the crater floor—using over 5 million laser pulses, or around one measurement per 100 square meters. These highly detailed observations show that the crater is nearly perfectly bowl-shaped, with extremely well-preserved walls and rim. In addition, the team used their new maps to date the crater, confirming a recent (circa 2008) dating of the crater at more than three billion years old—much older than the original estimate of closer to one billion years. For perspective, the Moon itself is around four and a half billion years old. How did these scientists estimate the age of the crater just using topographical maps? The relative age of different areas can be measured by counting the number of smaller impact craters. With a relatively constant rate of impacts, older surfaces have more craters. (The absolute age of some Moon craters was measured using returned samples from the Moon landings, allowing the dating of all the rest). The team performed this same analysis to establish the ages of different parts inside Shackleton. If the permanently shadowed regions had been accumulating water or other volatile compounds, their ages would likely be younger than the crater rim. However, the dating analysis showed that the shadowed areas are almost exactly as old as the rim—which is permanently exposed to sunlight. Moon one, ice zero. Surface reflectivity is another way to look for ice, since it is twice as bright as lunar soil at the wavelength of the laser beam used here. In an exciting result, and contradicting previous studies, the orbiter found that the floors of the crater are considerably brighter than the rim and surrounding terrain. This could mean that a thin surface layer consists of around 20 percent ice mixed with rock. However, the authors suggest a simpler explanation: the crater floor is brighter than the rim and surrounding areas because is it protected from micrometeorite impacts, which weather and darken the surface. Even so, this study only observed the surface of the crater floor, so there could still be ice underneath. Strangely, the sunlit walls of the crater are actually brighter than the floor. At first glance, this suggests ice on the walls, but this is unlikely since sunlight would evaporate ice on the Moon. Instead, the authors suggest that surface soil slid down the walls, potentially caused by "moonquakes," asteroid impacts, or even Earth’s gravitational pull.
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Although English vocabulary study can seem overwhelming at times for children (and adults, too!), it can be made more systematic with a good understanding of prefixes, suffixes and root words. In our 32-page Common Prefixes, Suffixes and RootsWorkbook are essential prefixes and suffixes, meanings, and many examples to help your child build their vocabulary. After learning the meanings of the prefixes and suffixes, your child will be able to put this knowledge to practice with the word search, crossword and other word puzzle combinations that test their understanding of words – and spelling! Prefixes are letters that are added to the beginning of a word to change its meaning. For example, the letters ‘re’ changes the meaning of a word to mean the redoing or reusing of the word. For example, ‘re’ + ‘cover’ changes the meaning of cover to ‘to get back’ (recover). Suffixes are a string of letters that go at the end of a root word to change or add to its meaning. A suffix can show whether a word is a noun, an adjective, an adverb or a verb. So, adding the suffix ‘ly’ to the end of a word usually changes it to an adverb. For example: ‘slow’ + ‘ly’ creates ‘slowly’, an adverb. A root word is a word in its simplest, basic form. It does not have a prefix or suffix added to it. For example, in the word ‘recycle’, the root word is ‘cycle’ and ‘re’ is the prefix.
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The literary term plot is used to sum up all the major events that take place throughout a story. This is often in the form of a major conflict or struggle between characters or their environment. The plot normal follows a sequence or pattern. Depending on the work the pattern may be predictable. Most highly esteemed works will have an unpredictable plot or at least a twist that was not easy for the reader to see coming. The plot normally ends in some form of resolution. Even stories that are carried over several works will form a resolution on sub-plots before ending a work. Most stories follow the same basic structure. They start by introducing the characters, setting, and central conflict (exposition), contain events that build in scope (rising action) until the "big event" (climax), after which, various conflicts are dealt with (falling action) until the end, where the lessons are learned or all conflicts are dealt with (resolution). These worksheets will have your students mapping essential elements of children's stories and fables to this pattern. Students will be required to pinpoint actions in very well-known works. We ask students to identify the exposition where a great deal of background information is shared. They will then identify the rising action where the main challenge is identified. The middle of the work will often result in a climax where tensions are their highest. As the resolution starts to take shape a falling action is able to be found. The story normally will end in a resolution to the conflict or challenge. Answer keys are provided as you might find them very helpful when grading. Fun Project Idea: Have your students bring in their favorite books or stories and perform the same exercise, and present the result to the class.
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In May 2018 Kīlauea volcano on the island of Hawaii erupted, touching off months of intense activity. Through August, incandescent lava from fissures spewed hundreds of feet in the air, and billowing ash clouds reached as high as six miles into the atmosphere. Huge lava flows inundated land up and down the Pacific island’s southeast coast, destroying hundreds of homes. Volcanoes erupt when molten rock called magma rises to the surface, and many factors, from the shape of the volcano to the composition of the magma, factor into the timing of eruptions. In the case of Kīlauea , a new, NASA-funded study published April 22 in the journal Nature points to another eruption factor: prolonged, sometimes heavy rainfall in the months leading up to the event. “We knew that changes to water content in Earth’s shallow crust can trigger earthquakes and landslides, and now we know that it can also trigger eruptions,” said Falk Amelung, professor of geophysics at the University of Miami Rosenstiel School of Marine and Atmospheric Science and co-author of the study. “Under pressure from magma, wet rock breaks easier than dry rock inside the volcano. That, in turn, forges pathways for magma to travel to Earth’s surface.” First, for the 2018 Kīlauea eruption researchers ruled out a common cause: increased pressure in the magma chamber, which, when it becomes great enough, is able to break through the surrounding rock. Scientists can infer increased magma pressure by observing the inflation, or rise, of the surrounding rock. “This pressurization causes the ground to inflate by a few tens of centimeters,” Amelung explained. “As we did not see any significant inflation in the year prior to the eruption, we started to think about alternative explanations, which led us to investigating precipitation.” Using a combination of ground-based and NASA satellite measurements of rainfall, the researchers modeled the evolution of fluid pressure caused by sustained rainfall that accumulated in the volcano’s interior–a factor that can directly influence the propensity for magma to break through the surrounding rock, ultimately driving volcanic activity. Based on pre-existing laboratory data and numerical simulations, their model results suggest that, in early 2018, fluid pressure had been at its highest in almost half a century, weakening the volcanic edifice, which the authors propose enabled magma to break through confining rock beneath the volcano and lead to the subsequent eruption. “Interestingly, when we investigate Kīlauea ‘s historical eruption record, we see that magmatic intrusions and recorded eruptions are almost twice as likely to occur during the wettest parts of the year,” said Jamie Farquharson, a postdoctoral researcher at the Rosenstiel School and lead author of the study. He argues that local rainfall patterns may contribute significantly to the timing and frequency of these phenomena at Kīlauea and perhaps at other volcanoes. While rainfall infiltration has been linked to small steam explosions and volcanic earthquakes, this is the first time that scientists attribute months of above-average rainfall to explain magmatic processes more than a mile below the surface. In the case of the Kīlauea eruption, the first quarter’s total rainfall over the volcano that year was about 2.25 meters compared to the 0.9-meter average for the area in that timeframe over the past 20 years. The authors note that if this process occurs as proposed at Kīlauea , then it is likely to occur elsewhere as well. A climatic link may also be at play, Farquharson said, as ongoing climate change is predicted to bring about changes in rainfall patterns. In particular, most models project increases in extreme precipitation over most of the globe, an effect that may be further amplified in mountainous volcanic regions. “As a result, we expect that rainfall-induced volcanic activity could become more common.” Header Image Credit : United States Geological Survey
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Introduce the concept of a frame and use a good free body diagram and the equations of equilibrium to solve for the forces and reactions acting on the frame. This demonstration should take 5-10 minutes. Frames and Machines are one way to classify a structure. As opposed to Trusses, Frames and Machines are comprised of at least one multi-force member. The difference between a Frame and Machine lies in the fact that a Machine uses moving parts to transmit forces and a Frame has no moving parts. Once you have introduced these definitions, it is good to show multiple examples of each interspersed with some that are not frames or machines. Bring as many examples to the class as you can find. Thereafter, talk about the techniques for solving for the forces acting on a frame comprised of members connected with frictionless pins (no moment transfer). This type of frame is used in order to be able to solve some simple structures and reinforce the concept. Introduce the concept of “pulling the pins” on this type of frame, drawing isolated free body diagrams of each of the members, and drawing in the equal and opposite pin reactions on each part of the free body diagram. If able, have several different Frames and Machines connected by pins that can be physically disassembled to use on the board or as hands-on physical models to hand around class. At this point we can solve for the forces acting on the structure using the equations of equilibrium on each of the member parts. What You Need |Frames and Machines||As many as you want||Pick as many or few as you would like. There are very few restrictions.| |Model of Pliers||1||The pliers model should be made of durable material and have magnets attached to its back so that It can be fixed to the board. It also should have the ability to be disassembled and isolated to solve for the pin forces. $15; 30 minutes| How It’s Done Before Class: None. In Class: One of the simpler examples to demonstrate the concepts discussed above is a pair of pliers. It is fairly simple to build and one can usually find a few pairs of old pliers that could be disassembled to hand around the classroom. Start with the example on the board with the pliers together and ask the students to classify it. Then ask how we would determine the force acting on the bolt given this free body diagram. Since we could not, use our new technique of pulling the pins to determine all the forces acting on each of the members. Taking the pliers apart on the board simplifies the time required to draw a Free body diagram, but also leads to better understanding of the equal and opposite forces involved in the pin connections. Then look at one of the parts of the pliers and apply the equations of equilibrium to it and solve for the forces at the pin connection and at the bolt. After this example, more complex frames can be tackled with ease.
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1. As a class, come to an agreement of the definition of these key terms: - Federal recognition 2. What do you know about the Indigenous people where you live? Go to this map and search your address to find out what Native American tribe(s) have historically called the land you are standing on home. Then, do some research to answer the following questions for one of the tribes: - Does this tribe have federal recognition? - Has the United States ever made a treaty with this tribe? If so, have its terms been upheld? - Where do members of this tribe live today? 1. Watch the following video. Answer the comprehension questions below while you watch. - What is a treaty, and who can make them? - To whom did treaties grant rights: the United States, or Native nations? - From the perspective of Indigenous nations, how many treaties have been upheld? - What is Mary Kathryn Nagle's response to people who question the relevance of treaties? - What example of the relevance of treaties in recent news does the video mention? 2. Discuss in pairs, then share with the class: - What examples of treaties can you think of between the U.S. and other countries? - What do you think would happen if the U.S. violated those treaties? 3. Listen to the following audio story. You can follow along with the transcript here. 4. As a class, discuss: - Why does Allison Herrera say the Salinan tribe remains unrecognized by the U.S. federal government? - Why do some Salinan people want to push for federal recognition? Why do other Salinan people disagree? Why does Herrera say that it's "ironic" that the Salinan tribe has to ask for recognition? 5. The video you watched mentioned Standing Rock as an example of the continued relevance of treaties and federal recognition to Indigenous people's lives today. In small groups, do some research to find an example of a tribal rights case brought before a court in the U.S. in recent years. Present your finding to the class, including the following information: - What did the Indigenous people involved in the case want? - Who won? What was the court's reasoning? - Were any treaties upheld or violated by the court's verdict? - What happened, or seems likely to happen, as a result? Who will be impacted? Choose one of the following stories and read it in full. Write a one-page response that addresses the following questions: - What did you learn from this story that you didn't know before? - Why might stories about Indigenous communities go under-reported? What can you do to help make these stories more visible in your own life and in your community? Story option 1. Indigenous people face challenges all over the world, and stories from Indigenous communities often go under-reported or misreported. In a full issue of Pacific Standard devoted to Indigenous peoples’ battles for land rights, safety, and good standards of living, six Magnum photographers traveled across the world to Greenland, Honduras, Tanzania, Azerbaijan, Malaysia, and the Philippines to document Indigenous struggles and resilience. Choose one story from the interactive map at the bottom of this page and read it in full. Story option 2. Explore Daniella Zalcman's double-exposure portraits of residential school survivors in Canada and read the associated article. Story option 3. Scroll through the photos, read, and listen to this interactive multimedia story on Indigenous people in the Amazon guarding the rainforest.
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The First Amendment: Free Speech Lesson Overview Overview Students will be asked to critically think about what the right to free speech means and why we have limitations to free speech. Students will examine several U.S. Supreme Court cases to explore the benefits and limits of free speech. Students will be able to: - Identify benefits of freedom of speech and identify limits to freedom of speech. - Define the term libel and how it applies to the First Amendment. - Copy of Free Speech Student Handout 1 - Copy of Free Speech Student Handout 2: Court Case Decisions Warm-up Introduction (5 minutes) Strategy: Walk the Line This strategy can be used as an introduction to a topic to gage student opinions and spark interest for what will be covered during the session. Procedure: Ask students to stand at the front of the room in a single horizontal line, all facing forward. Explain to students that they will be presented with several statements. If they agree with the statement they should step forward. If they disagree they should step back. After each statement a mentor or facilitator should have all students get back in line. Read the following statements The right to free speech protected in the First Amendment means: - You have the right to say whatever you want without consequence. - You have the right to write, print, and publish whatever you want without consequence. After students have made their decisions on each question ask: - Why or why not? Small Group Activity: Learning the limits to free speech (30 minutes) - Students break into smaller groups to review three Supreme Court cases and to learn about the limits to free speech. Student Handout 1 - Review the definition of libel with students before reading the court cases. - Ask students the following questions after each of the court cases. - After each court case small groups should share their discussion answers with the larger group. Case 1 Discussion Questions: Does the police commissioner have a valid libel case against the New York Times? Why or why not? What would be the difference between you taking space in a magazine to say derogatory things about a classmate or neighbor and criticizing the mayor of a city for neglecting his duties? When the police commissioner in this case assumed office did he relinquish his rights to some degree? Is it necessary to prove that every statement in a signed editorial or ad be true before a paper prints it? What would be the effect of such a policy on freedom of the press? What are the advantages of a totally free press? What are the disadvantages? Case 2 Discussion Questions Was the burning of the flag a form of expression? Or was burning the flag an action which the state had a right to regulate? What is the distinction between expression and action? What values are protected by the law against defiling the flag? What values are asserted by the act of burning the flag as a political protest? Which set of values should win in this case? Case 3 Discussion Questions Why would a school have the right to censor students? How does this limit students’ free speech? Do you think this is fair? Possible Questions for Further Discussion - Do you think that schools should have the right to censor what students say or wear in schools? Why or why not? - When should schools limit free speech? - Do you think it is harder to prove that someone is libel in the age of so many forms of digital communication like the internet and Twitter? Why or Why not?
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Primary Math - 2022 Edition Math K Concepts covered include: Sets (compare and order), quantities, count sequences, numerals, and number names through 20. Compose and decompose numbers to 20 into pairs as well as tens plus ones. Explore numbers 21 to 100 as tens and ones. Model joining and separating sets. Use +, -, and = to write number sentences. Represent and solve addition and subtraction stories with manipulatives, actions, drawings, and number sentences. Practice addition and subtraction in different contexts with words, models, fingers, and numerals. Describe, extend, and find missing terms in repeating shape patterns. Count by 10s. Use a variety of concrete (objects, fingers), pictorial, and symbolic models for addition and subtraction. Use objects to represent geometric figures. Model addition and subtraction stories with number sentences. Understand the = symbol in number sentences. Describe, compare, name, sort, and classify two-and-three-dimensional shapes. Describe and compare lengths and heights. Count and compare numbers of objects in categories. Build skills in comparing sets. Explain why solutions make sense and are correct. Use models to explain reasoning. Apply counting and comparing skills in a wide variety of contexts. Investigate measurement concepts. Interpret data in tally charts and bar graphs. Consult or download the complete Scope and Sequence for a full report of covered topics and concepts.
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Unit four is about right triangles and the relationships that exist between its sides and angles. Students apply their understanding of similarity, from unit three, to prove the Pythagorean Theorem. Trigonometric functions, which are properties of angles and depend on angle measure, are also explained using similarity relationships. Students determine when to use trigonometric ratios, Pythagorean Theorem, and/or properties of right triangles to model problems and solve them. Throughout the unit, students should be applying similarity and using inductive and deductive reasoning as they justify and prove these right triangle relationships. - What relationships exist between the sides of similar right triangles? - What is the relationship between angles and sides of a right triangle?
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Copyright © University of Cambridge. All rights reserved. 'Fractions in a Box' printed from http://nrich.maths.org/ Why do this problem? gives practice in calculating with fractions in a challenging setting. It also requires the use of factors and multiples. While doing the problem learners will need to express a smaller whole number as a fraction of a larger one and find equivalent fractions. This activity will require some estimating and trial and improvement, combined with working systematically. You could start by showing the picture in the problem and explaining the task orally to the group. Give them a chance to think on their own for a minute then ask them to talk to a partner about how they might start the problem. Sharing some ideas will help you ascertain whether learners understand the task and it will give you the chance to talk through any misconceptions they may have. It may be helpful to collate some known facts or suggestions on the board. At this stage, welcome all ideas for how to begin as long as they are backed up by logical reasons. It is likely that many will involve testing a size for the booklet, but different children may have different starting points for the size. Others might want to test total numbers of counters. After that encourage them to work in pairs on the problem from a printed sheet (this sheet is photocopiable) so that they are able to talk through their ideas with a partner. Make sure that learners have access to any resources that they require, such as squared paper, coloured pens/pencils, mini-whiteboards, plain paper, counters ... Warn them that you would like them to be able to explain how they approached the problem at the end of the lesson. You could ask each pair or group to produce a poster of their working. In the plenary, you could invite the class to look at each other's posters and ask each other questions about the methods used. What shape is the booklet? How are you going to work out its size? How many holes could the booklet could take up? What do you know about the factors of the total number of discs? Learners could find out possible fractions for the differently coloured discs if the square booklet was larger, say $6 \times 6$. Some children my find it helpful for you to structure the approach a little. You could suggest making a list of the possible sizes for the square booklet then working out the number of remaining small square holes for the coloured discs. This activity has been made into a group task here.
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Verbals: Gerunds, Prepositions, and Infinitives Use these worksheets for learning about verbals. Verbals are verb forms that take on the jobs of other parts of speech. Infinitives, participles, and gerunds are all verbals. Common Core alignment can be viewed by clicking the common core . A gerund is an -ing form of a verb that is used as a noun. Gerunds usually name activities or actions, such as dancing, laughing, or sneezing. Identify the gerund in each sentence. 2nd through 4th Grades An infinitive is the word to plus a verb. Infinitives can be used as nouns, adjectives or adverbs. Identify the infinitive in each sentence. Read each sentence. Find the past participles and present participles. Determine whether the underline words represent a gerund, a participle, or an infinitive. Browse our complete collection of grammar worksheets. Topics include nouns, verbs, adjectives, conjunctions, adverbs, pronouns, prepositions, and more.
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You need Adobe Reader software to view these materials. You can download Adobe for free: Tips for Teaching Math Ask your student what skills in math she has and what she wants to learn. Relate math skills to daily life. Can your student: use a calculator? use a ruler? use estimation strategies? balance a checkbook? read a thermometer? calculate a tip? read and interpret charts and graphs? Observe and analyze the kinds of computational errors your student makes and then teach the necessary skills. Teach your student strategies for solving word problems. Encourage your student to check his work with a calculator. Stress that HOW you do a problem is just as important as the correct answer. Use “hands-on” manipulatives when teaching math concepts. For example, use a ruler to measure objects, or coins to count change. Encourage frequent practice so that your student can master these skills. So often our students didn’t understand a concept in the classroom and were left behind when the class moved on to a new skill. This time ensure success by allowing your student time to really learn these skills.
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This program is designed to help students in introductory chemistry classes understand the concept of extent of reaction. The program starts with a simple reaction where it takes 2 moles of A and 1 mole of B to produce 2 moles of X. The reaction starts with 1 mole of A and 1 mole of B. As you move the reaction progress slider to the right, the extent of reaction increases, the amount of reactants A and B decrease, and the amount of X increases. If you move the slider to the end, all the moles of A will be used up and the reaction cannot progress any further. The slope of the lines on the graph is equivalent to their coefficient in the reaction, while their endpoints correspond to their amounts at minimum and maximum extent. You can change the coefficients on the products and reactants to simulate various reactions. You can also change the initial amounts of the products and reactants to simulate various conditions. To simulate the reaction of N2 + 3H2 ⇔ 2NH3, set the coefficient on A to 1, the coefficient on B to 3, the coffieicent on X to 2, and the coefficients on C, Y, and Z to 0. Then set the initial amounts to the desired values. You can also input reactions in terms of grams and molar mass. To do so, first select the mass mode. The program should then display a row of molar masses above the initial grams. Using these inputs, it is possible to vary the molar mass of the substance, and thus the initial moles of the substance
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Common Core Math Standards350+ math concepts in Kindergarten to Grade 5 aligned to your child's school curriculum Continue your child’s math learning Sign up for a FREE SplashLearn account. Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Geometry - K Grade Common Core Math Identify and describe shapes. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. Correctly name shapes regardless of their orientations or overall size. Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid"). Analyze, compare, create, and compose shapes. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length). Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?" Practice Kindergarten Math with Fun Games
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In order to paraphrase well, students need to be comfortable with a diversity of lexical and grammatical tools. While some students can easily draw on their own language skills, others struggle to access the skills they need to rephrase a selection in their own words. Rephrasing sentences with signal words is one useful strategy for building up to full paraphrasing. Use these skills to break apart or combine sentences, and encourage students to reorder the clauses. This is also a good time to make sure that students understand how to paraphrase without changing the meaning of a sentence, as changing one signal words can often change the meaning of a sentence. Help students change the signal words in these worksheets: Cause Effect Words (pdf) Contrast Words (pdf) Before starting on these activities, make sure that students have practiced or can use a resource that includes a variety of signal words, such as transitions, subordinators, and nouns/verbs for cause-effect and contrast. Encourage them to use phrases that they have read and understand, but don’t use much in their own writing. For example, “since” and “because” have the same meaning and grammar, so if a student overuses “because,” he or she can substitute “since.” Likewise, the student can divide a long sentence into two sentence and connect the ideas with the prepositional phrase “because of this.” Find more activities in Paraphrasing.
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Probability is simply how likely something is to happen. Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. The best example for understanding probability is flipping a coin: There are two possible outcomes—heads or tails. What’s the probability of the coin landing on Heads? We can find out using the equation P(H) = ?.You might intuitively know that the likelihood is half/half, or 50%. But how do we work that out? Probability = In this case: Probability of an event = (# of ways it can happen) / (total number of outcomes) P(A) = (# of ways A can happen) / (Total number of outcomes) There are six different outcomes. What’s the probability of rolling a one? What’s the probability of rolling a one or a six? Using the formula from above: What’s the probability of rolling an even number (i.e., rolling a two, four or a six)? - The probability of an event can only be between 0 and 1 and can also be written as a percentage. - The probability of event Ais often written as P(A) > P(B), then event Ahas a higher chance of occurring than event P(A) = P(B), then events Bare equally likely to occur. Practice basic probability skills on Khan Academy —try our stack of practice questions with useful hints and answers!
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How Different Magmas Form Both extrusive and intrusive igneous rocks are derived from magmas. The temperature and pressure conditions in the crust and upper mantle influence the melting temperatures of the minerals in the rocks. Temperature and pressure increase with depth from the surface and eventually reach a point at which rocks melt. The geothermal gradient is the rate at which temperature increases with depth. In the upper crust, the geothermal gradient is about 2.5 degrees centigrade for every 100 meters (330 feet). Geothermal gradients are higher in volcanic regions. Mantle plumes are “hot spots” in the crust where mantle material has ascended along deep penetrating cracks in the crust and contributes heat for higher‐level melting. Country rock can also be melted from the heat of adjacent intrusions. Friction is a source of heat in areas where large rock masses are grinding against one another—for example, during mountain‐building and plate tectonic activity. Heat is also released through the radioactive decay of elements such as uranium, a less important process that only marginally raises the geothermal gradient. Because of higher pressures, temperatures, changes in density, and gases in solution, magmas tend to rise toward the surface through deep cracks and faults. Being more viscous, felsic magmas rise more slowly than mafic magmas. As magma moves upward it begins to cool, and minerals begin to differentiate. A very hot magma assimilates the country rock it is moving through—that is, the country rock in contact with the magma melts and becomes part of the magma. If a magma assimilates a large amount of country rock, the chemistry of the magma changes. Different extrusive and intrusive rock types form from magmas according to the chemistry of the magma and the differentiation reactions that precipitate the various minerals that make up the igneous rock. Partial melting is the process by which a portion of the magma that is forming from a melting mass of rock separates and rises as a distinct magma. As a rock is being heated, the first liquid that forms contains a high proportion of the minerals that have lower melting temperatures. A good example is basaltic magma, which is thought to be the result of partial melting in the mantle; the remaining magma in the mantle is then ultramafic in composition. If the entire rock melts, and no magmatic phases escape, the earlier‐forming and later‐forming liquids mix to form a magma that has the same composition as the original rock.
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The Indian Removal Act of 1830 was a landmark in relations between the U.S. government and the American Indians. Before then, the federal government officially respected the legal and political rights of the Indians. The act changed U.S. policy by giving the president the power to grant Indian tribes unsettled western lands in exchange for their lands in existing states in the East. It began a process that eventually forced tens of thousands of Indians off their native lands. In the early 1800s white settlers spread throughout the territory east of the Mississippi River. By the mid-1820s it was clear that they would not allow the presence of even peaceful Indians near their settlements. They wanted the Indians to be removed, and President Andrew Jackson strongly agreed. On May 28, 1830, Jackson signed the Indian Removal Act into law. The act aimed to relocate the eastern Indians west of the Mississippi, to the Great Plains. At the time the region was considered to be the Great American Desert—a place where whites would never want to live. After the Indian Removal Act was passed, a number of northern tribes were peacefully resettled in western lands. Indians of the Southeast, however, were less willing to move. Members of what were known as the Five Civilized Tribes—the Cherokee, Chickasaw, Choctaw, Creek, and Seminole—did not want to trade their farms for unknown land in the Indian Territory (now Oklahoma). These tribes were well established on their native lands. They had homes, governments, and children in missionary schools, and some had trades other than farming. The Indian Removal Act called on the U.S. government to negotiate with the eastern tribes and pay them for their lands. In reality, though, the government resorted to force to remove the Indians. The U.S. military evicted about 100,000 eastern Indians in the 1830s. Up to 25 percent of the Indians, many in chains, died on forced marches westward. The sad trek of the Cherokee in 1838–39 is remembered as the Trail of Tears. Even more reluctant to leave their native lands were the Seminole of Florida. They fought resettlement for seven years (1835–42) in the second of the Seminole Wars. The Indian Removal Act promised the Indians ownership rights to the new lands they were granted. But in the years following the removal of the eastern tribes, white settlers continued to push farther westward. As they crossed the Mississippi, they forced Indians off the land that the act had “guaranteed” to them.
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http://www.mindbites.com/lesson/916 for the full video Reminding us of its definition, Professor Burger demonstrates how to work an inequality with an absolute value. You will need to convert the inequality from the absolute value to an inequality encompassing both the positive and negative points of that absolute value. This will look different, depending on whether the absolute value is less than or greater than. Prof. Burger walks you through several examples. For an introduction to inequalities, see this lesson: http://www.mindbites.com/lesson/913-beg-algebra-introduction-to-inequalities And for more on absolute values: http://www.mindbites.com/lesson/914-beg-algebra-solving-absolute-value-equations Questions about Beg Algebra: Solving Absolute Value Inequalities Want more info about Beg Algebra: Solving Absolute Value Inequalities? Get free advice from education experts and Noodle community members.
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To create a circular arc in a shapesheet’s Geometry section, requires the specification of where the arc ends and a cell called “A” that holds the measurement of how much the arc differs from a straight line between the end points of the arc. The deflection indicates how much the arc bows. It is possible to fragment a circular shape to get an idea of a value of “A”, but it is a value not a formula. So what is a formula to describe the content of the “A” cell? To determine a formula, you need to revisit your grade school trigonometry notes. A line that connects two points a circle is called a chord and has a few special properties. The largest chord passes through the center of the circle and is called the diameter. A triangle formed by the chord and the center of the circle forms an Isosceles triangle. The angles at either end of the chord are identical. If you use the half way point on the chord, call it B, to bisect the triangle through the center of the circle, call it C, you end up with two identical right angles triangles. The length from B to C divided by the hypotenuse of the right angle triangle is the sine of the angle of the right angle triangle at the center of the circle. In this case, the hypotenuse is the radius of the circle and the angle is half the value of the angle formd by Isosceles triangle. So the length of BC is: Radius x Cosine (angle/2). So the formula for cell “A” is: Radius – Radius times Cosine (angle/2) or Radius (1 – Cosine(angle/2)) John… Visio MVP
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Grade Level: Middle school Time Required: 1 hour Expendable Cost/Group: US $0.75 Group Size: 2 Subject Areas: Measurement, Physical Science Bolded words are vocabulary and concepts to highlight with students during the activity. What is density? Density is equal to the mass of an object per unit volume. For example, a brick is heavier than a Styrofoam block of the same size (volume); this means the brick is denser than the Styrofoam. If an object is less dense than a liquid, the object will float in the liquid. If an object is denser than a liquid, then the object will sink in the liquid. If we put a ball of clay in water, it sinks; clay is denser than water. So, how can we make a boat out of clay that floats? We must make the clay buoyant by forming it into a shape that helps it float on top of the water. This only works if we can make the clay into a shape that displaces a mass of water equal to or greater than the mass of the clay itself. Why is this important? Buoyancy is what makes things float, and understanding this principle helps us design things that work, such as ships, hot air balloons and life-vests. Each group needs: - 2 oz. (60 g) clay - 12" (30 cm) masking tape - 1 sheet wax paper - 4-5 paper towels - tub of water (shared) - washers, pennies, etc. (shared, used as weight) Instruct students to work in teams of two. First, they design their boats, keeping in mind that the boats must float while holding weight and that they have a limited amount of clay to use. Students can test their designs and make changes as often as they like. The goal is to create boats that can hold as much weight as possible while staying afloat. Building and Testing Boats Note: Be sure students dry the clay with a paper towel after taking it out of the water and between trials, otherwise it will become too wet to manipulate. - Instruct students to tape a piece of wax paper to their desks to serve as their "work stations." - Hold a brainstorming session with students about ways to make a ball of clay into a floating object. Ask them what shapes they think will work best and have them make predictions about how many weights their boats will hold. - Instruct students to spend a few minutes constructing a floating object with their clay. One group at a time, place it in the tub of water to see if it floats. - If it floats, help students add weights, one at a time, until it sinks. On the classroom board, track how many weights each group's boat held before failure, for each trial. - Encourage students to try a variety of designs to determine which works the best. - After testing, have each team share its best boat design and how much weight it held. Have students discuss common themes between the successful designs and how the designs compare to real-world, full-size boats and rafts. Wrap Up - Thought Questions - Which designs worked the best? Why? - Which designs did not work well? Why not? - Why does a piece of steel sink in water while a steel boat floats? More Curriculum Like This Students use modeling clay, a material that is denser than water and thus ordinarily sinks in water, to discover the principle of buoyancy. They begin by designing and building boats out of clay that will float in water, and then refine their designs so that their boats will carry as great a load (m... Students learn that buoyancy is responsible for making boats, hot air balloons and weather balloons float. They calculate whether or not a boat or balloon will float, and calculate the volume needed to make a balloon or boat of a certain mass float. Students explore motion, rockets and rocket motion while assisting Spacewoman Tess, Spaceman Rohan and Maya in their explorations. First they learn some basic facts about vehicles, rockets and why we use them. Then, they discover that the motion of all objects—including the flight of a rocket and mo... Students are introduced to the important concept of density. Students devise methods to determine the densities of solid objects, including the method of water displacement to determine volumes of irregularly-shaped objects. Copyright© 2013 by Regents of the University of Colorado Last modified: March 24, 2017
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Maths games for practising fractions. The Writing Process In Year Five we are working hard to develop our writing skills, becoming confident and effective writers who are able to use our creativity to inform and entertain others. One of the most important aspects of writing is to understand, and use, the writing process. So what is it? What do we want to write? What is the overall feeling in the room? What are the stand out features? - think about size, shape, colour and position. Then, focus in... What is on the desk? Where is it? What is it doing there? Then, focus in again... This plan shouldn't have full sentences. We are looking for short phrases, clauses and key descriptive words. We can extend them into our sentences during the next stage. Year 5 were posed the following problem: Imagine two red frogs and two blue frogs sitting on lily pads, with a spare lily pad in between them. Frogs can slide onto adjacent lily pads or jump over a frog; frogs can't jump over more than one frog. Can we swap the red frogs with the blue frogs? This was extended to 3 frogs of each colour. Children were able to solve in any way they liked. Some drew pictures, some used objects (including their friends) and some wrote instructions.
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By Brian D. As with any exam that tests mathematical knowledge, you’re going to need to know the basics. These include topics like exponents, factors, etc. Here we will be doing a brief review of the basic information that you should know for this test, and many others in general. Laws of Exponents Here is how exponents are typically represented in a problem. a represents the base and b represents the exponent. · The base is the number that is being multiplied. · The exponent is the number of times the base is multiplied by itself. If you have a negative exponent, then it simply means that you need to convert it to fractional form, in which the numerator is always 1 and the denominator is the base raised to the exponent with a positive sign rather than a negative sign. If you have a base with a fractional exponent, then the first thing you do is put the base raised to the fraction’s numerator under a radical sign. The radical will be raised to the denominator’s root. So to sum it up, the numerator goes under the radical sign and the denominator goes outside. If you’re presented with a situation in which you’re asked to multiple numbers that have the same base but different exponents, then what you do is add the exponents while keeping the base the same. On the other hand, if the exponents are the same but the bases are different, then you will not be able to multiple them this way. You’ll either have to use a calculator or use the specific circumstances to find a way short of manually multiplying the numbers (not only will that be time consuming but also very prone to mistakes). The same above applies to division of bases with exponents. Instead of adding the exponents (if applicable) you subtract them. If you have an entire fraction raised to an exponent, then you simply raise both the numerator and denominator to that exponent. If you have a term nested in parentheses raised to a power, then you raise every term within those parenthesis raised to that power. For instance: (XY)n = XnYn But if there are no parenthesis, then you do not raise the entire term to that power XYn! = XnYn Factor trees are a visual method of determining factors and ultimately, prime factors. This is not recommended because it is time consuming. In the time used to draw an entire tree (especially for larger numbers), you could have been solving other problems that present a greater challenge or require more attention. You should use this only if you do not feel comfortable with (prime) factorization because you have the multiple choice working to your advantage, if you plug in rather than spending the time to do the problem the long way. If you do decide to use factor trees, then you simply find factors of the specified number and keep on doing that until you have only prime numbers and 1. When nothing more can be further simplified, then you have your prime factors. If the number at the top of the tree cannot be further simplified however, then it is already a prime number.
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Money Comes and Goes This lesson printed from: A budget is a plan that shows how much money comes in (income) and how much money goes out (expenses). We use a budget to make sure we have enough money to buy the things we need and really want. A budget also helps us set aside money for things that we can’t afford to buy right now. The money we set aside is called savings. You will learn the different parts of a budget. You will also create a budget you could use to reach a savings goal. Read the story Tim’s Turn to Learn and answer the questions on the worksheet. When you are finished, you will discuss the worksheet answers with your class. Tim and Money Mouse reduced their spending in order to save money for the future. Another way they could have saved more money is by increasing their income. Read the story Heather Learns About Earning to find out how Heather increased her income. Then, answer these questions about the story: - What was Heather’s problem? - How did she earn the money she needed? - What else might Heather have done to earn the money she needed? Now that you know what income and expenses are, can you find the income and expenses in this budget? A budget helps us keep track of our money so that we can use it on things we really need and want. A budget also helps us save for things that we can’t afford to buy right now. A balanced budget has money in (income) equal to money out (spending and saving). Now it is your turn to create a budget!: www.econedlink.org/interactives/EconEdLink-interactive-tool-player.php?filename=em483_budget2.swf&lid=483 - Read the story, Alexander Who Used to Be Rich Last Sunday. Discuss with your class what happened to Alexander’s money. Also discuss how you can keep from buying things that you don't need. - Think of something special that you would like to save money for. Use the “Spending Tale” to keep a personal spending diary. Then create a budget that will help you reach your savings goals.
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Fairness definition Fairness is the idea that people who don’t share their values should not be able to participate in the process of creating or making an impact on society. Fairness means that people should be able and should not feel that they have to conform to the rules of the society they live in or that others must. It is a goal that is shared by almost all of the world’s major religions and cultures. It means that those who have less than the best of things are expected to act like trash. It also means that if a group of people is less than equally deserving, they should be treated equally. That is what the concept of fairness is about. There are a number of ways to achieve this. One common way to achieve fairness, is to provide fair access to information, resources, and services. In the United States, many public schools provide free access to textbooks, computer labs, and even some of the internet to students, while the government does not. This can help schools be more inclusive and encourage more students to participate and learn in the community. Fair access to educational resources and services is important to achieving fair outcomes in education. In Australia, for example, the Government has a national Fair Access Policy and Fair Access Network, which aims to achieve a fair and equal distribution of educational resources to all Australians. This includes all students, parents, teachers, and staff, with equal access to all resources, including computer labs and internet access. Another way to ensure fairness is to ensure that students are offered equal opportunities to achieve their goals. In India, the Ministry of Education and Training has set up a National Fair Access Framework that aims to help schools achieve fair outcomes. The National Fair Education Programme in India also has a set of goals that students, teachers and parents can work towards to achieve fairness in education: a school environment that is free from discrimination and intolerance, inclusive of all students and their diverse backgrounds, and which supports students’ academic success and learning. A fair education is a fair education and a fair society. It requires that every child has access to education, including those who need it most. This is particularly important for young children who are already disadvantaged in school. It can be challenging to implement a fair educational environment when there is no data on the impact of education on the achievement of young children, but the results are there. In Canada, a number new national Fair Education Standards have been set for schools and parents. These new standards will guide and support the implementation of fair education for students and parents by improving the quality and availability of educational materials and support services. The Fair Education Framework in Canada is a national program and was announced in 2014 by the Minister of Education, Science and Innovation. The Framework is based on recommendations from the National Commission on the Quality and Availability of Educational Materials and Support Services and other expert bodies. This National Fair education plan is supported by the Department of Education in partnership with the provinces of Ontario and Quebec. In 2017, the Minister also established a national pilot project to increase access to higher education for disadvantaged students. The pilot project aims to provide students in primary schools and other schools with access to up to two hours of free access every week to educational materials, computer lab, and internet. This pilot project is funded by the government through the Ontario Public School Education Fund and is being piloted across Ontario and Canada. This plan is also supported by provincial governments, and by the federal government. It provides support to students and families who are currently disadvantaged in the classroom. It does not provide financial assistance to students or families who have been denied access to school. This model will ensure that the quality of education is maintained in primary and secondary education for all students.
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When presenting the target language, the teacher has several methods. No one method proves more ably suited than another for the class. However, the teacher will almost always use several methods to clarify the information, as all the following methods work in tandem. What follows are four methods, namely: Method One: Explanations If a teacher were introducing zero conditionals, for example, the explanation would likely explain that the grammar structure is used to talk about always or almost always true statements. It consists of an if-clause or a when-clause which states the condition, followed by the action taken under that condition. Zero conditionals usually use the present tense, but can sometimes be used in the past tense too. Method Two: Visual Aids Timelines, pictures, and diagrams all fall into the category of visual aids. The teacher can draw a diagram or timeline on the board to highlight how to use the target language. This works especially well when introducing new grammar structures. Pictures work equally well, as they can show the meaning of the word. For example, flashcards can be used to introduce new vocabulary, or videos can be used to show gestures and facial expressions. In short, a visual aid may be anything in which the students can visually link the key language of the lesson with the explanation. Method Three: Examples For the class on zero conditionals, the teacher might provide two or three examples on the board: If it looks like rain, I bring an umbrella. I almost always bring an umbrella on dark, cloudy days. For a class on adverbs of frequency, the teacher might write the following on the board: I always eat breakfast in the morning. Students can more readily see and understand the target language because of the examples. They further can see how the target language fits into sentences and other structures. Method Four: Elicitation The teacher may think to provide more examples, in order to provide a lot of sentences for reference and models. However, too many examples from the teacher tend to establish a teacher-centered classroom. Students will look to the teacher for examples as a means for added clarity. They won't attempt to generate their own examples, which then places too much reliance on the teacher. In addition, when practicing the language, students may very well be less likely to deviate from what the teacher has given, in fear of being wrong. In addition, elicited examples allow the teacher to effectively asses if the students understand both the form and the function of the newly presented material. If the examples fail to use the language correctly, or stick far too closely to the examples provided by the teacher, then this serves as a signal for the teacher to further clarify the target language. Students don't yet fully understand the form and/or meaning. Let's look at two examples. In the first example class on conditionals, the teacher calls on the students for some sentences using the target language. He writes the following on the board after making some minor grammar corrections for articles and singular/plural. If I'm hungry, I go to restaurants. All of the sentences elicited from the class demonstrate that the structure is sound, but the meaning isn't quite correct. Does the student always go to restaurants when hungry, no matter that it's breakfast, lunch, dinner, or a snack? Does the second student always play tennis during his free time? In other words, he does nothing else? The teacher realizes that additional examples and a clearer explanation are required on his part. He returns to the presentation before allowing the students to practice. After all, if he simply stated that the examples weren't zero conditionals, made corrections, and then began a practice activity, then the students would still likely be unable to correctly use the structure. The other example on adverbs of frequency sees the teacher elicit the following: I always study for my tests. His class obviously understands the structure, and so should move on to practice it. Although the teacher may opt to use only one of the above methods, improved comprehension and use of the language in the initial stages of the lesson results when a combination of methods are used. Each reinforces another method. In addition, it also taps into select learning styles, giving consideration to auditory learners, visual learners, and others. Lastly, with elicitation, the teacher can gauge comprehension among the class in general, and choose to move on to the practice portion of the lesson or to provide additional explanation.
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Students can learn about the Exponential form here.They can solve problems based on the methodology explained in the solved examples. In Algebra, the study of working with algebraic equations and variables is an important topic. The study of exponents is also an important topic. The Exponential form is a way of expressing variables. It has 2 components: - The Base- which could be a number or a variable - The Exponent- the power to which the base is raised to. The exponential form often represents the degree of an equation. The exponents mean the number of times the variable or a number is multiplied with itself. Example: `x^(2)` is x * x `2^(4)`= 2*2*2*2= 16 Definition of Exponential Form Students can learn the definition of exponential form here. Exponential function can be defined as when a function or number increases at constant rate. The numeric function is called exponential if it is in the form, [ f(a)=`e^(a)` ] here a is independent variable. * e constant value is e = 2.71828183 * Exponential functions are represented by either e or d The rules for expressing in exponential form are: 1) `x^(a+b)` = `x^(a)` `x^(b)` 2) `x^(ab)` = xab 3) `x^(0)` = 1 4) `x^(-a)` = [1/`x^(a)`] Calculating Exponentials Online Students can learn Calculating exponentials online. They can also get help from the online tutors for understanding the steps involved. Example 1: 270000 here we can see it has four zeroes. Therefore we can write as 27 x 104 Example 2: Write the number in exponential form in one digit - 13,2000 0000. Here it is asked to write in single digit. 1.32 x `10^(9)` we can write after the 1st digit 2 there were 9 digits. so we wrote it as power 9. Example 3: 63/10000 let us change denominator to power of 10 here 10,000 = `10^(4)` so 1/10,000 = `10^(-4)` then 63/ `10^(4)` can be written as 63 * `10^(-4)` or for single digit we write it as [(6.3)*10] *`10^(-4)` so 6.3 * `10^(-3)` Students can get more help with the topic on the algebra homework help page.
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We use correct phonics terminology as much as possible when teaching. Below are the definitions for words we use. Phoneme - The sound a letter makes. Phonemes can be put together to make word e.g. 'c-a-t'. Digraph - Two letters that makes just one sound e.g. 'sh' or 'qu'. Trigraph - Three letters that makes just one sound e.g. 'igh' or 'air'. Blending- This is when you look at a word, find out which sound each letter makes and then putting the sounds (phonemes) together in order to read the word. For example, if a child sees the word 'cat' they will know the sound each letter makes . They will then be able to put the sounds together to read the word. This is the basis of reading. Segmenting - This is when you hear a whole word and can then split the word up into its individual sounds (phonemes). For example, knowing the word 'cat' is split up into the 'c', 'a' and 't' phonemes. Children need to be able to do this in order to spell words.
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“Remote sensing” is a term used to describe many different types of observations carried out at a distance. Aerial photos, satellite images of the Earth and planets, and telescope views of our solar system are all forms of remote sensing used to understand geology, climate, hazards, and changes over time. Not all remote observations use the wavelengths of light visible to humans; there is a wealth of information contained in how a surface reflects or emits radiation across the spectrum from radio waves to gamma radiation. Scientists at the National Air and Space Museum's Center for Earth and Planetary Studies use radar signals, transmitted from satellites in lunar orbit or from the largest radio dishes on Earth, to probe below the dusty surface of the Moon. Radio waves, which have a much longer wavelength than visible light (the Museum's research uses signals with 12.6-centimeter and 70-centimeter wavelengths), penetrate up to 30-40 meters into dry material and reflect from buried layers or rocks suspended in the thick dust. By carefully measuring the time between the transmitted and received radar signals, and the subtle changes in frequency caused by the rotation of the Moon, the radar “echoes” can be assembled into an image that resembles a photograph, but revealing aspects of lunar geology often hidden from optical cameras. Studies using the new radar maps trace the outlines of ancient lava flows now buried by material hurled from giant impact craters, find rocky material in resource-rich areas that might pose hazards to robotic exploration, and “light up” for the first time areas near the poles that are in permanent shadow from the Sun. Ongoing work suggests that some areas of the smooth lunar “seas," or maria, may have very rugged, boulder-covered lava flows hidden by billions of years of overlying dust; how such rough deposits might form remains a mystery. The lessons learned from studies of the Moon are guiding efforts to design a radar sensor for Mars that will look beneath that dust-covered surface to reveal additional geologic signatures of past and present water. A 12.6-centimeter wavelength radar view of the lunar crater Aristoteles (87 km diameter). Rugged areas, such the northern interior wall of the crater, appear bright to the radar, and smooth or dusty parts of the surrounding region appear dark. The radar lighting comes from the lower left, so the walls of the crater cast "radar shadows" just as they would for illumination by the Sun. The surrounding clusters and chains of smaller craters were formed by debris ejected from the main crater.
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http://www.mindbites.com/lesson/916 for the full video Reminding us of its definition, Professor Burger demonstrates how to work an inequality with an absolute value. You will need to convert the inequality from the absolute value to an inequality encompassing both the positive and negative points of that absolute value. This will look different, depending on whether the absolute value is less than or greater than. Prof. Burger walks you through several examples. For an introduction to inequalities, see this lesson: http://www.mindbites.com/lesson/913-beg-algebra-introduction-to-inequalities And for more on absolute values: http://www.mindbites.com/lesson/914-beg-algebra-solving-absolute-value-equations Questions about Beg Algebra: Solving Absolute Value Inequalities Want more info about Beg Algebra: Solving Absolute Value Inequalities? Get free advice from education experts and Noodle community members.
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To output a value, use the print function. When you print something, it will appear in the output viewer (aka "the console"). You can print variables, strings, integers, floats, and all data types. We'll get to data types soon. print("Hello") print(1) print(99.99) The code above will output: Hello 1 99.99 Now, there are also other ways to use the print function, including: # strings can be in single or double quotes print("Message") print('Message') # You can print multiple arguments; you separate arguments with a comma # When the arguments are printed, they are separated by a space by default print('Message', 'with', 'arguments') # would have spaces # You can even use string concatenation ("adding" strings together) # String concatenation puts strings together w/o spaces (be careful about this) print('Message' + 'with' + 'concatenation') # would not have spaces The output of that: Message Message Message with arguments Messagewithconcatenation To input a value, use the input()function gets user input from the keyboard. When using it, make sure to assign the input()to a variable that way you store it and can print it. It is also worth noting that the input prompt goes inside the input function's parentheses. For example, if you wanted to provide the prompt: "How are you? ", you'd do: status = input("How are you? ") print("Hello World") name = input("What is your name? ") print(name) # prints the name that the user entered If you're confused about variables, click this.
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Africans represent many different people, each with distinct cultures, religions, and languages. The first Africans arrived in America to Jamestown, Virginia in 1619, just as indentured servants arrived in America from Europe, when a Dutch ship brought the first slaves from Africa to the shores of North America against their will. At first, indentured servants were poor Europeans who wanted to escape harsh conditions and take advantage of opportunities in America. The Africans were brought to America’s developing colonies at a time when workers were needed to keep the economy running. The entire southern American economy and the states needed laborers to work on the plantations where they grew tobacco, cotton, and other crops. These plantations required large numbers of laborers. Slavery was less profitable in the North where economic activity centered on small farms. Therefore, few people in the North owned slaves. Most indentured servants had a contract to work without wages for four to seven years, after which they became free. Blacks brought in as slaves however had no right to eventual freedom. Slavery spread quickly in the American colonies. At first the legal status of Africans in America was poorly defined, and some, like European indentured servants, managed to become free after several years of service. From 1619 to about 1640, Africans could earn their freedom working as laborers for the European settlers. In 1630, English colonists began to make a sharper distinction between the status of white servants and black slaves. Discrimination against black slaves began to increase. By 1640, Maryland became the first colony to institutionalize slavery. They became slaves who could be bought, sold, and solely owned by their masters. During the mid-1600s, the colonies began to pass laws called slave codes. These codes prohibited slaves from owning weapons, receiving an education, and testifying against white...
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So far, you have only seen how to manipulate data directly or through names to which the data is bound. Now that you have the basic understanding of how those data types can be manipulated manually, you can begin to exercise your knowledge of data types and use your data to make decisions. In this chapter, you learn about how Python makes decisions using False and how to make more complex decisions based on whether a condition is In this chapter you learn: How to create situations in which you can repeat the same actions using loops that give you the capability to automate stepping through lists, tuples, and dictionaries. How to use lists or tuples with dictionaries cooperatively to explore the contents of a dictionary. How to use exception handling to write your programs to cope with problematic situations that you can handle within the program. False in Chapter 3, but you weren't introduced to how they can be used. False are the results of comparing values, asking questions, and performing other actions. However, anything that can be given a value and a name can be compared with the set of comparison operations that return
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Everyone Has a Culture - Everyone Is Different This activity invites students to identify aspects of culture that influence our own behavior and sometimes make it difficult to understand the behavior of other people. Culture is a complex idea, and teachers should be prepared to offer students many examples of cultural features. - Students will be able to define culture. - Students will recognize that some differences among people stem from culture and that some stem from personal traits and preferences. - Write the following statements on the board. - No one is exactly like me. - I have many things in common with the members of my family and community. - Every person in the world needs some of the same things I need. - Ask students to share ideas that support these statements. - Point out that people in various groups often look at people in other groups as "different." - Ask students to describe some of these differences. Why may people in one group behave differently from people in another? - Explain that many differences are related to culture—ways of living and beliefs that are handed down from one generation to the next. Working from the list on the board, explain that all people share basic needs (food, shelter, etc.), that each of us learns a set of behaviors and beliefs from the people we grow up with (the kinds of houses we build and foods we eat), and that each individual has unique talents and preferences (I'm good at math; I don't like chocolate). When we talk about the behaviors and beliefs that a group of people have in common, we are talking about culture. - Ask students to complete the worksheet (link above) in order to help them identify aspects of their own cultures. Explain that each student should answer each question with one sentence or phrase. Then students should rank each item as to how important they feel it is to their culture. - After students have completed the worksheets, ask them to share their answers in small groups. Ask the groups to compare various aspects of their individual cultures. - In some schools, students may share many cultural traits. Some students may not identify with a particular ethnic or foreign culture. Ask students if they think there is one American culture. Discuss characteristics of your region (immigration patterns, geographic location, etc.) that might explain the similarities and differences among student responses to the worksheet. DebriefingUse the following questions to focus discussion on the role culture plays in forming our behaviors and beliefs. - How does it feel to know you are part of a cultural group that shares many ideas and beliefs? - What happened when you compared your worksheets? How many different cultures are represented in the class? - What did you learn from this activity? - Does culture explain why other people sometimes seem "different"? - What are some things that you do that you learned from your culture? - Are all of our behaviors related to culture? (Possible answer: Some behaviors are related to individual preferences and personality traits.) - What can you do to learn about and understand other cultures? - What if you were part of another culture? How might you be different from the way you are now? - How can we use what we learned in this lesson to improve our community? - Have students explore their community's history to trace the influence of various cultures. Who were the original inhabitants of the area? Over the years, what other cultural groups have come to the area? What are some of the features of your community that represent these groups (e.g., architecture, place-names, types of restaurants, religious organizations)? - Ask students to imagine a community that allowed no resident to display or practice any element of cultural identity. Have students write short stories describing a typical day in such a community. When students have completed their stories, ask volunteers to read their compositions. Are the fictitious communities desirable or interesting places to be? Would it be possible or desirable to create such a community in reality?
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Worksheets dealing with the scientific method should include all the questions answered while going through a scientific procedure. These questions include everything from describing the problem to reaching a final conclusion.Continue Reading Instructors should begin any worksheet by asking students to describe the problem and what they are testing. The next step should include outside research, which asks if others researchers have also done work on this or a similar problem. This worksheet should then ask students to formulate a hypothesis using a simple if/then formula. Afterward, a student should be asked to design the experiment itself. This step needs to include materials and the proper steps to be taken during experimentation. Worksheets should remember to ask students to collect data as they are going through the experimentation step. With that data in hand, students should then be asked to begin reaching conclusions based on their observations. Data should be summarized in written form and also presented in graphical form. This allows the student to communicate their ideas both in detailed verbal descriptions, as well as with graphical aids that allow for a quick summarization of the data. Finally, the worksheet should ask students to make conclusions based on their observations. Was the hypothesis confirmed? Was it proven wrong? What lessons could be made and how might they apply to other experiments? Students can then be asked to review all the steps they took during this initial experiment and apply them to a second experiment.Learn more about K-12
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Phonics is a way of teaching children to read skillfully. They are taught how to: recognise the sounds that each individual letter makes; identify the sounds that different combinations of letters make – such as ‘sh’ or ‘oo’; and blend those sounds together from left to right to make a word. Children can then use this knowledge to ‘decode’ new words that they see or hear. This is the first important step to learning to read. Research shows that when phonics is taught in a structured way – starting with the easiest sounds and progressing through to the most complex – it is the most effective way of teaching young children to read. It is particularly helpful for children aged 5 to 7. Almost all children who receive good teaching of phonics will learn the skills they need to tackle new words. They can then go on to read any kind of text fluently and confidently, and read for enjoyment. Children who have been taught phonics also tend to read more accurately than those taught using other methods, such as ‘look and say’. This includes children who find learning difficult to read. Please see www.gov.uk/government/collections/phonics for more information. Taken form the Government 'Learning to read through phonics' information for parents sheet.
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What our Decimal Comparison – Hundredths lesson plan includes Lesson Objectives and Overview: Decimal Comparison – Hundredths teaches students how to compare two decimal numbers. Students will reason about the size of the numbers to figure out which is larger or smaller. By the end of the lesson, they should be able to compare two decimal numbers correctly to the hundredths place. The lesson contains three content pages. It first reminds students how to compare numbers. Then students will learn how to compare decimal values. There is a table that displays several examples of how to represent decimals using blocks. Students will use these blocks in some of the worksheets, so make sure they understand fully how to use this method. The lesson provides several more examples for them to analyze and practice with before they begin the worksheets. INSTRUCTION POSTER ACTIVITY Students will work with a partner for the activity worksheet. (You can also have them work alone or in groups instead if you prefer.) Students will work together to create a poster that teaches people about the hundredths place in decimals. They will explain what it means and how to compare them. There is a blank box on the bottom half of the worksheet page that students can use to draw a rough draft or take notes of what they want to include. Then partners will meet with other students to compare work and demonstrate their methods. SHADE THE BLOCKS PRACTICE WORKSHEET The practice worksheet has two sections. For the first section, students must shade the blocks to represent certain decimals. There are four decimals in this section. The second section requires students to use the inequality symbols to compare decimals. There are nine problems in this section. DECIMAL COMPARISON – HUNDREDTHS HOMEWORK For the homework assignment, students will first use inequality symbols to compare 15 different decimal pairs. Then they will sort the decimals in each row from smallest to largest. Finally, they will draw models to show three different comparisons. They can use extra paper if they need to.
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This is our first lesson from the unit, Proportional Reasoning. Here, we begin with ratios and discuss how to build up a ratio in order to create a proportion. Let's go over the assignment for lesson 1. This is our second lesson from the unit, Proportional Reasoning. Here, we begin with ratios and discuss how to build down a ratio in order to create a proportions. We also discus comparing ratios Let's go over the assignment for lesson 2. A quick introduction to variables and a discussion about Cross-Product. We'll use what we learned from the previous two lessons and apply multiplication and division to finding missing values to proportions. Let's go over the assignment for lesson 3. Let's apply what we've learned to some real-world examples of proportions. They are everywhere! Let's go over the assignment for lesson 4. We begin the second section of our first unit by discussing the concept of unit ratios. Let's go over the assignment for Lesson 5. In this lesson, we talk about multiplicative comparisons and dividing fractions. We discuss these topics in order to make sense out of unit rates. All of this will be applied to how we represent proportions within tables, graphs, and equations. Let's go over the worksheet for Lesson 6. In this lesson, we begin to discuss table representations for proportional reasoning. Our goal is to apply our thinking about ratios and proportional with the organization of tables. Let's go over the worksheet for Lesson 7. In this lesson, we continue our work depicting proportional relationships with representations by discuss graphs. We try to understanding how the slope connects with the constant of proportionality. Let's go over the worksheet for Lesson 8. In this lesson, we finalize our work on representations by discussing equations and how they relate to proportional reasoning. By using tables and graphs, we can see how variables play a role in modeling proportions with equations. Let's go over the worksheet for Lesson 9. In this lesson, we take reflective approach on what we've covered in this unit and try to make connections between ratios, proportional reasoning, and the representations we covered. This unit is a great first step in developing mature mathematical thinking about how we can model the real world with mathematics. Let's go over our final worksheet for the Proportional Reasoning Unit!
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