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Title: What's the Question Again?
Description:
This lesson focuses on problem solving strategies with word problems that are 2 or more steps. Students are forced through the strategies to focus on the content of a problem before attempting to answer the "question" which tells what they are to solve. Visualization and communication are reinforced throughout the lesson. The strategies are generic. Included are problems for 3rd, 4th, and 5th grade computation. However, these same strategies can be used for all grade levels.
This is a College and CareerReady Standards showcase lesson plan.
Standard(s): [MA2013] (3) 8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] [MA2013] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (5) 12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5NF2] [MA2013] (5) 16: Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF6]
Subject: Mathematics (3  5)
Title: What's the Question Again?
Description: This lesson focuses on problem solving strategies with word problems that are 2 or more steps. Students are forced through the strategies to focus on the content of a problem before attempting to answer the "question" which tells what they are to solve. Visualization and communication are reinforced throughout the lesson. The strategies are generic. Included are problems for 3rd, 4th, and 5th grade computation. However, these same strategies can be used for all grade levels.
This is a College and CareerReady Standards showcase lesson plan.
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Title: What's Your Question? Multiplication Word Problems
Description:
Students will explore multiplication and word problems. They will work cooperatively to examine a story scenarioand list possible questions to develop a completed word problem and solve it using a variety of strategies. The students will also create a word problem using an online story creator.
Standard(s): [MA2013] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 10: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT5]
Subject: Mathematics (4)
Title: What's Your Question? Multiplication Word Problems
Description: Students will explore multiplication and word problems. They will work cooperatively to examine a story scenarioand list possible questions to develop a completed word problem and solve it using a variety of strategies. The students will also create a word problem using an online story creator.
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Title: Little Red Riding Hood's Journey to Grandma's
Description:
The students will listen to the story of Little Red Riding Hood and work subtraction word problems connected to the story. The problems are related to distance traveled. They will work cooperatively with partners and share subtraction strategies with their peers. At the end of the lesson they will work a subtraction story problem and show strategies for solving.
Standard(s): [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 9: Fluently add and subtract multidigit whole numbers using the standard algorithm. [4NBT4] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2] [TC2] (35) 12: Create a product using digital tools.
Subject: Mathematics (4), or Technology Education (3  5)
Title: Little Red Riding Hood's Journey to Grandma's
Description: The students will listen to the story of Little Red Riding Hood and work subtraction word problems connected to the story. The problems are related to distance traveled. They will work cooperatively with partners and share subtraction strategies with their peers. At the end of the lesson they will work a subtraction story problem and show strategies for solving.
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Title: Nursery Rhyme Word Problems
Description:
In this lesson students will create basic addition, subtraction, multiplication, and division word problems using common nursery rhymes. Students will distinguish the key elements of word problems and incorporate those elements into a nursery rhyme.
Standard(s): [MA2013] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 9: Fluently add and subtract multidigit whole numbers using the standard algorithm. [4NBT4] [MA2013] (4) 10: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT5] [MA2013] (4) 11: Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT6] [TC2] (35) 2: Use various technology applications, including word processing and multimedia software. [TC2] (35) 10: Use digital environments to collaborate and communicate. [TC2] (35) 12: Create a product using digital tools.
Subject: Mathematics (4), or Technology Education (3  5)
Title: Nursery Rhyme Word Problems
Description: In this lesson students will create basic addition, subtraction, multiplication, and division word problems using common nursery rhymes. Students will distinguish the key elements of word problems and incorporate those elements into a nursery rhyme.
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Title: All squared up!
Description:
In this AMSTI 5 E lesson plan students will be engaged in an investigation to discover the patterns in squared numbers then be able to apply the concepts needed to evaluate the expression.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Standard(s): [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3]
Subject: Mathematics (4)
Title: All squared up!
Description: In this AMSTI 5 E lesson plan students will be engaged in an investigation to discover the patterns in squared numbers then be able to apply the concepts needed to evaluate the expression.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
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Title: Exploring Prime Numbers
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Exploring Prime Numbers is a handson, mindson math lesson that engages students in the discovery of prime numbers through the construction of multiplication arrays. Students then extend on their background knowledge of multiples and their new understanding of prime and composite numbers to complete an Eratosthenes’ Sieve.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Standard(s): [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (5) 12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5NF2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (5) 12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5NF2]
Subject: Mathematics (4  5)
Title: Exploring Prime Numbers
Description: Exploring Prime Numbers is a handson, mindson math lesson that engages students in the discovery of prime numbers through the construction of multiplication arrays. Students then extend on their background knowledge of multiples and their new understanding of prime and composite numbers to complete an Eratosthenes’ Sieve.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
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Title: Math at Dinner!
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Each group of students will use word processing software to create a restaurant menu complete with food titles and prices. Groups will then exchange menus and use the menus to order a meal. Each student will total their meal, add 10% sales tax, 15% gratuity and figure their change from $20.00.
This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [TC2] (35) 2: Use various technology applications, including word processing and multimedia software. [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2]
Subject: Mathematics (4), or Technology Education (3  5)
Title: Math at Dinner!
Description: Each group of students will use word processing software to create a restaurant menu complete with food titles and prices. Groups will then exchange menus and use the menus to order a meal. Each student will total their meal, add 10% sales tax, 15% gratuity and figure their change from $20.00.
This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Fun with Problem Solving
Description:
The object of this lesson is to teach students that problem solving can be interesting and fun. It is important to pay attention to what is asked and information that is in the problem.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [ELA] (5) 2: Use a range of strategies, including drawing conclusions such as opinions about characters based on their actions and summarizing passages, to comprehend fifthgrade recreational reading materials in a variety of genres. [ELA] (5) 4: Use a wide range of strategies and skills, including using text features to gain meaning, summarizing passages, and drawing conclusions, to comprehend fifthgrade informational and functional reading materials. [TC2] (35) 1: Use input and output devices of technology systems. [TC2] (35) 2: Use various technology applications, including word processing and multimedia software. [ELA2013] (5) 29: Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources. [W.5.8] [ELA2013] (5) 16: Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently. [RI.5.7] [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 9: Fluently add and subtract multidigit whole numbers using the standard algorithm. [4NBT4] [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5]
Subject: English Language Arts (5), or English Language Arts (5), or Mathematics (3  5), or Technology Education (3  5)
Title: Fun with Problem Solving
Description: The object of this lesson is to teach students that problem solving can be interesting and fun. It is important to pay attention to what is asked and information that is in the problem.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Estimation Station
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During this lesson students will learn the difference between estimation and guessing. Knowing how to estimate is an essential skill that will help students determine approximate totals as well as check the reasonableness of their answer to a problem. After listening to the book Betcha by Stuart J. Murphy, the students will be given opportunities to practice the strategies that are presented. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [CE] (012) 8: Cooperation [CE] (012) 22: Creativity [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3]
Subject: Character Education (K  12), or Mathematics (3  4)
Title: Estimation Station
Description: During this lesson students will learn the difference between estimation and guessing. Knowing how to estimate is an essential skill that will help students determine approximate totals as well as check the reasonableness of their answer to a problem. After listening to the book Betcha by Stuart J. Murphy, the students will be given opportunities to practice the strategies that are presented. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Number Clues
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This lesson allows students to observe and participate in problem solving activites involving mystery numbers, clues, and characteristics of numbers.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3]
Subject: Mathematics (3  4)
Title: Number Clues
Description: This lesson allows students to observe and participate in problem solving activites involving mystery numbers, clues, and characteristics of numbers.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Comparing Fuel Economy (adapted from CMP "Comparing and Scaling" Investigation 4.1)
Description:
In this lesson students will explore rates. They will use the concept of rates to compute and compare fuel economy.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] (7) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3]
Subject: Mathematics (4  7)
Title: Comparing Fuel Economy (adapted from CMP "Comparing and Scaling" Investigation 4.1)
Description: In this lesson students will explore rates. They will use the concept of rates to compute and compare fuel economy.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Thinkfinity Lesson Plans
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Title: Picture This
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In this lesson, from Illuminations, students compose number sentences based on mathematics stories and then conduct a survey to determine how various people interpret pictures mathematically. They analyze and summarize the data they collect, and draw conclusions from their findings.
Standard(s): [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [MA2013] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 22: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots. [4MD4] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2]
Subject: Mathematics Title: Picture This
Description: In this lesson, from Illuminations, students compose number sentences based on mathematics stories and then conduct a survey to determine how various people interpret pictures mathematically. They analyze and summarize the data they collect, and draw conclusions from their findings. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
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Title: Classroom Paper
Description:
In this lesson, one of a multipart unit from Illuminations, students investigate data in connection with recyclable materials and develop plans to help the environment. Students gather and graph information about their classroom paper use over a period of several days and then interpret graphical information and use the data as a basis for future planning.
Standard(s): [MA2013] (1) 18: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. [1MD4] [MA2013] (2) 23: Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph. (See Appendix A, Table 1.) [2MD10] [MA2013] (3) 1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] [MA2013] (3) 2: Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. [3OA2] [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [MA2013] (4) 1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. [4OA1] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 22: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots. [4MD4] [MA2013] (5) 2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5OA2] [MA2013] (5) 13: Interpret a fraction as division of the numerator by the denominator (^{a}/_{b} = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF3] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] [MA2013] (5) 15: Interpret multiplication as scaling (resizing), by: [5NF5] [MA2013] (5) 17: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)
[5NF7] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2] [MA2013] (5) 24: Represent realworld and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. [5G2]
Subject: Mathematics,Science Title: Classroom Paper
Description: In this lesson, one of a multipart unit from Illuminations, students investigate data in connection with recyclable materials and develop plans to help the environment. Students gather and graph information about their classroom paper use over a period of several days and then interpret graphical information and use the data as a basis for future planning. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2,3,4,5
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Title: Mathematics and Football: Unit Overview
Description:
In this fivelesson unit, from Illuminations, students participate in activities in which they analyze information represented graphically. Students are asked to discuss, describe, read, and write about the graphs and the information they contain. These activities focus on connections between mathematics and football by using the Super Bowl. Students are asked to look at the Super Bowl not just as the big game but as an opportunity to apply mathematics to some interesting problems. This unit includes an individual activity for four different levels plus one for parents to complete with their child at home.
Standard(s): [MA2013] (2) 1: Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Appendix A, Table 1.) [2OA1] [MA2013] (3) 8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] [MA2013] (3) 16: Tell and write time to the nearest minute, and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. [3MD1] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2]
Subject: Mathematics Title: Mathematics and Football: Unit Overview
Description: In this fivelesson unit, from Illuminations, students participate in activities in which they analyze information represented graphically. Students are asked to discuss, describe, read, and write about the graphs and the information they contain. These activities focus on connections between mathematics and football by using the Super Bowl. Students are asked to look at the Super Bowl not just as the big game but as an opportunity to apply mathematics to some interesting problems. This unit includes an individual activity for four different levels plus one for parents to complete with their child at home. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2,3,4,5,6,7,8
Web Resources
Interactives/Games
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Title: Power Lines
Description:
An interactive game that has students problemsolving math combinations to solve the puzzle. It gives 8 levels and after completing the 8th level they get a code to move on.
Standard(s): [MA2013] (3) 8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3]
Power Lines
http://www.oswego.or...
An interactive game that has students problemsolving math combinations to solve the puzzle. It gives 8 levels and after completing the 8th level they get a code to move on.
Thinkfinity Informational Materials
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Title: Number and Operations Web Links
Description:
This collection of Web links, reviewed and presented by Illuminations, offers teachers and students information about and practice in concepts related to arithmetic. Users can read the Illuminations Editorial Board's review of each Web site, or choose to link directly to the sites.
Standard(s): [MA2013] (0) 1: Count to 100 by ones and by tens. [KCC1] [MA2013] (0) 2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1). [KCC2] [MA2013] (0) 3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects). [KCC3] [MA2013] (0) 4: Understand the relationship between numbers and quantities; connect counting to cardinality. [KCC4] [MA2013] (0) 5: Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects. [KCC5] [MA2013] (3) 1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] [MA2013] (3) 2: Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. [3OA2] [MA2013] (3) 3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Appendix A, Table 2.) [3OA3] [MA2013] (3) 4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. [3OA4] [MA2013] (3) 5: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3OA5] [MA2013] (3) 6: Understand division as an unknownfactor problem. [3OA6] [MA2013] (3) 7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. [3OA7] [MA2013] (3) 8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] [MA2013] (3) 9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. [3OA9] [MA2013] (3) 10: Use place value understanding to round whole numbers to the nearest 10 or 100. [3NBT1] [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (3) 12: Multiply onedigit whole numbers by multiples of 10 in the range 10  90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. [3NBT3] [MA2013] (3) 13: Understand a fraction ^{1}/_{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction ^{a}/_{b} as the quantity formed by a parts and size ^{1}/_{b}. [3NF1] [MA2013] (3) 14: Understand a fraction as a number on the number line; represent fractions on a number line diagram. [3NF2] [MA2013] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3NF3] [MA2013] (3) 16: Tell and write time to the nearest minute, and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. [3MD1] [MA2013] (3) 17: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^{3} and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of "times as much").) (See Appendix A, Table 2.) [3MD2] [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [MA2013] (3) 20: Recognize area as an attribute of plane figures, and understand concepts of area measurement. [3MD5] [MA2013] (3) 21: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). [3MD6] [MA2013] (3) 22: Relate area to the operations of multiplication and addition. [3MD7] [MA2013] (3) 23: Solve realworld and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. [3MD8] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (3) 25: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [3G2] [MA2013] (4) 1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. [4OA1] [MA2013] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 4: Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite. [4OA4] [MA2013] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4OA5] [MA2013] (4) 6: Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. [4NBT1] [MA2013] (4) 7: Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [4NBT2] [MA2013] (4) 8: Use place value understanding to round multidigit whole numbers to any place. [4NBT3] [MA2013] (4) 9: Fluently add and subtract multidigit whole numbers using the standard algorithm. [4NBT4] [MA2013] (4) 10: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT5] [MA2013] (4) 11: Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT6] [MA2013] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4NF1] [MA2013] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4NF2] [MA2013] (4) 14: Understand a fraction ^{a}/_{b} with a > 1 as a sum of fractions ^{1}/_{b}. [4NF3] [MA2013] (4) 15: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. [4NF4] [MA2013] (4) 16: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) [4NF5] [MA2013] (4) 17: Use decimal notation for fractions with denominators 10 or 100. [4NF6] [MA2013] (4) 18: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. [4NF7] [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2] [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3] [MA2013] (4) 22: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots. [4MD4] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 24: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. [4MD6] [MA2013] (4) 25: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in realworld or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4MD7] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (4) 28: Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. [4G3] [MA2013] (5) 1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [5OA1] [MA2013] (5) 2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5OA2] [MA2013] (5) 3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. [5OA3] [MA2013] (5) 4: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and ^{1}/_{10} of what it represents in the place to its left. [5NBT1] [MA2013] (5) 5: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. [5NBT2] [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 7: Use place value understanding to round decimals to any place. [5NBT4] [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5] [MA2013] (5) 9: Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5NBT6] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5NF1] [MA2013] (5) 12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5NF2] [MA2013] (5) 13: Interpret a fraction as division of the numerator by the denominator (^{a}/_{b} = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF3] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] [MA2013] (5) 15: Interpret multiplication as scaling (resizing), by: [5NF5] [MA2013] (5) 16: Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF6] [MA2013] (5) 17: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)
[5NF7] [MA2013] (5) 18: Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, realworld problems. [5MD1] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2] [MA2013] (5) 20: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. [5MD3] [MA2013] (5) 21: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5MD4] [MA2013] (5) 22: Relate volume to the operations of multiplication and addition, and solve realworld and mathematical problems involving volume. [5MD5] [MA2013] (5) 23: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [5G1] [MA2013] (5) 24: Represent realworld and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. [5G2] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [MA2013] (5) 26: Classify twodimensional figures in a hierarchy based on properties. [5G4]
Subject: Mathematics Title: Number and Operations Web Links
Description: This collection of Web links, reviewed and presented by Illuminations, offers teachers and students information about and practice in concepts related to arithmetic. Users can read the Illuminations Editorial Board's review of each Web site, or choose to link directly to the sites. Thinkfinity Partner: Illuminations Grade Span: K,1,2,3,4,5,6,7,8,9,10,11,12
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Title: Communicating about Mathematics Using Games: Playing Fraction Tracks
Description:
Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. This eexample from Illuminations contains an interactive version of a game that can be used in the grades 35 classroom to support students' learning about fractions. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations.
Standard(s): [MA2013] (3) 1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] [MA2013] (3) 2: Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. [3OA2] [MA2013] (3) 3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Appendix A, Table 2.) [3OA3] [MA2013] (3) 4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. [3OA4] [MA2013] (3) 5: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3OA5] [MA2013] (3) 6: Understand division as an unknownfactor problem. [3OA6] [MA2013] (3) 7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. [3OA7] [MA2013] (3) 8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] [MA2013] (3) 9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. [3OA9] [MA2013] (3) 10: Use place value understanding to round whole numbers to the nearest 10 or 100. [3NBT1] [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (3) 12: Multiply onedigit whole numbers by multiples of 10 in the range 10  90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. [3NBT3] [MA2013] (3) 13: Understand a fraction ^{1}/_{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction ^{a}/_{b} as the quantity formed by a parts and size ^{1}/_{b}. [3NF1] [MA2013] (3) 14: Understand a fraction as a number on the number line; represent fractions on a number line diagram. [3NF2] [MA2013] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3NF3] [MA2013] (3) 16: Tell and write time to the nearest minute, and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. [3MD1] [MA2013] (3) 17: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^{3} and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of "times as much").) (See Appendix A, Table 2.) [3MD2] [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [MA2013] (3) 21: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). [3MD6] [MA2013] (3) 22: Relate area to the operations of multiplication and addition. [3MD7] [MA2013] (3) 23: Solve realworld and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. [3MD8] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (3) 25: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [3G2] [MA2013] (4) 1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. [4OA1] [MA2013] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 4: Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite. [4OA4] [MA2013] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4OA5] [MA2013] (4) 6: Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. [4NBT1] [MA2013] (4) 7: Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [4NBT2] [MA2013] (4) 8: Use place value understanding to round multidigit whole numbers to any place. [4NBT3] [MA2013] (4) 9: Fluently add and subtract multidigit whole numbers using the standard algorithm. [4NBT4] [MA2013] (4) 10: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT5] [MA2013] (4) 11: Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT6] [MA2013] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4NF1] [MA2013] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4NF2] [MA2013] (4) 14: Understand a fraction ^{a}/_{b} with a > 1 as a sum of fractions ^{1}/_{b}. [4NF3] [MA2013] (4) 15: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. [4NF4] [MA2013] (4) 16: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) [4NF5] [MA2013] (4) 17: Use decimal notation for fractions with denominators 10 or 100. [4NF6] [MA2013] (4) 18: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. [4NF7] [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2] [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3] [MA2013] (4) 22: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots. [4MD4] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 24: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. [4MD6] [MA2013] (4) 25: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in realworld or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4MD7] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (4) 28: Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. [4G3] [MA2013] (5) 1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [5OA1] [MA2013] (5) 2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5OA2] [MA2013] (5) 3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. [5OA3] [MA2013] (5) 4: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and ^{1}/_{10} of what it represents in the place to its left. [5NBT1] [MA2013] (5) 5: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. [5NBT2] [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 7: Use place value understanding to round decimals to any place. [5NBT4] [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5] [MA2013] (5) 9: Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5NBT6] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5NF1] [MA2013] (5) 12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5NF2] [MA2013] (5) 13: Interpret a fraction as division of the numerator by the denominator (^{a}/_{b} = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF3] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] [MA2013] (5) 15: Interpret multiplication as scaling (resizing), by: [5NF5] [MA2013] (5) 16: Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF6] [MA2013] (5) 17: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)
[5NF7] [MA2013] (5) 18: Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, realworld problems. [5MD1] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2] [MA2013] (5) 20: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. [5MD3] [MA2013] (5) 21: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5MD4] [MA2013] (5) 22: Relate volume to the operations of multiplication and addition, and solve realworld and mathematical problems involving volume. [5MD5] [MA2013] (5) 23: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [5G1] [MA2013] (5) 24: Represent realworld and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. [5G2] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [MA2013] (5) 26: Classify twodimensional figures in a hierarchy based on properties. [5G4]
Subject: Mathematics Title: Communicating about Mathematics Using Games: Playing Fraction Tracks
Description: Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. This eexample from Illuminations contains an interactive version of a game that can be used in the grades 35 classroom to support students' learning about fractions. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations. Thinkfinity Partner: Illuminations Grade Span: 3,4,5

