zilongwang/ReadingBank huggingface dataset:
Second Grade Geometry Section 1: 2-Dimensional Shapes Table of Contents Suggested Number of Days Page No. 2-D Geometry Part 1 Polygons and Their Attributes Polygon Sort Cards Pentagon Recording Sheet 6 to 12-sided Polygons Recording Sheets Identifying Polygons Guided Practice Problems Part 2 Quadrilaterals Labels Part 3 Decomposing and Composing 2-D Shapes Guided Practice Problems Part 4 Additional 2-D Resources 3 days (11/30 – 12/2) 1 day (11/3) 1 day (11/4) 1 4 16 17 21 27 30 33 34 39 46
On the board, write down students’ thoughts on the rules you are using to sort the shapes. Be sure to have the students use the word attribute when discussing their “rules.” For example, “One attribute of a polygon is straight sides.” After the shapes are sorted and the rules have been determined, trade the label “B” for “Polygons.” Replace label “A” with “Non-Polygons.” Take each shape from the “Non-Polygon” circle and discuss what attribute keeps it from being a polygon. IMN Activities: Discuss and complete the definition of a polygon. A polygon is a ______-dimensional shape with _____ or more ________________ sides and it is a _______________ shape. This document can be found in MATH_2_A_5 2D POLYGON IMN 2015_RES. Display cards used for the polygon sort for students to use when completeing the following activity: Draw a polygon that wasn’t on the cards. Explain what attributes make it a polygon. This document can be found in MATH_2_A_5 2D POLYGON IMN 2015_RES.
3. Shape Construction (Play-Doh and straws) To provide students with an opportunity to examine the attributes of a regular and irregular polygon, they will construct one using Play-Doh and coffee stirrers or straws. Materials needed: Play-Doh balls and coffee stirrers or straws (Suggestion: Have one baggie with the same length and one baggie with different lengths.) pictures of 2-D shapes pentagon recording sheet recording sheets labeled 6 ‒ 12 sided polygons Display pictures of 2-D shapes. Explain to students that we call these shapes two-dimensional or 2-D shapes because they have no thickness — they are flat. The only two dimensions you can measure are the height and width. A. Show the students how to make a pentagon. They should use stirrers/straws of the same length for all sides. Take one straw and put one Play-Doh ball on each end. Take a side and attach it to a vertex. Take more stirrers/straws and Play-Doh balls to create a regular pentagon. B. Ask the following questions: How many stirrers/straws did we use for the pentagon? 5
Objective 4 3 2 1 Uses manipulatives to demonstrate the process of 3-Digit Addition and Subtraction with and without regrouping The student is able to manipulate the blocks correctly without teacher help. The student is able to manipulate the blocks with only a few mistakes, but is able to self-correct when they are pointed out. The student is able to manipulate the blocks with mistakes and needs help to correct the mistakes. The student is not able to manipulate the blocks correctly without teacher assistance.
Second Grade Length Section 1 Table of Contents Content Suggested Number of Days Page No. Part 1: Metric Length– Centimeter and Meter Picture vs. Real Life Finding Length Using Concrete Models Deciding on the Best Unit of Measurement Inverse Relationship Between the Size of the Unit and the Number of Units Needed Measuring with a Centimeter Ruler Measuring and Comparing Lengths Using Centimeters Scavenger Hunt Measuring with a Meter Stick Measuring and Comparing Lengths Using Meters Guided Practice Problem #1 Part 2: Customary Length – Inch, Foot, and Yard Inch Measuring and Comparing Lengths Using Inches Foot Yard Determining the Best Unit of Measure Guided Practice Problem #2 Mixed Practice 4 days ½ day (2/6) ½ day (2/6) ½ day (2/9) ½ day (2/9) ½ day (2/10) ½ day (2/10) ½ day (2/11) ½ day (2/11) 5 days 1 day (2/12) ½ day (2/13) 1 day (2/13 - 2/17) ½ day (2/17) 1 day (2/18) 1 day (2/19) 2 2 3 4 6 8 10 11 13 13 17 18 18 20 20 25 26 27 26 Additional Resources: “Gingerbread Man Attributes” PowerPoint (_2_A_LENGTH GINGERBREAD 2014_) “My Long, Tall, High, and Wide Book” (_2_A_LENGTH MEASURING ATTRIBUTES 2014_) About a Meter or About a Centimeter? (_2_A_LENGTH METRIC SORTING CARDS 2014_), “Let’s Build a House for Mouse” (MATH_2_H_LENGTH 2014_ENR)
Second Grade Place Value to 1,200 Section 4: Number Lines Table of Contents Topic Suggested Number of Days Page No. Part 1 Number Lines Increments of One Hundreds Chart Increments of One – Number Lines for Partner Practice Increments of Ten Increments of Ten – Number Lines for Partner Practice Increments of One Hundred Increments of Tens or Hundreds – Number Lines for Partner Practice Part 2 Open Number Lines Locating 2-Digit Numbers on an Open Number Line Partner Practice 1A Partner Practice 1B Locating 3-Digit Numbers on an Open Number Line Partner Practice 2 Locating 4-Digit Numbers on an Open Number Line 2 days (9/17 ‒ 9/18) 3 days (9/21 – 9/23) 1 2 6 7 8 11 12 14 15 15 18 19 20 22 23
Tuesday Richard made the largest 3-digit number he could with the cards below. He used each card only once. What number did he make? A. 793 B. 973 C. 273 D. 972 Find the difference between sixty-five and thirteen. Find the sum of ninety-nine and seven. What two names can we call these shapes? A. quadrilateral and pentagon B. polygon or hexagon C. polygon or triangle D. polygon or pentagon Find the differences.
Second Grade • Daily Math • Week 30 Name: ___________________ Monday Mom cut cupcakes in half and put them on the table. Write 2 ways to show how many cupcakes are shown below. ______wholes and ___________ What is one way this time can be written? 30 minutes past 7 30 minutes after 6 25 minutes until 6 25 minutes before 7 Betty Butterfly likes numbers greater than 10. Solve each problem. Write the sums on the flowers. If the sum is greater than 10, color the flower.
Wednesday The carnival had 300 cookies to sell. 155 of the cookies were chocolate chip, and the rest of them were peanut butter. How many cookies were peanut butter? 255 245 455 145 Carl Caterpillar likes numbers less than 5. Solve each problem. Write the differences on the leaves. If the difference is less than 5, color the leaf. What is the difference in the area of Room A and Room B?
Instructional Resources Tasks Additional Resources (Illustrative Mathematics) Back to: Geometry NC Math 1 NC Math 2 NC Math 3 Analytic & Euclidean Focus on coordinate geometry Distance on the coordinate plane Midpoint of line segments Slopes of parallel and perpendicular lines Prove geometric theorems algebraically Focus on triangles Congruence Similarity Right triangle trigonometry Special right triangles Focus on circles and continuing the work with triangles Introduce the concept of radian Angles and segments in circles Centers of triangles Parallelograms A Progression of Learning Integration of Algebra and Geometry Building off of what students know from 5th – 8th grade with work in the coordinate plane, the Pythagorean theorem and functions. Students will integrate the work of algebra and functions to prove geometric theorems algebraically. Algebraic reasoning as a means of proof will help students to build a foundation to prepare them for further work with geometric proofs. Geometric proof and SMP3 An extension of transformational geometry concepts, lines, angles, and triangles from 7th and 8th grade mathematics. Connecting proportional reasoning from 7th grade to work with right triangle trigonometry. Students should use geometric reasoning to prove theorems related to lines, angles, and triangles. Geometric Modeling Connecting analytic geometry, algebra, functions, and geometric measurement to modeling. Building from the study of triangles in Math 2, students will verify the properties of the centers of triangles and parallelograms.
Math 2 Regular Instructional Scope at a Glance Unit 1 - The Number System 5 Weeks Module 1 - Adding and Subtracting Integers Lesson 1.1 - Adding Integers with the Same Sign (MAFS.7.NS.1.1) Lesson 1.2 - Adding Integers with Different Signs (MAFS.7.NS.1.1) Lesson 1.3 - Subtracting Integers (MAFS.7.NS.1.1c) Lesson 1.4 - Applying Addition and Subtraction of Integers (MAFS.7.NS.1.3) Module 2 - Multiplying and Dividing Integers Lesson 2.1 - Multiplying Integers (MAFS.7.NS.1.2) Lesson 2.2 - Dividing Integers (MAFS.7.NS.1.2) Lesson 2.3 - Applying Integer Operations (MAFS.7.NS.1.3) Module 3 - Rational Numbers Lesson 3.1 - Rational Numbers and Decimals (MAFS.7.NS.1.2d) Lesson 3.2 - Adding Rational Numbers (MAFS.7.NS.1.1d) Lesson 3.3 - Subtracting Rational Numbers (MAFS.7.NS.1.1c) Lesson 3.4 - Multiplying Rational Numbers (MAFS.7.NS.1.2) Lesson 3.5 - Dividing Rational Numbers (MAFS.7.NS.1.2) Lesson 3.6 - Applying Rational Number Operations (MAFS.7.EE.2.3) Unit 2 - Ratios and Proportional Relationships 3 Weeks Module 4 - Rates and Proportionality Lesson 4.1 - Rates (MAFS.7.RP.1.1) Lesson 4.2 - Constant Rates of Change (MAFS.7.RP.1.2) Lesson 4.3 - Proportional Relationships and Graphs (MAFS.7.RP.1.2a)
The next part of a video game models a biker jumping off a ramp at a motocross event. The biker’s path can be modeled by the relation , where h is the biker’s height above the ground and d is the biker’s horizontal distance from the end of the ramp, both in meters. What is the biker’s initial height above the ground (when d = 0)? (2) What is the vertex of the parabola? What information do the coordinates of the vertex give about the biker’s position? (4) Sketch a graph of the biker’s path. (2) A basketball was thrown upward. The basketball’s path is given by the relation , where h is the basketball’s height above the ground and d is the basketball’s horizontal distance from where it was thrown, both in meters. What was the basketball’s initial height above the ground? (2) What was the basketball’s greatest height above the ground? What was the basketball’s horizontal distance at this point? (2) The basketball was thrown toward a net 6 m away and 3 m above the ground. Will the basketball go through the net? Justify your answer. (3)
Rectangle Square Parallelogram Rhombus Trapezoid Attributes: 2 sets(pairs) of parallel lines 4 right angles Opposite sides congruent (same) 4 sides polygon Attributes: 2 sets(pairs) of parallel lines 4 right angles All sides congruent (same) 4 sides polygon Attributes: 2 sets(pairs) of parallel lines 4 angles Opposite sides congruent (same) 4 sides polygon Attributes: 2 sets(pairs) of parallel lines 4 angles All sides congruent (same) 4 sides polygon Attributes: 1 set(pair) of parallel lines 4 angles 4 sides polygon
Triangle Pentagon Hexagon Octagon Attributes: A polygon with _____ sides and _____ angles. Attributes: A polygon with _____ sides and _____ angles. Attributes: A polygon with _____ sides and _____ angles. Attributes: A polygon with _____ sides and _____ angles. Attributes: A polygon with _____ sides and _____ angles. *Draw 1 irregular shape for each column
Triangle Pentagon Hexagon Octagon Attributes: A polygon with __3__ sides and __3__ angles. Attributes: A polygon with __4__ sides and __4__ angles. Attributes: A polygon with __5__ sides and __5__ angles. Attributes: A polygon with __6__ sides and __6__ angles. Attributes: A polygon with __8__ sides and __8__ angles. *Draw 1 irregular shape for each column
Oh, So Many Ways… Algorithm Set - Up Relating to Base-Ten Relating to Place Value Relating to Properties Relating to Number Lines Relating to Relationships Oh, So Many Ways… Algorithm Set - Up Relating to Base-Ten Relating to Place Value Relating to Properties Relating to Number Lines Relating to Relationships Oh, So Many Ways… Algorithm Set - Up Relating to Base-Ten Relating to Place Value Relating to Properties Relating to Number Lines Relating to Relationships
My Work Monday Tuesday Wednesday Thursday My Progress MONDAY # of questions _____ # correct _____ I need more help with… ______________ _____________________ _____________________ TUESDAY # of questions _____ # correct _____ I need more help with… ______________ _____________________ _____________________ WEDNESDAY # of questions _____ # correct _____ I need more help with… ______________ _____________________ _____________________ THURSDAY # of questions _____ # correct _____ I need more help with… ______________ _____________________ _____________________
Inquiry Questions (Engaging- Debatable): How are the models of rational and radical equations related? Can the graphs of rational and radical functions be transformed in the same way as quadratic and linear functions? Unit Strands Number and Quantity: The Real Number System Algebra: Reasoning with Equations and Inequalities Algebra: Arithmetic and Polynomials and Rational Expressions Concepts properties of operations, rational expressions, rational equations, radical equations, properties of integer exponents, properties of rational exponents Generalizations My students will Understand that… Guiding Questions Factual Conceptual Properties of operations transform rational expressions with the intention of creating more efficient forms of the expression. (MA10-GR.HS-S.2-GLE.3-EO.g) How can inspection, long division and computer algebra systems be used to rewrite rational expressions? How do you use factoring to rewrite a rational expression? Why do we rewrite rational expressions in different forms? Why can computers solve problems that humans cannot? (MA10-GR.HS-S.2-GLE.4-IQ.3) Solving rational and radical equations can result in extraneous solutions. (MA10-GR.HS-S.2-GLE.4-EO.b.ii) How do you check for extraneous solutions? When do extraneous solutions arise? How can you determine if a solution is not viable? Why do extraneous solutions occur? The properties of integer exponents extend to rational exponents. MA10-GR.HS-S.1-GLE.1-EO.a) What are the properties of exponents? What is the relationship between rational exponents and radicals? How can properties of exponents be used to transform rational expressions into radical expressions or vice versa? How are radical expressions simplified? Why do we need both radicals and rational exponents? Key Knowledge and Skills: My students will… What students will know and be able to do are so closely linked in the concept-based discipline of mathematics. Therefore, in the mathematics samples what students should know and do are combined.
Focusing Lens(es) Modeling Standards and Grade Level Expectations Addressed in this Unit MA10-GR.HS-S.1-GLE.2 MA10-GR.HS-S.2-GLE.2 MA10-GR.HS-S.2-GLE.3 MA10-GR.HS-S.2-GLE.4 Inquiry Questions (Engaging- Debatable): What are the parameters that affect gas mileage in a car and how would you model them? (MA10-GR.HS-S.2-GLE.2-EO.b.i) What are the consequences of a population that grows exponentially? Unit Strands Algebra: Reasoning with Equations and Inequalities Algebra: Creating Equations Algebra: Seeing Structure in Expressions Functions: Interpreting Functions Functions: Linear and Exponential Models Concepts Models, quantity, growth, decay, constant rate of change, constant rate of growth, functions, linear functions, exponential functions, exponentially, linearly, quadratically, polynomial function, arithmetic sequence, geometric sequence, relationships, tables, graphs, equations, parameters, equations, inequalities, real world contexts Generalizations My students will Understand that… Guiding Questions Factual Conceptual Linear and exponential functions provide the means to model constant rates of change and constant rates of growth, respectively (MA10-GR.HS-S.2-GLE.2-EO.a) How do you determine from an equation whether an exponential function models growth or decay? How do you determine whether a situation can be modeled by a linear function, an exponential function, or neither? What are typical situations modeled by linear functions? What are typical situations modeled by exponential functions? Why are differences between linear and exponential functions visible in equations, tables and graphs? Why does a common difference indicate a linear function and common ratio an exponential function? A quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. How does the rate of growth in linear and exponential functions differ? How can you determine when an exponential function will exceed a linear function? Why can so many situations be modeled by exponential growth? Why is important to consider the limitations of an exponential model?
Stated assumptions, definitions, and previously established results help in the construction of proofs. (MA10-GR.HS-S.4-GLE.1-EO.c) How are assumptions and definitions used in proof? How can you prove relationships between angles formed when transversal intersects parallel lines? How do previously proved ideas about parallel lines support conjectures and proofs about triangles and parallelograms? Why are proofs an integral part of geometry? How does writing a proof deepen your understanding of geometric concepts? The coordinate plane models algebraically geometric relationships. What information is needed to calculate the perimeters of polygons and area of triangles and rectangles in the coordinate plane? How can you determine the slope of line parallel or perpendicular to a given line? Why is it helpful to model geometric relationships on the coordinate plane? Geometric transformations create functions that take points in the plane as inputs and give unique corresponding points as outputs. What function operations work with transformations? How can you compare transformations? Why are transformations functions? Rigid transformations preserve distance and angle. (MA10-GR.HS-S.4-GLE.1-EO.a) What do non-rigid transformations preserve? How can I use transformations to prove to figures are congruent? Why is it important that rigid transformations preserve distance and angle? Key Knowledge and Skills: My students will… What students will know and be able to do are so closely linked in the concept-based discipline of mathematics. Therefore, in the mathematics samples what students should know and do are combined.
5.7f MATHEMATICS-SPECIFIC TECHNOLOGIES Apply mathematical content and pedagogical knowledge to select and use instructional tools and make sound decisions about when such tools enhance teaching and learning, recognizing both the insights to be gained and possible limitations of such tools. NCTM 4e 5.8a Verify that secondary students demonstrate conceptual understanding. NCTM 5a 5.8b Verify that secondary students demonstrate procedural fluency. NCTM 5a 5.8c Verify that secondary students demonstrate the ability to formulate, represent, and solve problems. NCTM 5a 5.8d Verify that secondary students demonstrate logical reasoning and continuous reflection on that reasoning. NCTM 5a 5.8e Verify that secondary students demonstrate productive disposition towards mathematics. NCTM 5a 5.8f Verify that secondary students demonstrate the application of mathematics in a variety of contexts within major mathematical domains. NCTM 5a 5.9 Collect, organize, analyze, and reflect on diagnostic, formative, and summative assessment evidence and determine the extent to which students’ mathematical proficiencies have increased as a result of their instruction. NCTM 5c 5.10 Take an active role in their professional growth by participating in professional development experiences that directly relate to the learning and teaching of mathematics. (In ways other than membership in organizations.) NCTM 6a 5.11 Utilize resources from professional mathematics education organizations such as print, digital, and virtual resources/collections. NCTM 6c 5.12 Develop knowledge, skills, and professional behaviors across middle or high school settings; examine the nature of mathematics, how mathematics should be taught, and how students learn mathematics; and observe and analyze a of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment, and assessment. NCTM 7c 5.13 TC plans for the learner use of current and emerging digital tools and other mathematics specific technologies to support 21st century learning. NCTM 4e
procedures): Ask the girls how many money they bring to the school. Introduce the lesson by a power point of the grade two restaurants. Starting a lesson to counting by dirhams. Show them how to order the DH from biggest to smallest. Chose some student to answer in the board. Making our own menu. my instruction: Give each student colourful Starting with me in each steps They will write the food name with prices drew and colour the food. After I finished the list of the menu I will go around the class to help them Put some song when they work. If they need colours or pencil just hand up. This activity take for 6 to 8 min (“Encourages students to draw on their everyday and academic knowledge and skills, including language, and share them collectively and the importance of creating a connection between the academic and the everyday. (Gutstein, Lipman, Hernandez, & de los Reyes, 1997). From that the teacher link it her lesson by our life because the student know the answer of daily life and when they going to shop to buy some things they know how to counting and its good to add the money.also the student like to have a created lesson which mean like the environment of teaching will be like the same of our life to using their imagination and play the role in really. money their bring it to school to eat in the canteen and they will answer me. After that I will start t lesson by showing the girls there restaurants and some food with prices and dh. Also, I make some questions that include the lesson the first two I will explain to them after that I will chose some student to explain whole class to see if they understanding the way of answering.so, I will give them an activity to used it in next class and to see if they understand the lesson. The students will be active to do the activity because like to learn by doing. min Close (wrap up, discussion, brief review activity or assessment): Ask students to open their booklets to solve the question to see if they understanding and I will walk around them to check there are understandings. ( in that way the teacher know if the student or not by they answering all the questions corrects with few mistakes also its show how they learn by what they know and sympathetic of teacher strategy of created in the class and student improve their skills. -Students will open their booklet and start to solve money question. 10 min
Materials: 10 connecting cubes, Workbook Materials: ordinal number flash cards, smart board lesson Materials: cubes and rods, tens and ones smart board lesson Guided Practice (SW) SW verbally repeat vocabulary word and use fingers to represent the ordinal number. SW form a line based on their number card. SW arrange themselves in order. SW complete workbook pages. Guided Practice (SW) SW repeat vocabulary words. SW listen to song. SW stand in a row facing the class. SW identify where each person is in the row. SW identify ordinal numbers and match to the number word. Guided Practice (SW) SW verbally identify numbers in ones and tens place using divided number chart. SW use rods and ones cubes to represent numbers. Guided Practice (SW) SW identify both numbers in ones and tens place. SW identify total number of cubes in ones place. Repeat using tens rods. Guided Practice (SW) SW participate in skill review. SW complete assessment.
Closure : TW review ordinal vocabulary. Closure: TW review ordinal vocabulary. Closure: TW review ones and tens place. Closure: TW review double digit addition. Closure: Independent: SW identify ordinal numbers by drawing a picture and labeling first, second, third, fourth, fifth. Math Centers Independent: SW identify ordinal numbers by adding to their drawing from yesterday to show sixth, seventh, eighth, ninth, and tenth. Math Centers Independent: SW complete place value sheet. Math Centers Independent: SW complete exit ticket. Math Centers Independent: SW complete math assessment. Math Centers
5. Self-Awareness Gain awareness of identity, character, and vocational calling 4.4 Intrapersonal Awareness: Gaining an awareness of options for employment, voluntary service, and/or graduate education in one’s specialized area of study Graduates will gain an awareness of options for employment, voluntary service and/or graduate education in mathematics or closely related fields. MATH 195, 494 Students will complete assignments in both MATH 195 and MATH 494 related to vocational and educational options in mathematics and mathematics education. Once every 5 years, the department will randomly select 5 graduates of the MATH/MATT major and analyze the quality of these assignments longitudinally, looking for evidence of gained awareness, according to a rubric written by the department. Among the 5 samples of student work selected, 4 or 5 will show evidence of at least satisfactory growth in understanding and awareness. Every 5 years 3. Faith knowledge & application Develop informed and mature convictions about Christian faith and practice 4.5 Faith knowledge & application: Articulating how faith connects to one’s specialized area of study and to potential career options in that area of study Graduates will articulate a maturing understanding of how faith connects to mathematics and how the biblical call to vocation relates to potential career options in mathematical sciences. MATH 195, 494 (Same measure as above row; likely the same assignments) (See above) Every 5 years 4.3 Specialized skills Become proficient in the scholarship of their discipline and demonstrate specialized skills needed to pursue a career and/or 4.3 Specialized skills: Developing proficiency in one’s specialized area of study sufficient to pursue a career and/or continue education at the Graduates will demonstrate sufficient skills to use technology to enhance understanding and simplify computation and to present work professionally with technology. MATH 111, 112, 211, 308, 341, 382, STAT 291, 324, 325, 326, PHYS 211/212 Samples of student work in courses using different technologies In each measurement cycle, samples of both basic and advanced use of at least three technological tools will be identified, representing work from at least four different courses.
Principle 10 Candidates foster relationships with school colleagues, parents and agencies in the larger community to support students’ learning and well being. entries were included in portfolio and does not clearly explain how they relate to this INTASC standard were included but fails to clearly explain how they relate to this INTASC standard samples have been included in the portfolio and how they relate this INTASC standard samples have been included in the portfolio, describes how they relate to this INTASC standard, and elaborates on how they best exemplify an aspect of good teaching Standards USA- INTASC: Principles from the Model Standards for Beginning Teacher Licensing and Development (1992) Principle: 10: The teacher fosters relationships with school colleagues, parents, and agencies in the larger community to support students’ learning and well-being.
Side B Length = Width = Area side B = Side C Length = Width = Area side C = Side D Length = Width = Area side D = Side E Length = Width = Area side E = Side F Length = Width = Area side F = Total surface area = Card board box factory worksheet – Answer key Directions: Use the following table to record the results from the previous page. Net #1 Side A Length = 2 ft. Width = 2 ft. Area side A = 4 ft.2 Side B Length = 7 ft. Width = 2 ft. Area side B = 14 ft.2 Side C Length = 2 ft. Width = 2 ft. Area side C = 4 ft.2 Side D Length = 7 ft. Width = 3 ft. Area side D = 21 ft.2 Side E Length = 7 ft. Width = 2 ft. Area side E = 14 ft.2 Side F Length = 7 ft. Width = 3 ft. Area side F = 21 ft.2 Total surface area = 78ft.2 Net #2 Side A Length = 6 ft. Width = 3 ft. Area side A = 18 ft.2 Side B Length = 3 ft. Width = 4 ft. Area side B = 12 ft.2 Side C Length = 6 ft. Width = 4 ft. Area side C = 24 ft.2 Side D Length = 3 ft. Width = 4 ft. Area side D = 12 ft.2 Side E Length = 6 ft. Width = 3 ft. Area side E = 18 ft.2 Side F Length = 6 ft. Width = 4 ft. Area side F = 24 ft.2 Total surface area = 108 ft.2
Service Rep Outcome #12 Writing mathematical expressions and equations A mathematical expression uses math symbols instead of words. Examples: 9 + n means “the sum of nine and the number n”. N – 12 means “a number n decreased by twelve.” 7 x n and 7n both mean “seven times the number n.” n/6 and n ÷ 6 both mean “a number n divided by six.” Underline the correct mathematical expression. The sum of 13 and 26 2) Nine added to negative 5 13 x 26 9 + -5 13 + 26 9 + 5 3) Seven decreased by a number z 4) Ten less than a number x 7 – z x – 10 Z – 7 10 – x Five times the sum of a number x 6) Eight less than the result of and a number d dividing a number a by b 5x ÷ d a/b – 8 5 x (x ÷ d) a – 8 B Write as mathematical expressions. a number x decreased by eleven the product of 12 and a number g a number t decreased by a number j the product of ten and a number v, divided by 4
Name: Weekly Math Homework - 2 Teacher: Monday Tuesday Wednesday Thursday Use >, <, or = to solve the inequality below. 5.7 _____5.77 Find the FACTORS of 48. Use >, <, or = to solve the inequality below. ____ Find the first five MULTIPLES of 7. Find the product. 2,736 x 57 Find the quotient. ______ 4 ) 6,476 Find the product. 37 x 2.1 Find the quotient. 4.026 ÷ 0.6 There are 8 students in a group. There is ¾ of a cake. How much of the cake will each student get if it is split evenly between the students? Find the quotient. ÷ = Melissa is making clothes for her dolls. She has 7/8 of a yard of fabric. Each doll shirt requires 2/7 of a yard of fabric. How many shirts can she make for her dolls? Find the quotient. ÷ = When adding or subtracting two decimals, what is the first thing you must do? Find the product. 78.01 x 0.4 Find the sum. 54,394 + 13,768 Find the product. 23.7 x 2.03 When multiplying decimals, how do you determine where to place the decimal in the answer? Find the quotient. 7.868 ÷ 1.4 Find the difference. 857,288 – 38,927 Find the quotient. 43.622 ÷ 0.02
My Work Monday Tuesday Wednesday Thursday My Progress MONDAY # of questions _____ # correct _____ I need more help with… ______________ _____________________ _____________________ TUESDAY # of questions _____ # correct _____ I need more help with… ______________ _____________________ _____________________ WEDNESDAY # of questions _____ # correct _____ I need more help with… ______________ _____________________ _____________________ THURSDAY # of questions _____ # correct _____ I need more help with… ______________ _____________________ _____________________
Beth has 401 blue blocks. When she mixes them with some red blocks, Write down the expression of that condition! 401 + R There are 826 blocks in all. How many red blocks Beth has? 401 + R = 826 R = 826-401 = 425 Jing bought a box of crackers. He ate 6 of them. Write down the expression of that condition! J - 6 Jing had 10 left. How many crackers were in the box? J - 6 = 10 J = 10 + 6 = 16 Jane picked some oranges and divided them evenly into 55 bags. Write down the expression of that condition! J : 55 Each bag had 12 oranges. How many oranges Jane picked? J : 55 = 12 J = 12 X 55 = 660 Johnny has G gumballs. Anna has 67 fewer gumballs than Johnny. Write down the expression of that condition! G - 67 If G is 100. Find out how many gumballs Anna had! 100 - 67 = 33 Isaac has R red peppers and 68 green peppers. Write down the expression of that condition! R + 68 How many peppers in total does Isaac has if R is 32? 32 + 68 = 100 Jason received 68 dollars for his birthday. He went to a sporting goods store and bought some baseball gear. Write down the expression of that condition! 68 - G Jason had 31 dollars left over, How much did he spent on the baseball gear ? 68 - G = 31 G = 68 - 31 = 37 Sara had 35 peaches left at her roadside fruit stand. She went to the orchard and picked more peaches to stock up the stand. Write down the expression of that condition! 35 + P There are now 65 peaches at the stand, how many did she pick ? 35 + P = 65 P = 65 – 30 = 35
XXXX Related Work or Minor 3 31 Credit Hours for Year Senior Year Course Number Course Title Credit Hours General Education W/O Course Notes Fall Semester MATH 4051 Computer Exploration and Generation of Data 3 X O OPRS 4113 Game Theory 3 MATH 3XXX Upper-Level Math Elective 3 Must be MATH, STAT, or OPRS 3000-level or above XXXX Related Work or Minor 3 XXXX Elective 3 Spring Semester MATH 2164 Linear Algebra 3 OPRS 4114 Dynamic Programming 3 XXXX Related Work or Minor 3 XXXX Elective 3 27 Credit Hours for Year
perspectives. perspectives but didn’t discuss them. global perspectives. Limitations and Expectations 0 Student did not discuss possible limitations and/or extensions. 1 Student indicated possible limitations and/or extensions but did not explain them. 2 Student discussed possible limitations and/or extensions. Conclusion 0 Student did not have a conclusion related to their aim and rationale. 1 Conclusion somewhat relates to aim or rationale. 2 Conclusion directly relates to aim and rationale. Bibliography 0 Student did not have a complete bibliography and sources cited. 2 Student has complete bibliography and all sources cited. Level of Math 0 Math was not used OR math used was not at an appropriate level OR student was not able to explain why they chose the math concepts represented in their drafts. 1 Level of math is appropriate but student was not able to explain the reason for using the concepts selected. 2 Level of math was appropriate and student was able to explain the reason for using the concepts selected. Personal Engagement 0 Student did not show any personal engagement in their draft. 1 Student showed some personal engagement in the draft – it is limited and superficial. 2 Student demonstrated genuine personal engagement in the topic.
(NC) state k when A-1 exists. Solve using matrices b) _______________________ Answers: a) -2 b) 26 a) x = 8, y = 1 b) x = 1, y = -2, z = -2 Topic 5—Vectors (NC) A = (2,3) and B = (5,7). Find magnitude of Calculate the distance between the points (2, 0, 3) and (1, 6, 4). (NC) Find the unit vector in the direction of _______________________ Answers: a) b) 6.16 (NC) Consider the vectors and . Calculate the scalar product. (NC) Find k so that vectors and are parallel
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Fifth Grade Curriculum Equations and Expressions Table of Contents Topic Page Balancing Equations Balancing Expressions Part I Example 1 Example 2 Example 3 Example 4 Example 5 Balancing Expressions – Balance Me Writing Equations with a Variable 1 – 2 3 – 4 4 – 5 6 – 7 7 – 8 9 10 - 11
Ex: Subtraction start unknown Ex: Part-part-whole whole unknown Ex: Part-part-whole part unknown Ex: Comparison difference unknown Ex: Comparison larger part unknown Ex: Comparison smaller part unknown Note(s): Grade Level(s): Kindergarten explained the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number sentences. Grade 2 will add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations. Various mathematical process standards will be applied to this student expectation as appropriate. TxRCFP: Solving problems involving addition and subtraction TxCCRS: I. Numeric Reasoning II.D. Algebraic Reasoning – Representations VIII. Problem Solving and Reasoning IX. Communication and Representation X. Connections Generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20. Generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20. Generate, Solve PROBLEM SITUATIONS WHEN GIVEN A NUMBER SENTENCE INVOLVING ADDITION OR SUBTRACTION OF NUMBERS WITHIN 20 Including, but not limited to:
Ex: Commutative property Sum does not change when the order of the addends are switched. Ex: Plus 0 (additive identity) Adding zero to a number does not affect the total. Ex: 1 + 0 = 1; 2 + 0 = 2; 3 + 0 = 3; etc. Ex: 1 = 1 + 0; 2 = 2 + 0; 3 = 3 + 0; etc. Plus 1 Adding 1 related to sequential counting Ex: 9 + 1 = 10 or 10 = 9 + 1 Counting on Begin with one addend and count on the amount of the other addend. Ex: Recall With Automaticity BASIC FACTS TO SUBTRACT WITHIN 20 Including, but not limited to: Whole numbers Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n} Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n} Automaticity – executing a basic fact with little or no conscious effort Subtraction Difference – the remaining amount after the subtrahend has been subtracted from the minuend Minuend – a number from which another number will be subtracted Subtrahend – a number to be subtracted from a minuend Subtraction of whole numbers within 20 Solutions recorded with a number sentence Number sentence – a mathematical statement composed of numbers, and/or an unknown(s), and/or an operator(s), and an equality or inequality symbol Equal sign at beginning or end Ex: 6 = 10 – 4; 10 – 4 = 6 Decompose numbers – to break a number into parts or smaller values Basic fact subtraction strategies leading to automaticity
Minuend – a number from which another number will be subtracted Subtrahend – a number to be subtracted from a minuend Subtraction of whole numbers within 1,000 With or without regrouping Term – a number and/or an unknown in an expression separated by an operation symbol(s) Expression – a mathematical phrase, with no equal sign, that may contain a number(s), an unknown(s), and/or an operator(s) Number sentence – a mathematical statement composed of numbers, and/or an unknown(s), and/or an operator(s), and an equality or inequality symbol Number sentences, or equations, with an equal sign at the beginning or end Ex: 10 = 6 + 4; 6 + 4 = 10 Ex: 6 = 10 – 4; 10 – 4 = 6 Represent mathematical and real-world problem situations Concrete models Objects represent the quantities described in the problem situation. Base-10 blocks, place value disks, etc. Pictorial models Pictures drawn represent the quantities described in the problem situation. Base-10 pictorials, number lines, strip diagrams, etc. Numbers Numbers represent the quantities described in the problem situation. Oral and written descriptions Explanation of relationship between objects, pictorials, and numbers and the information in the problem situation Solve mathematical and real-world problem situations with the result unknown. One-step problems Connection between information in the problem and problem type Addition result unknown a + b = __ Ex: Part-part-whole whole unknown a + b = __ Ex: Comparison larger quantity unknown a + b = __ Ex: Subtraction result unknown
Result unknown Ex: Part-part-whole problems Part unknown Ex: Whole unknown Ex: Compare problems Difference unknown Ex: Larger part unknown Ex: Smaller part unknown Ex: Multiplicative structures Product unknown Ex: Factor unknown Ex: Division structures Partitive division Total amount known Number of groups known Size or measure of each group unknown Ex: Quotative division (also known as Measurement division) Total amount known Size or measure of each group known
Including, but not limited to: Point – a specific location in space Has no dimension and is usually represented by a small dot Ex: Line – a set of points that form a straight path that goes in opposite directions without ending Line labels Lines named according to two points on a line Ex: Lines named by one lower case cursive or print letter Ex: Parallel lines – lines that lie in the same plane, never intersect, and are always the same distance apart Various orientations including vertical, horizontal, diagonal, and parallel lines of even, uneven, or off-set lengths Ex: Intersecting lines – lines that meet or cross at a point Various orientations including vertical, horizontal, diagonal, and intersecting lines of even, uneven, or off-set lengths Ex: Perpendicular lines – lines that intersect at right angles to each other to form square corners Various orientations including vertical, horizontal, diagonal, and perpendicular lines of even, uneven, or off-set lengths Notation is given as a box in the angle corner to represent a 90° angle. Ex: Lines in pictorial models and polygons Ex: Extending lines beyond pictorial models Ex: Ex: Line segment – part of a line between two points on the line, called endpoints of the segment
4 vertices Opposite sides congruent 2 pairs of parallel sides 2 pairs of perpendicular sides 4 right angles Ex: Rhombus 4 sides 4 vertices All sides congruent 2 pairs of parallel sides Opposite angles congruent Ex: Square (a special type of rectangle and a special type of rhombus) 4 sides 4 vertices All sides congruent 2 pairs of parallel sides
Enhanced TEKS Clarification Mathematics Grade 5 2014 - 2015 Grade 5 §111.1. Implementation of Texas Essential Knowledge and Skills for Mathematics, Elementary, Adopted 2012. Source: The provisions of this §111.1 adopted to be effective September 10, 2012, 37 TexReg 7109. §111.7. Grade 5, Adopted 2012.
1 6 1 6 1 6 1 6 1 6 1 6 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 Fraction Blocks Number Line Pattern Block Template
Original Problem In this column, copy the original problem from the test. Correction In this column, work the problem correctly, showing all work and circling your answer. Comments/Explanation In this column, write an explanation of what you did wrong and a comment that might help you in the future. Problem #____ Problem #____ Problem #____ Problem #____ Problem #____
Original Problem In this column, copy the original problem from the test. Correction In this column, work the problem correctly, showing all work and circling your answer. Comments/Explanation In this column, write an explanation of what you did wrong and a comment that might help you in the future. Problem #____ Problem #____ Problem #____ Problem #____ Problem #____
Example Name Terms 7 6x monomial 1 term 3t – 1 12xy3 + 5x4y binomial 2 terms 2x2 + 3x – 7 trinomial 3 terms Nonexample Reason 5mn – 8 variable exponent n-3 + 9 negative exponent
3g3 + 6g2 – g – 7 Subtract Polynomials Add the inverse. Example: (4x2 + 5) – (-2x2 + 4x -7) (Add the inverse.) = (4x2 + 5) + (2x2 – 4x +7) = 4x2 + 5 + 2x2 – 4x + 7 (Group like terms and add.) = (4x2 + 2x2) – 4x + (5 + 7)
8 + 5x = 8 + x ∙ 5 Associative Property of Multiplication (ab)c = a(bc) Examples: (1 ∙ 8) ∙ 3 = 1 ∙ (8 ∙ 3) (3x)x = 3(x ∙ x)
Mathematical Notation Set Builder Notation Read Other Notation {x|0 < x 3} The set of all x such that x is greater than or equal to 0 and x is less than 3. 0 < x 3 (0, 3] {y: y ≥ -5} The set of all y such that y is greater than or equal to -5. y ≥ -5 [-5, ∞)
The median is 8.5. Mode Data Sets Mode 3, 4, 6, 6, 6, 6, 10, 11, 14 6 0, 3, 4, 5, 6, 7, 9, 10 none 5.2, 5.2, 5.2, 5.6, 5.8, 5.9, 6.0 5.2 1, 1, 2, 5, 6, 7, 7, 9, 11, 12 1, 7 bimodal A measure of central tendency Examples:
Example Name Terms 7 6x monomial 1 term 3t – 1 12xy3 + 5x4y binomial 2 terms 2x2 + 3x – 7 trinomial 3 terms Nonexample Reason 5mn – 8 variable exponent n-3 + 9 negative exponent
Squaring a Binomial (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2 Examples: (3m + n)2 = 9m2 + 2(3m)(n) + n2 = 9m2 + 6mn + n2 (y – 5)2 = y2 – 2(5)(y) + 25 = y2 – 10y + 25
Parent functions can be transformed to create other members in a family of graphs. g(x) = f(x) + k is the graph of f(x) translated vertically – k units up when k > 0. k units down when k < 0. g(x) = f(x − h) is the graph of f(x) translated horizontally – h units right when h > 0. h units left when h < 0.
Transformations of Parent Functions Parent functions can be transformed to create other members in a family of graphs. g(x) = -f(x) is the graph of f(x) – reflected over the g(x) = f(-x) is the graph of f(x) – reflected over the
Transformations of Parent Functions Parent functions can be transformed to create other members in a family of graphs. g(x) = a · f(x) is the graph of f(x) – vertical dilation (stretch) if a > 1. vertical dilation (compression) if 0 < a < 1.
g(x) = f(ax) is the graph of f(x) – horizontal dilation (compression) if a > 1. horizontal dilation (stretch) if 0 < a < 1. Transformational Graphing Linear functions g(x) = x + b
Relations and Functions Probability and Statistics Revisions: October 2014 – removed Constant Correlation; removed negative sign on Linear Equation (slope intercept form) July 2015 – Add Polynomials (removed exponent); Subtract Polynomials (added negative sign); Multiply Polynomials (graphic organizer)(16x and 13x); Z-Score (added z = 0)
Prime Polynomial Cannot be factored into a product of lesser degree polynomial factors Example r 3t + 9 x2 + 1 5y2 – 4y + 3 Nonexample Factors x2 – 4 (x + 2)(x – 2) 3x2 – 3x + 6 3(x + 1)(x – 2)
x2 – 6x + 8 = 0 (x – 2)(x – 4) = 0 (x – 2) = 0 or (x – 4) = 0 x = 2 or x = 4 Graph the related function f(x) = x2 – 6x + 8. Quadratic Equation ax2 + bx + c = 0 a 0 Example solved by factoring:
Quadratic Equation: Number of Real Solutions ax2 + bx + c = 0, a 0 Examples Graphs Number of Real Solutions/Roots x2 – x = 3 2 x2 + 16 = 8x 1 distinct root with a multiplicity of two
Mathematical Notation Set Builder Notation Read Other Notation {x|0 < x 3} The set of all x such that x is greater than or equal to 0 and x is less than 3. 0 < x 3 (0, 3] {y: y ≥ -5} The set of all y such that y is greater than or equal to -5. y ≥ -5 [-5, ∞)
g(x) = f(x) + k is the graph of f(x) translated vertically – k units up when k > 0. k units down when k < 0. g(x) = f(x − h) is the graph of f(x) translated horizontally – h units right when h > 0. h units left when h < 0. Transformations of Parent Functions Parent functions can be transformed to create other members in a family of graphs.
family of graphs. Dilations g(x) = a · f(x) is the graph of f(x) – vertical dilation (stretch) if a > 1. vertical dilation (compression) if 0 < a < 1. g(x) = f(ax) is the graph of f(x) – horizontal dilation (compression) if a > 1. horizontal dilation (stretch) if 0 < a < 1. Transformational Graphing Linear functions g(x) = x + b
Example: 5 people to fill 3 chairs (order matters). How many ways can the chairs be filled? 1st chair – 5 people to choose from 2nd chair – 4 people to choose from 3rd chair – 3 people to choose from # possible arrangements are 5 ∙ 4 ∙ 3 = 60 Permutation To calculate the number of permutations n and r are positive integers, n ≥ r, and n is the total number of elements in the set and r is the number to be ordered.
Students Handout Line Graphs A line graph displays data that change over time. A line graph: Is easy to draw and to read Can have a zigzag symbol on the vertical axis when the data start at a large number Is best used to show data gathered over time Can be used to estimate values between data points and beyond data points. (This should be done carefully as the trend may not continue.) Double Bar Graphs A double bar graph displays two sets of data that can be counted. The lengths of the bars are used to represent and to compare data. A double bar graph: Is easy to draw and to read Can be used to directly compare two sets of data Can only be used to show discrete data May be difficult to read accurately depending on the scale used Pictograph Symbols are used to show data in a pictograph. The key shows what each symbol stands for. Pictograph : Easy to read but not easy to draw Interesting Cannot represent the actual value of data Bar Graph Bars are used to show data in a bar graph. Numbers on the axis show the scale.