zilongwang/ReadingBank huggingface dataset:
Represent mathematical ideas in concrete, pictorial, and symbolic forms (Use local materials gathered outside for concrete and pictorial representations.) Connecting and reflecting Reflect (sharing the mathematical thinking of self and others, including evaluating strategies and solutions, extending, and posing new problems and questions) on mathematical thinking Connect mathematical concepts to each other and to other areas and personal interests (to develop a sense of how mathematics helps us understand ourselves and the world around us (e.g., daily activities, local and traditional practices, the environment, popular media and news events, social justice, and integration) Incorporate (how ovoid has different look to represent different animal parts; invite local First Peoples Elders and knowledge keepers to share their knowledge.) First Peoples worldviews and perspectives to make connections (Bishop’s cultural practices: counting, measuring, locating, designing, playing, patterning; online video and text: Small Number Counts to 10; Change in quantity (numerically describing a change in quantity (e.g., for 6 + n = 10, visualize the change in quantity by using hundred charts, etc.)) using pictorial and symbolic representation symbolic representation of equality and inequality financial literacy (counting simple mixed combinations of coins to 100 cents; Introduction to the concepts of spending and saving, integrating the concepts of wants and needs.; role-playing financial transactions (e.g., using bills and coins)) — coin combinations to 100 cents, and spending and saving Evidence of Experience (Show)
explaining aboriginaleducation.ca; Teaching Mathematics in a First Nations Context,; FNESC fnesc.ca/k-7/) to mathematical concepts BIG IDEA (Understand…) What do we want students to DO? (Activities, lessons…) Content (& Elaborations) (Know) Objects and shapes have attributes (describe, measure, and compare spatial relationships) that can be described, measured, and compared. Questions to support inquiry with students: What 2D shapes live in objects in our world? How can you combine shapes to make new shapes? direct linear measurement (centimetres and metres; estimating length; measuring and recording length, height, and width using standard units), introducing standard metric units Multiple attributes of 2D shapes and 3D objects (sorting 2D shapes and 3D objects using two attributes, and explaining the sorting rule; describing, comparing, and constructing 2D shapes, including triangles, squares, rectangles, circles; identifying 2D shapes as part of 3D objects; using traditional northwest coast First Peoples shapes (ovoids, U, split U, and local art shapes) reflected in the natural environment) Evidence of Experience (Show)
It takes Josephine minutes to complete her homework assignment of problems. If we assume that she works at a constant rate, we can describe the situation using a function. Predict how many problems Josephine can complete in minutes. Answers will vary. Write the two-variable linear equation that represents Josephine’s constant rate of work. Let be the number of problems she can complete in minutes. Use the equation you wrote in part (b) as the formula for the function to complete the table below. Round your answers to the hundredths place. Time taken to complete problems () Number of problems completed () After minutes, Josephine was able to complete problems, which means that she was able to complete problem, then get about halfway through the next problem. Compare your prediction from part (a) to the number you found in the table above. Answers will vary. Use the formula from part (b) to compute the number of problems completed when . Does your answer make sense? Explain. No, the answer does not make sense in terms of the situation. The answer means that Josephine can complete problems in minutes. This obviously does not make sense. For this problem, we assumed that Josephine worked at a constant rate. Do you think that is a reasonable assumption for this situation? Explain. It does not seem reasonable to assume constant rate for this situation. Just because Josephine was able to complete problems in minutes does not necessarily mean she spent the exact same amount of time on each problem. For example, it may have taken her minutes to do problem and then minutes total to finish the remaining problems. Closing (4 minutes) Summarize, or ask students to summarize, the main points from the lesson: We know that a function is a rule or formula that assigns to each input exactly one output. We know that not every function can be expressed by a mathematical rule or formula. The rule or formula can be a description of the assignment.
MATHEMATICAL PRACTICE April/May (3 weeks) Pythagorean Theorem 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. May/June (3 weeks) Statistics 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.SP 2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. 8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively MP4 Model with mathematics. MP6 Attend to precision. MP8 Look for and express regularity in repeated reasoning.
(1 Point) (2 Points) incorrect answer. (3 Points) (4 Points) Topic E K.CC.3 K.CC.4a K.CC.4b K.CC.5 K.MD.3 The student shows little evidence of writing or counting numerals, no understanding of the 5group, and is almost non-responsive. The student inconsistently counts the cubes. The student may or may not say and write the correct number. The student is unable to identify the and is unable to state a reason why she knows there are 8 cubes. The student correctly counts and states the number of cubes (with more time elapsed), but struggles with writing the numerals and identifying the The student is able to verbalize how she knows there are 8 cubes, but is unclear in her explanation. The student correctly: Counts the linking cubes and puts them in a row. Writes the number 6. Counts to 7 in the circular configuration, writes the number 7, and identifies the 5-group. Counts 8 cubes and gives a reasonable answer to how she knows there are 8 (e.g., “I counted all of the cubes one at a time,” or “I see 4 on top and 4 on the bottom, and I know 4 and 4 is 8”). Topic F K.CC.3 K.CC.4a K.CC.4b K.CC.5 The student shows little evidence of understanding zero or how to solve put together with result unknown problems. Numbers are illegible. The student shows an early understanding of how to solve put together with result unknown problems and demonstrates weak explanation skills with incomplete reasoning. The student has difficulty counting and writing the numbers. The student completes of the four tasks. For example, the student solves the put together with result unknown problem, but cannot clearly explain his thinking. He correctly writes the numbers. The student correctly: Solves the put together with result unknown problem using cubes. Explains thinking, citing the solution process. Writes the number 9 and adds 1 more bear and says and writes 10.
Class Record Sheet of Rubric Scores: Module 1 Student Names: E: Working with Numbers 6–8 in Different Configurations Topic F: Working with Numbers 9–10 in Different Configurations G: One More with Numbers 0–10 Topic H: One Less with Numbers 0–10 Next Steps:
to add 2 + 1, but either lacks an understanding of how to add or how to interpret the expression. to add; or, the student accurately explains the process of addition, but adds 2 + 1 incorrectly. Breaks apart 3 to show the decomposition of 3 as 2 and 1 or 1 and 2. Topic D K.CC.3 K.CC.4a K.CC.4b K.CC.5 The student little evidence of understanding how to count items in a category. The student is beginning to form some numbers. The student shows evidence of beginning to understand counting items in a category. The student is unsure of the word and meaning of zero. The student writes some numerals correctly, with reversals. The student correctly counts the items in each category. The student gives some explanation about how she knows there are 5 toys but is unclear in her explanation (e.g., “I just know”). The student answers none when about the cats. The student writes four out of six numerals correctly, with a maximum of one reversal. The student correctly: Identifies the number of items in each category (counting all in the toy category is acceptable). Gives a reasonable answer as to how he knows there are 5 toys (e.g., “I counted them all one at a time,” or “I knew it was 3 up to the doll, then I just counted 2 more toys”). Understands and uses the word zero when asked how many cats there are. Writes numerals 0–5. Record Sheet of Rubric Scores: Module 1 Student Topic A: Attributes of Two Related Objects Topic B: Classify to Make Categories and Count Topic C: Numbers to 5 in Different Configurations, Math Drawings, Topic D: Concept of Zero and Working with Numerals 0–5 Next
Lesson 26 Objective: Count 10 objects in linear and array configurations (5 and 5). Match with numeral 10. Place on the 5-group mat. Dialogue about 9 and 10. Write numeral 10. Suggested Lesson Structure Practice (12 minutes) Application Problem (5 Development (25 minutes) Student Debrief (8 minutes) Total Time (50 minutes) Fluency Practice (12 minutes) Roll, Count, Show the Number K.CC.4a (4 minutes) Match Movements to Counts K.CC.4b (4 minutes) See, Count, Write Numbers to 10 K.CC.5 (4 minutes) Roll, Count, Show the Number (4 minutes) Conduct the activity as outlined in Lesson 9. Be sure to cover the 6-dot side to represent 0, ensuring that the total number of dots does not exceed 10. Match Movements to Counts (4 minutes) Select two students. One student chooses a number from 1 to 10; the other student selects a movement or exercise to do that number of times. For each movement, maintain an even pace. Do not allow students to count too quickly. Do the movement with the class, but do not count with them. Student A: The number is 4. Student B: Clap hands. T: So, what do we do, everyone? S: Clap our hands 4 times. T: Ready? Go! S: 1 (clap), 2 (clap), 3 (clap), 4 (clap). Choose two more students and repeat with different numbers and movements.
A Progression Toward Mastery Assessment Task Item STEP 1 Little evidence of reasoning without a correct answer. (1 point) STEP 2 Evidence of some reasoning without a correct answer. (2 points) STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 points) STEP 4 Evidence of solid reasoning with a correct answer. (4 points) Topic A K.G.1 K.G.2 K.G.4 The student: Is unable to select, position, or describe indicated shapes. Takes considerable time to complete tasks, looks to the teacher for help often. The student: Sorts indicated shapes randomly, resulting in some correct and some incorrect shapes in the group. Struggles to select, position, and describe indicated shapes. The student: Identifies a shape from the environment, but is unable to discuss its attributes. Sorts most of the indicated shapes. Correctly selects both of the indicated shapes, but places them in the wrong position. The student correctly: Identifies and describes several attributes of the shape from the environment that match the shape being shown to him. Sorts all indicated shapes from several typical, variant, and distracting shapes. Selects indicated shape, and positions this shape below, next to, or beside another indicated shape. Topic B K.G.1 K.G.2 K.G.4 The student: Is unable to select, position, or describe indicated shapes. Takes considerable time to complete tasks, looks to the teacher for help often. The student: Sorts indicated solids randomly, resulting in some correct and some incorrect solids in the group. Struggles to select, position, and describe indicated solids. The student: Identifies a solid from the environment, but is unable to discuss its attributes. Sorts most of the indicated solids. Correctly selects both of the indicated solids, but places them in the wrong position. The student correctly: Identifies and describes several attributes of the solid from the environment that match the solid being shown to him. Sorts all indicated solids. Selects indicated solid, and positions this solid above, in front of, or behind the indicated solid.
Topic C K.G.3 K.MD.3 The student: Incorrectly groups the shapes. Is not able to verbalize reasoning, or reasoning is not sound. The student: Can sort the shapes into a group, but is not able to verbalize reasoning. Cannot make a second grouping. The student: Is able to sort the shapes into two groups, but may or may not be able to verbalize reasoning. Is able to sort the shapes a second time, but is unable to verbalize reasoning. The student: Correctly sorts the shapes into two groups, and is able to clearly state the reason the shapes belong to each group. Is able to sort the shapes again according to a different attribute, and is able to state such attribute.
support and more time to identify partners of 8 and write the correct parts in the number bond. (Again, make note if the student uses the 5-stick.) all parts of the number bond. Writes a correct combination of parts for the number 8. Topic C K.OA.1 K.OA.2 The student shows little evidence of understanding the addition expressions or addition equations, and is unable to complete most of the tasks. The student: Incorrectly states some or all of what each number represents. Writes incorrect numbers in the blanks or puts the correct numbers in the wrong places. Writes an incorrect addition sentence for the story. The student requires teacher support to correctly answer the questions and/or misses one out of the three questions. The student correctly and independently: States what each number in the number sentence refers to. Writes all the correct numbers in the blanks: 5 + 3 = 8. Writes an addition sentence to match his own story, e.g., 7 = 3 + 4.
Topic D K.OA.1 K.OA.2 K.OA.3 The student shows little evidence of understanding subtraction expressions or subtraction equations, and shows little understanding that the same number can be decomposed in different ways. He is unable to complete most of the tasks. The student: Incorrectly states some or all of what each number represents. Writes incorrect numbers in the blanks or puts the correct numbers in the places. Writes an incorrect subtraction sentence for the story. The student requires teacher support to correctly answer the questions and/or misses one out of the three questions. The student correctly and independently: States what each number in the number sentence refers to. Writes all the correct numbers in the blanks: 8 – 5 = 3. Writes an addition sentence to match her own story, e.g., 7 – 3 = 4. Class Record Sheet of Rubric Scores: Module 4 Student Names: Topic A: Compositions and Decompositions of 2, 3, 4, and 5 B: Decompositions of 6, 7, and 8 into Number Pairs Topic C: Addition with Totals of 6, 7, and 8 Topic D: Subtraction from Numbers to 8 Next Steps:
chance enables us to compare and interpret) from the results of an experiment can be used to predict the theoretical probability of an event and to compare and interpret. What is the relationship between theoretical and experimental probability? What informs our predictions? What factors would influence the theoretical probability of an experiment? Single-outcome probability ( single-outcome probability events (e.g., spin a spinner, roll a die, toss a coin); listing all possible outcomes to determine theoretical probability; comparing experimental results with theoretical expectation; Lahal stick games) , both theoretical and experimental
A Progression Toward Mastery Assessment Task Item and Standards Assessed STEP 1 Little evidence of reasoning without a correct answer. (1 point) STEP 2 Evidence of some reasoning without a correct answer. (2 points) STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 points) STEP 4 Evidence of solid reasoning with a correct answer. (4 points) A K.CC.4d K.G.5 The student: Does not build a closed figure. Struggles to select a real world object that matches the shape they built or does not choose any object. Is unable to identify the position of the third, seventh, first, and ninth shape in any orientation of the pattern block template. The student: Builds a rectangle or some other shape. Struggles to select a real world object that matches the square they built or chooses an object with no matching shape. Correctly identifies the position of some of the shapes but is clearly confused when the template is turned or requires teacher support on The student: Builds a square but considers the two different length straws before building with four equal length straws. Selects a real object that matches the square with some hesitation. Correctly identifies the position of at least two shapes: third, seventh, first, and ninth shapes. The student correctly: Builds a square using four equal straws. Selects a real world object that matches the square built. Identifies the third and seventh shape from the beginning of the horizontal line. Identifies the first and ninth shape from the beginning of the vertical line.
where to start. Topic B K.G.6 The student: Does not join the triangles, and does not make a rectangle. No attempt at putting the pieces together, may not know what a square is, and may just line up the pieces. Places random pattern blocks on the puzzle with no understanding of spatial relationships between the pattern blocks and the puzzle. The student: Puts the triangles together so that two sides are touching but does not make a rectangle. Keeps moving the pieces around but is unable to make the square. Places some correct pattern block pieces on the puzzle, but several pieces are incorrect and sticking out of the puzzle border. The student: Makes a rectangle after several attempts. Makes the square with more time elapsed and more trial and error. Completes the puzzle trying several different pieces with more time elapsed due to the and error of choosing different shapes to fit in the puzzle. The student correctly: Makes a rectangle without much hesitation. Makes the square with very little trial and error. Completes the puzzle using the correct pattern blocks so that nothing extends past the puzzle border.
Grade PK • Module 3 • Topics E–H Family Math Newsletter Spotlight on Math Models Children will use key mathematical models throughout their elementary years. One of these models is the number path, a tool Pre-K students will use to connect counting and numbers 1–10. Sample Activity (from Module 3, Lesson 29) Pollen Café As waiters at the Pollen Café, students place bee customers in special seats on the number path. Then, they tally the orders for flowers. Number Path The number path is used in Pre-K, Kindergarten, and Grade 1 to help children work with numbers and visualize the number sequence. The number path starts at 1 and has a single space for each number. A color change at 5 shows the relationship between 5 and the numbers 6, 7, 8, 9, and 10. Starting in Module 1, children began to see the number path to 5 using stairs that show the total number at each step (as pictured on right). In this module, children continue to build the number path to 10, noticing that each number in the sequence is 1 larger. In Module 3, children work with the path in a new way, placing one object
Q32 Mr. Ramirez bought 6 tickets to the circus. He spent a total of $12.00. He used the equation below to determine the cost of each ticket, t. 6t = 12.00 How much money did Mr. Ramirez spend on each ticket? A $72.00 B $18.00 C $6.00 D $2.00 Q33 What is the value of the expression below when r = 2? 9 - 3r A 0 B 3 C 6 D 12 Q34 The table below shows the points earned by five teams in a mathematics game. What is the list of the points in from greatest to least? A B C D Q35 A clothing store had 30 jackets. If j represents the number of jackets the store then sold, which expression can be used to determine the total number of jackets that were not sold? A 30j B C 30 - j D 30 + j
Name: Math 6 Winter Break Practice Teacher: Monday Tuesday Find the quotient. ÷ = Find the quotient. 28,275 ÷ 87 Find the difference. 764.7 – 45.39 Find the product. 48.2 x 0.39 Find the missing number of each unit rate. = = What is the GCF of 64 and 32? What is the LCM of 6 and 4? How many mL are there in 4.5 L? There are 1000 mL in 1 L. What is 55% of 125? What is the value of 3x2 + 5x when x = 3 ? Evaluate the expression. 33 + 3(4 + ) What is the value of y? Circle the correct answer. 62y = 434 y = 7 y = 5 Use the distributive property to create an equivalent expression to 9x + 21 Jackie made bracelets for 8 days. When he was done he had 96 bracelets. Write an equation to express how many bracelets Jackie made each day. Amanda was 48 inches. She grew n inches last year and is now 56.5 inches. Write an expression that represents the number of inches Amanda grew. Solve for g 72 - g = 36 Solve for x 67 = 18 + x the inequality this number line represents. Write the inequality this number line represents.
13.5 Indirect Measurement Indirect Measurement Record your group’s measurements in the table below: Name of Students in Group Viewing Angle Height of Observer’s Eye Distance from Observer to Flag Pole Calculated Height of Flag Pole (Method 1) Length of Shadow of Meter Stick Length of Shadow of Flag Pole Calculated Height of Flag Pole (Method 2) Flagpole Person Height of Eyes
Lesson Worktext Pages Practice & Review Objectives Lesson Objectives Chapter 11: Compose Numbers 75 149–50 Count to 80 by 1s and by 10s Identify the number that comes before, after, or between Determine the set with more or fewer objects Distinguish between coins and dollar bills Identify the uses of money Relate pennies with coins Count sets of 1–10 pennies 76 151–52 Identify the numbers 1–39 Identify and make dot patterns 0–10 Identify larger or smaller objects Recognize a penny Count sets of 1–10 pennies Count pennies to purchase items 77 153–54 Count 1–80 Write the numbers 1–20 Identify dot patterns 1–10 Use pennies to show addition Count pennies to purchase items 78 155–56 Identify the number that comes before, after, or between Name the days of the week in order Identify the name of the day for a given date Identify the numbers 11–15 as 10 and some more Count 1–15 objects in random arrangement 79 157–58 Count 80 objects Identify the ordinal positions of the days of the week Write an addition sentence for a picture Identify the numbers 16–20 as 10 and some more Count 1–10 objects in random arrangement 80 159–60 pennies to purchase items Identify the numbers 11–20 as 10 and some more 81 161–62 Cumulative Review Chapter 12: More Addition 82 163–64 Count to 90 by 1s and by 10s Play Around the World with dot patterns 0–10 Write the numbers 28 and 29 Join sets of objects to demonstrate addition Apply the Zero Principle of Addition Decompose the number 6 83 165–66 Count up to 90 objects by 1s and by 10s Play ticktacktoe with shapes Write the numbers 30 and 31 Join sets of objects to demonstrate addition Write an addition sentence for a word problem 84 167–68 Count up to 90 objects by 1s and by 10s Identify over, under, front, and back Write the numbers 32 and 33 Join sets of objects to demonstrate addition Recognize the addition of 1 more Recognize addition in vertical form 85 169–70 Count to 90 by 10s Identify left, right, top, middle, and bottom Write the numbers 34 and 35 Join sets of objects to demonstrate addition Recognize the addition of 1 more Draw pictures to show an addition word problem 86 171–72 Complete a part-whole model for an addition problem Join sets of objects to demonstrate addition Write an addition sentence for a word problem 87 173–74 Cumulative Review
2. Domino Little Book or cards On each page, draw dominos and add together the dots. Write the sentence on each page like this. Five and two make seven. ___ and ___ make ___. 3. Lego Words Make short or long words with Legos. Make your name with Lego’s too! Try to draw what you made. 1.“Ten Black Dots” book or picture Read the book then make your own pictures with black dots. Write down what you made. You could also make an “8 Black Dots” or “13 Black Dots” book.
GSE Math 7 Milestones Review 2017-2018 ANSWER KEY OPERATIONS WITH RATIONAL NUMBERS Problem Standard Answer 1. MCC7.NS.2 B 2. MCC7.NS.3 B 3. MCC7.NS.1 D 4. MCC7.NS.3 B 5. MCC7.NS.1 A 6. MCC7.NS.2 D 7. MCC7.NS.1 C 8. MCC7.NS.3 A 9. MCC7.NS.3 C 10. MCC7.NS.2 17 EXPRESSIONS AND EQUATIONS Problem Standard Answer 11. MCC7.EE.1 D 12. MCC7.EE.2 A 13. MCC7.EE.4 A 14. MCC7.EE.4 C 15. MCC7.EE.3 C 16. MCC7.EE.4 D 17. MCC7.EE.4 B 18. MCC7.EE.3 x = -155.25 19. MCC7.EE.4 RATIOS AND PROPORTIONAL RELATIONSHIPS Problem Standard Answer 20. MCC7.RP.2 C 21. MCC7.RP.3 B 22. MCC7.RP.1 C 23. MCC7.RP.1 C 24. MCC7.RP.3 C 25. MCC7.RP.2 D INFERENCES Problem Standard Answer 26. MCC7.SP.1 B 27. MCC7.SP.4 C 28. MCC7.SP.4 B 29. MCC7.SP.3 D 30. MCC7.SP.3 A 31. MCC7.SP.4 A 32. MCC7.SP.4 A 33. MCC7.SP.1 B GEOMETRY Problem Standard Answer 34. MCC7.G.6 C 35. MCC7.G.2 C 36. MCC7.G.4 B 37. MCC7.G.6 B 38. MCC7.G.1 A 39. MCC7.G.6 B STATISTICS AND PROBABILITY Problem Standard Answer 40. MCC7.SP.5 B 41. MCC7.SP.6 B 42. MCC7.SP.5 D 43. MCC7.SP.5 A 44. MCC7.SP.7 A 45. MCC7.SP.5 C
the local community and other cultures Communicating and representing Use mathematical vocabulary and language to contribute to mathematical discussions Explain and justify ( using mathematical arguments) mathematical ideas and decisions Communicate ( concretely, pictorially, symbolically, and by using spoken or written language to express, describe, explain, justify, and apply mathematical ideas; may use technology such as screencasting apps, digital photos) mathematical thinking in many ways dreamcatcher, overlaying coordinate plane on traditional maps) combinations of transformations ( four quadrants, integral coordinates; translation(s), rotation(s), and/or reflection(s) on a single 2D shape; combination of successive transformations of 2D shapes; tessellations; First Peoples art, jewelry making, birchbark biting) Evidence of Experience (Show) BIG IDEA (Understand…) What do we want students to DO? Content (& Elaborations) (Know)
(Activities, lessons…) Data from circle graphs can be used to illustrate proportion and to compare and interpret. Questions to support inquiry with students: How is a circle graph similar to and different from other types of visual representations of data? When would you choose to use a circle graph to represent data? How are circle graphs related to ratios, percents, decimals, and numbers? How would circle graphs be informative or misleading? Circle graphs ( constructing, labelling, and interpreting circle graphs; translating percentages displayed in a circle graph into quantities and vice versa; visual representations of tidepools or traditional meals on plates) experimental probability (experimental probability, multiple trials (e.g., toss two coins, roll two dice, spin a spinner twice, or a combination thereof); dice games with two independent events
Place Value 3.1 The student will a) read and write six-digit numerals and identify the place value and value of each digit Linguistic Complexity Language Forms and Conventions Vocabulary What digit is in the ____ place? ___ is in the ___ place. What is the value of the digit in the ___ place? The value is ____. expand-expanded one-ones ten-tens Digit, Place value, Number, Numeral, Standard form, Expanded form Here are ALL the place value places you know! That’s a lot! Write what the 9 represents in the numeral: 394,819? a number with a 9 in the hundreds place. Find the digit in the thousands place in the numeral: 284,098 4,000 673 or 600 or 699…lots of right answers! 4 Write a number that has a 2 in the thousands place. Write a number that has a 9 in the tens place. In the number 852,929 what place is the 8 in? In the number 40,751 what is the value of the 7? Circle the 3 numbers that have a 4 in the ten thousands place 1,841 43,181 408,127 64,087 340,167 197,194 10,401 948,054 Standard Form Expanded Word form 7,293 7,000+200+90+3 Seven thousand, two hundred ninety three Use the number 6,529 to complete the below: Standard form Expanded Word form Rounding 3.1 The student will b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and Linguistic Complexity Language Forms and Conventions Vocabulary What would ___ round to? ___ rounds to ___ because ____. round-rounds-rounded-rounding Rounding, Estimation Round 768 to the nearest ten Round 768 to the nearest hundred Round 768 to the nearest thousand 770 800 1,000
Vocabulary Congruent Angles Right Angles Acute Angles Obtuse Angles Supplementary Angles Complementary Angles Vertical Angles Task Descriptions Tasks Task Name Task Type/ Grouping Content Addressed Standards Performance Task Individual/Partner Drawing geometric shapes with given conditions MGSE.7.G.2 **Building Bridges (FAL) Formative Assessment Lesson Partner/Small Group Determining whether triangles can be made with given conditions MGSE.7.G.2
Purchased Resources McGraw-Hill Georgia Math Grade 7 Chapter 8: Lessons 5 McGraw-Hill Georgia Math Grade 7 Plus Chapter 2: Lessons 4 Holt Mathematics Course 1 Text Chapter 8: Geometric Relationships Holt Mathematics Course 2 Text Chapter 8: Geometric Figures Holt Mathematics Course 3 Text Chapter 7: Foundations of Geometry Adopted Online Resources Teacher User ID: ccsde0(enumber) Password: cobbmath1 Student User ID: ccsd(student ID) Password: cobbmath1 General Login: User: georgiamath1 PW: demo123 Suggested Manipulatives Moonsand or Clay or Sand or Water Folding Geometric Solids Geosolids 3D Stamps Dental Floss or Fishing Wire Web Resources Vocabulary Cross Section Task Descriptions Task Name Task Type/ Grouping Content Addressed Standards Learning Task Indiv/Partner/SmGrp Describing/sketching polygons produced MGSE.7.G.3
circumference entire lesson plan area/circum. surface area/volume https://learnzillion.com/lessonsets/452-find-the-area-volume-and-surface-area-of-two-and-three-dimensional-objects Vocabulary Pi Circumference Diameter Radius Task Descriptions Task Name Task Type/ Grouping Content Addressed Standards Brief Description Applying Angle Theorems (FAL) Formative Assessment Lesson Partner/Small Group Angle measurements of polygons MGSE.7.G.4 MGSE.7.G.5 MGSE.7.G.6 Applying Angle Theorems (FAL) Learning Task Indiv/Partner/SmGrp Proving the relationship between
circumference and diameters as the value of pi. Deriving the formula for the circumference of a circle MGSE.7.G.4 Scaffolding Task Indiv/Partner/SmGrp Derive the formula for area of a parallelogram and triangle. MGSE.7.G.6 Learning Task Indiv/Partner/SmGrp Deriving the formula for the area of a circle MGSE.7.G.4 Formative Assessment Lesson Partner/Small Group Solve problems involving angle measure, area, surface area, and volume Scaffolding Task Indiv/Partner/SmGrp Determine volume and surface area of cubes and prisms. MGSE.7.G.6 Scaffolding Task Indiv/Partner/SmGrp Determine volume and surface area of cubes and prisms. MGSE.7.G.6 Scaffolding Task Indiv/Partner/SmGrp Ordering volume and surface area MGSE.7.G.6 Learning Task Group Determine the surface area of a cylinder Extension of MGSE.7.G.6 Three Little Pig Builders (only prisms) Culminating Task Indiv/Partner/SmGrp Solving application problem involving volume and surface area of prism MGSE.7.G.6 Three Little Pig Builders (only prisms)
Find the perimeter of figure ABCDE to the nearest ½ inch. Find the perimeter of figure FGHJ to the nearest centimeter (cm). Identify the vertices of each figure. Identify each polygon. Use the straightedge or the straight line tool to draw segment FH in figure FGHJ. Classify the two resulting triangles according to sides and according to angle measures. Classify each angle in figure ABCDE. Use the straightedge or the straight line tool to draw a line segment from B to point D on figure ABCDE; identify and name the polygons that result after subdividing the figure. Question 3 Use the ruler tool to practice measuring. Find the perimeter of figure ABC to the nearest centimeter (cm). Measure the length of segment NH to the nearest centimeter (cm) and/or millimeter (mm). Identify the vertices of each figure. Name each polygon. Classify each angle in figure ABC and in figure HJKLMN. Name two segments that appear parallel in figure HJKLMN. Use the straightedge or the straight line tool to draw a line segment from point N to point K on figure HJKLMN; identify and name the polygons that result after subdividing the figure. Question 4 Use the ruler to practice measuring. Measure the length of line segment BC to the nearest 1/8 inch. Measure the length of line segment EF to the nearest centimeter (cm). Identify a ray. Identify a line segment. Name an angle. Identify the vertex of each angle.
To square 2 digit numbers ending with ‘5’ eg 75 × 75 1. The answer will end with ‘25’ 2. Take the first digit ‘7’ multiply by the number after ‘7’ => 7 × 8 = 56 75 × 75 = 5625 Test it out with 95 × 95. Did you get 8125? Squaring any number take any number and find out how much to add to get it to the nearest tens subract and add that number to the orignal number multiply add the square example: (999+1) (999-1) + (1^2) (998) (1000) + 1 999^2 + 998001 Squaring a number A math trick I noticed when I was young. If you are squaring a number it is always equal to the total of the number times 2 subtract one of the previous squared number. This is helpful if you dont want to write it out. For instance most people know that 10×10=100 or 11×11=121 even 12×12=144 so let’s say you don’t know 13×13. Its equal to (13×2)-1(plus the previous squared number which was 12×12)144=169 Squaring two digit numbers Suppose AB is the number, Then arrange the number as follows, A*A|2*A*B|B*B ( if A*A or A*B is one digit add 0 prior to that – eg: 4 should be written as 04, 5 should be 05 etc..) Take a number : 35 09|30|25 ( 3*3 | double of 3*5 | 5*5 ) From right to left, keep the right most number as it is and add the number coming both side of | symbol.
Name: McKenzie Chenoweth Period_2_ Occupation name/title How does the occupation fit your skills and interests? What will you be doing in the occupation? What is the necessary education and/or training? Occupation #1 Farmer/Ranch Manager I love to work with large farm animals. In addition, I am interning at a cattle ranch right and am enjoying it a lot. I also can hold my own weight around with the heavy lifting. It is somewhat also I want to own my own ranch be it pig or cattle. Making sure, the ranch goes steady and livestock is up to state regulations. Also Set wages and price of product. At least have a high school diploma and some postsecondary education such as associate's degree or a bachelor degree in agriculture. In addition, they need to have lots of on hand experience outside of school. No training needed if you have both. Occupation #2 Mechanic I find myself wanting to know how they work and how to fix them have taken a small motors Basic cake for vehicle all the way to complicated fixes. Repair and replace parts and talk to customers on options. High school courses in métiers and math. Vocational or other postsecondary education program in automotive service
class and loved it. Working in the grease. technology, also an associate’s degree helps. Little to no training if you have other stuff. Occupation #3 Librarian I love reading and am good at it used to ta for the library at scenic also volunteered at a library in California for 3 years. In addition, I have a mini library at home. Help library patrons conduct research and find the information they need. Teach classes about information resources. Help patrons evaluate search results and reference materials. Organize library materials so they are easy to find, and maintain collections. Plan programs for different audiences, such as storytelling for young children. Develop and Students need a bachelor’s degree in any major to enter MLS programs. Master’s degree in library science. A degree from an American Library Association accredited program may lead to better job opportunities. Typically need a teacher’s certification. No training needed.
Assessment Part 1 Start with the end in mind! Consider here a sample question or performance task students will need to do as evidence of mastery of this objective. Possible misconceptions or learning gaps Complete the above task yourself; think about what might be hardest for students to grasp? Students may believe that fractions have to be less than 1. Students count pieces without concern for whole. STAGE 3: Learning Plan ~ What are the strategies and activities you plan to use? Snapshot / Warm-up Activate knowledge and get students thinking about & motivated for today’s lesson. Give each student a picture fraction card. Students are to walk around and read each other’s card and switch afterwards. Read, Switch and Move. Do this for 1-2 minutes.
Work Stations Workstations where students will: Practice new skills, apply strategies to new materials, and review previously taught skills Differentiate activities based on students’ needs! Workstation #1 Practice representing fractions using dry erase boards. Workstation #2 Complete TEI–like Cards on representing fractions. Workstation #3 Work with a partner to complete Pizza Portions (fraction and mixed number) naming word problems, using the Interactive Notetaking Pages 3.3 a,b. Workstation #4 Computer programs: Fractions Greater Than One Gizmo CONSIDERATIONS AS YOU PLAN WHOLE AND SMALL GROUP INSTRUCTION: Instructional Strategies in term of high yield strategies, such as: Reinforcing effort and providing recognition Nonlinguistic representations Cooperative learning Setting objectives and providing feedback Questions, cues, and advance organizers Differentiation Some ideas include: Flexible grouping Tiered instruction Task cards Checking for Understanding Check throughout the lesson using: Question and Answer Class discussions Group Response Demonstrations Practice sheets Quick Quizzes
Factoring (10 hours) 7.1 An Introduction to Factoring 7.2 “Factoring out” the GCF p.176 1—6 7.3 Differences of squares p.179 1—14 7.4 Quadratic trinomials I. Monic trinomials p.184 1—15 7.5 7.6 Quadratic trinomials II. The ac-method Factoring by grouping p.191 1--10 p.195 1—6 Radicals expressions (8 hours) 8.1 Quadratic equations 8.2 Radical expressions p.209 1—15 8.3 Introduction to complex numbers p.213 1—6 8.4 Arithmetic of radical expressions p.218 1—16 Quadratic Functions (10 hours) 9.1 Solving Quadratic Equations I. p.228 1—11 9.2 Solving quadratic equations II. Completing the square p.234 1—10 9.3 9.4 9.5 9.6 Solving quadratic equations III. The quadratic formula Solving quadratic equations IV. Factoring Summary and applications Quadratic equation in two variables and parabolas p.239 1--10 p.242 1--10 p.248 1--19 p.255 1—6 August 2016 AM
3-4 The student sometimes makes appropriate deductions when solving simple and more-complex problems in familiar contexts. I am able to find the probability of winning the Jackpot and make progress in solving the other questions. 5-6 The student generally makes appropriate deductions when solving challenging problems in a variety of familiar contexts. I am able to find many of the probabilities correctly. I attempt to use the formula to calculate the expected return of the game. 7-8 The student consistently appropriate deductions when solving challenging problems in a variety of contexts including unfamiliar situations. I am able to find most of the probabilities correctly and make only minor errors in the others. I am able to calculate the expected return of the game. Self Assessment Comment: Criterion D – Reflection and Evaluation Level of Achievement Descriptor Indications 0 The student does not reach a standard described by any of the descriptors given below. I do not reach a standard described by any of the descriptors given below. 1-2 The student attempts to explain whether his or her results make sense in the context of the problem. The student attempts to describe the importance of his or her findings in connection to real life. I have tried to illustrate the probabilities of winning using non-mathematical examples. I attempt to analyze the fairness of the lottery using expected return. 3-4 The student correctly but briefly explains whether his or her results make sense in the context of the problem and describes the importance of his or her findings in connection to real life. The student attempts to justify the degree of accuracy of his or her results where appropriate. I have given appropriate examples to illustrate the probabilities of winning. I analyze the fairness of the lottery, with my conclusion being consistent with my findings. 5-6 The student critically explains whether his or her results make sense in the context of the problem and provides a detailed explanation of the importance of his or her findings in connection to real life. The student justifies the degree of accuracy of his or her results where appropriate. The student suggests improvements to the method when necessary. I have given detailed and accurate examples to illustrate the probabilities of winning the lottery. I have used my expected return calculation to analyze the fairness of the game and have given an appropriate suggestion to make it fair. I have given an alternative method of calculating the probability of winning the Jackpot and have explained it clearly. Self Assessment Comment:
Factor a polynomial into linear factors, using complex coefficients when necessary. (3.4) Find vertical, horizontal, and slant asymptotes of rational functions. (3.5) a rational function, showing intercepts and asymptotes. (3.5) State the Fundamental Theorem of Algebra. (3.4) Section Objectives covered in that section - other topics are optional. 3.1 (objectives 1-4) Complete the square to put a quadratic function into standard form. Find the vertex and max/min values of a quadratic function. 3.2 Graph a showing x- and and proper end behavior. Solve Factor a into linear and/or intercepts .
Trigonometric Identities. (i) sin2 + cos2 =1 (ii) 1 + tan2 = sec2 (iii) 1 +cot2 = cosec2 Trigonometric Ratios of some specific angles. 0o 30o 45o 60o 90o sin 0 ½ 1/2 3/2 1 cos 1 3/2 1/2 1/2 0 tan 0 1/3 1 3 Not defined cot Not defined 3 1 1/3 0 sec 1 2/3 2 2 Not defined cosec Not defined 2 2 2/3 1 Trigonometric ratios of complementary angles. sin (90o - ) = cos cos (90o - ) = sin tan (90o - ) = cot cot (90o - ) = tan sec (90o - ) = cosec cosec (90o - ) = sec
7. 8. vertical asymptotes: ; horizontal asymptote: 9. vertical asymptote: ; missing point at 10. 11. 12. 13. (a) $25,646.69 (b) $25,647.32 14. 4.11 years 15. (a) 1161.68 feet (b) 13.29 feet 16. 17. (a) no asymptotes (b) vertical asymptotes at where n is an integer (c) vertical asymptotes at n is an integer (d) no asymptotes (e) horizontal asymptotes: 18. (a) (b) (c) (d) (e) (f) 19. (a) (b) (c) (d) {} 20. (a) 3.9731, 5.4516 (b) 1.1372, 5.1459 (c) 1.7619, 4.9036 21. The answer is in working the problems. 22. (a) B ≈ 46.94°, C ≈ 103.06°, a ≈ 8.21 (b) A ≈ 58.54°, B ≈ 78.62°, C ≈ 42.84°
(c) A ≈ 65.8°, a ≈ 13, b ≈ 13 (d) no triangle (e) B1 ≈ 12.19°, C1 ≈ 145.81°, b1 ≈ 5.636; B2 ≈ 123.81°, C2 ≈ 34.19°, b2 ≈ 22.180 23. ≈ 20.6 square units 24. (a) (b) (c) 25. (a) (b) (c) 26. (a) (b) , etc
11th Grade Level 1 Understanding Priority Cluster Algebra Target D: Interpret the structure of expressions. Level 1 should be able to identify parts of an expression, such as terms, factors, coefficients, exponents, etc. Target E: expressions in equivalent forms to solve problems. Level 1 students should be able to write a quadratic expression with integer coefficients and a leading coefficient of 1 in an equivalent form by factoring of exponents to expand a single variable (coefficient of 1) with a positive integer exponent into an equivalent form and vice versa, e.g. x3=xxx. Target F: Perform arithmetic operations on polynomials. 1 students should be able to add, subtract and multiply polynomials of degree 2 or less. Target G: Create equations that describe numbers or relationships. Level 1 students should be able to create and use one-step linear equations in one variable to model a familiar situation and to solve a familiar problem. Target H: Understand solving equations as a process of reasoning and explain the reasoning. Level 1 students should be able to explain solution steps for solving one-step linear equations in one variable. Target I: equations and inequalities in one variable. Level 1 students should be able to solve one-step linear equations in one variable. Target J: Represent and solve equations and inequalities graphically. Level 1 students should be able to represent a linear equation with an integer-valued slope in two variables graphically on a coordinate plane. Functions Target K: Understand the concept of a function and use function notations. Level 1 students should be able to distinguish between functions and nonfunctions. They should be able to state the domain and range given a graph.
Course End Competencies By the completion of the course, the student should be able to: Integrate the necessary algebraic skills with the theory of calculus to arrive at the appropriate conclusion. Integrate the necessary and relevant graphing and computer skills with the theory of calculus to arrive at the appropriate conclusion. Expand differentiation and integration techniques to include more complex functions, and use technology effectively as an aid in problem solving. Apply differentiation and integration techniques to models of real-life situations in order to arrive at the appropriate conclusion. Understand and be able to use the Infinite Series as a tool in math and science applications. Analyze and verify algebraic results through the use of graphing calculators and/or computers. Classroom Policies/ Procedures A student who does not officially withdraw from the course may receive a of “F” for the course grade. ATTENDANCE IS REQUIRED. Attendance will be taken daily. If you must miss a class, it is your responsibility to find out what you missed that day on your own time not during class. See Quizzes and Tests below for makeup policy. If a student does not demonstrate active pursuit of completion of course objectives (demonstrated by attending regularly and on time, taking tests, quizzes, and submitting homework), that student may be reported to the administration of the college as non-pursuing. Tardiness: Keep in mind that quizzes may be given at the start of the class period. If a quiz or test is in progress when a student comes in late, that student will not be given extra time to work on the quiz or test. If a student arrives after a quiz has ended the student has missed the quiz and will not be allowed to take it. If a student arrives late during a test or quiz after another student has finished and turned in his test or quiz and left the room, the late student will not be allowed to take the test or quiz and will receive a zero score. No one is allowed to leave the room during a test or quiz without permission from the instructor. No electronic devices are allowed on or near the desk during a test or quiz except those calculators approved by the instructor. Keep Cell Phones Off and Out Of While In Class. No phone use allowed during class.