 # Standard 1 : Use the four operations with whole numbers to solve problems. (Major Cluster) (Archived)

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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

### General Information

Number: MAFS.4.OA.1
Title: Use the four operations with whole numbers to solve problems. (Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Domain-Subdomain: Operations and Algebraic Thinking

#### Related Standards

This cluster includes the following benchmarks
 Code Description MAFS.4.OA.1.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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. MAFS.4.OA.1.2: 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. MAFS.4.OA.1.3: Solve multistep word problems posed with whole numbers and having whole-number 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. MAFS.4.OA.1.a: Determine whether an equation is true or false by using comparative relational thinking. For example, without adding 60 and 24, determine whether the equation 60 + 24 = 57 + 27 is true or false. MAFS.4.OA.1.b: Determine the unknown whole number in an equation relating four whole numbers using comparative relational thinking. For example, solve 76 + 9 = n + 5 for n by arguing that nine is four more than five, so the unknown number must be four greater than 76.

#### Related Access Points

This cluster includes the following access points.

#### Access Points

 Access Point Number Access Point Title MAFS.4.OA.1.AP.2a: Solve multiplicative comparisons with an unknown using up to two-digit numbers with information presented in a graph or word problem (e.g., an orange hat costs \$3. A purple hat costs two times as much. How much does the purple hat cost? [3 x 2 = p]). MAFS.4.OA.1.AP.3a: Solve and check one- or two-step word problems requiring the four operations within 100. MAFS.4.OA.1.AP.1a: Use objects to model multiplication involving up to five groups with up to five objects in each and write equations to represent the models. MAFS.4.OA.1.AP.2b: Determine the number of sets of whole numbers, ten or less, that equal a dividend. MAFS.4.OA.1.AP.aa: Determine whether an equation with quantities less than 100 is true or false. MAFS.4.OA.1.AP.ba: Find the unknown number in an equation (+, - ) relating four whole numbers.

#### Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

#### Original Student Tutorials

 Name Description Space: Division as Comparison: Discover how multiplicative comparison problems, from outer space, can be solved using division in this online tutorial. Think Different: Relationships in Math: Learn how to think differently to see if an equation is true or false, without even having to do the given math problem in this interactive tutorial on addition and subtraction relationships. Think Fast! Comparative Strategies: Part 3: Learn how to find a missing value when there are subtraction expressions on both sides of an equal sign by using comparative relational thinking and a number line in this interactive tutorial. This is part 3 in a 3-part series. Click below to open the other tutorials in the series on comparative strategies. Think Fast! Comparative Strategies: Part 2: Learn how to think fast to find a missing value when there are subtraction expressions on both sides of an equal sign by using using comparative relational thinking and a part-whole board in this interactive tutorial. This is part 2 in a 3-part series. Click below to open the other tutorials in the series on comparative strategies. Part 1: Think Fast! Comparative Strategies (Addition expressions on both sides of the equal sign) Part 3: Think Fast! Comparative Strategies [COMING SOON] Think Fast: Comparative Strategies: Part 1: Learn how to think fast and compare the parts in addition expressions on different sides of the equal sign to find an unknown number with this interactive tutorial. Space: Multiplication as Comparison: Launch into solving word problems that use multiplicative comparisons, drawings, and symbols in this space-themed interactive tutorial. Field Trip Frenzy (Part 4): Learn when to write the remainder of a multi-step division process as a fraction or decimal in this interactive tutorial. This is the final tutorial in the Field Trip Frenzy Series about remainders. Click below to open the other tutorials in this series. Part 1 Part 2 Part 3 Part 4 Note: This tutorial extends beyond whole number quotients with whole number remainders to whole number quotients with fractional or decimal remainders. Field Trip Frenzy (Part 3): Learn how to interpret remainders in multi-step division problems in this interactive tutorial This is the third tutorial in the Field Trip Frenzy Series about remainders. Click below to open the other tutorials in this series. Part 1 Part 2 Part 3 Part 4 Field Trip Frenzy (Part 2): Learn how to interpret remainders in multi-step division problems related to a field trip in this interactive tutorial. This tutorial is Part 2 in a four-part series about remainders. Click below to open the other tutorials in this series. Part 1 Part 2 Part 3 Part 4 Field Trip Frenzy (Part 1): Take a field trip while learning how to interpret remainders in multi-step division word problems. This is part 1 of a four-part series of interactive tutorials. Click below to open the other tutorials in this series. Part 1 Part 2 Part 3 Part 4 Multiplying Math Magic: Learn how to write multiplication equations based on multiplication comparisons and story problems in this magical math online tutorial!

#### Formative Assessments

 Name Description Comparative Relational Thinking in a Multiplication Equation: Students use comparative relational thinking to determine the value of an unknown number. Comparative Relational Thinking in a Division Equation: Students are asked to use comparative relational thinking to determine the value of an unknown number. True and False Multiplication Equations: Students are asked to determine if each of two equations is true without performing any operations. True and False Division Equations: Students are asked to determine if each of two equations is true by comparing mathematical expressions and without actually carrying out the indicated calculations. Determining If an Equation Is True: Students are asked to determine if each of two equations involving subtraction is true by comparing mathematical expressions and without actually carrying out the calculations. Are the Equations True?: Students are asked to determine if each of two equations is true without performing any operations. Comparative Relational Thinking in an Addition Equation: Students use comparative relational thinking to determine the value of an unknown number. Comparative Relational Thinking in a Subtraction Equation: Students use comparative relational thinking to determine the value of an unknown number. Picking Strawberries: Students are asked to solve a three-step word problem. Making Necklaces: The student is asked to solve a multiplicative comparison word problem comparing 6 inches of string to 24 inches of string. Dogs as Pets: Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems. Books and Yarn: Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems. Throwing Footballs: Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems. Kate and Her Doll: Students are given a context for a multiplicative comparison and asked to explain the comparison. Pet Snakes: Students discuss the relationship between the lengths of two snakes in a multiplicative comparison problem that includes an equation. Writing an Equation to Match a Word Problem: Students write an equation to match a given word problem. Animal Photographs: Students read a multiplicative comparison word problem and are asked to write an equation that matches the problem. Juice Boxes: Students are given a two-step word problem and are asked to solve the problem and write an equation with a letter representing the unknown in the equation. Roller Coaster Rides: Students are given a multi-step word problem to solve that requires interpreting remainders. Estimating the Solution: Students are asked to use a mental estimation strategy to evaluate the solution of a multistep word problem.

#### Perspectives Video: Teaching Idea

 Name Description Deciphering Cryptic Operations through Mathematical Reasoning: Sideways or wayside, math word problems can be a ton of fun, no matter how you look at them.

 Name Description Comparing Growth, Variation 2: The purpose of this task is to assess students’ understanding of multiplicative and additive reasoning. We would hope that students would be able to identify that Student A is just looking at how many feet are being added on, while  Student B is comparing how much the snakes grew in comparison to how long they were to begin with. Comparing Growth, Variation 1: The purpose of this task is to foster a classroom discussion that will highlight the difference between multiplicative and additive reasoning. Some students will argue that they grew the same amount (an example of "additive thinking"). Students who are studying multiplicative comparison problems might argue that Jewel grew more since it grew more with respect to its original length (an example of "multiplicative thinking"). Carnival Tickets: The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases. Comparing Money Raised: The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money. Karl's Garden: The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication. Since addition is both commutative and associative, we can reorder or regroup addends any way we like. Students often believe the same is true for multiplication. What is 23 ÷ 5?: When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them. Comparing Products: The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades. It builds on applying properties of operations as strategies to multiply and divide and interpreting a multiplication equation as a comparison. Converting Fractions of a Unit into a Smaller Unit: The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.

#### Teaching Ideas

 Name Description True, False, and Open Sentences: "Students first explore arithmetic sentences to decide whether they are true or false. The lesson then introduces students to sentences that are neither true nor false but are algebraic equations, also called open sentences, such as x + 3 = 7 or 2 x = 12." from Math Solutions. Engineers Speak For The Trees: Students begin by reading Dr. Seuss' "The Lorax" as an example of how overdevelopment can cause long-lasting environmental destruction. Students discuss how to balance the needs of the environment with the needs of human industry. Jump or Be Lunch! SeaWorld Classroom Activity: Students will predict how high they can jump and then compare the height of their jumps to how high a rockhopper penguin can jump out of the water. They will practice mathematical skills for determining averages.

#### Text Resource

 Name Description All About Multiplication: Bibliography: List of five children's books with a multiplication focus (found on NCTM Illuminations site under "All About Multiplication").

#### Tutorial

 Name Description Division: Intro to remainders: In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

#### Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

#### Original Student Tutorials

 Title Description Space: Division as Comparison: Discover how multiplicative comparison problems, from outer space, can be solved using division in this online tutorial. Think Different: Relationships in Math: Learn how to think differently to see if an equation is true or false, without even having to do the given math problem in this interactive tutorial on addition and subtraction relationships. Think Fast! Comparative Strategies: Part 3: Learn how to find a missing value when there are subtraction expressions on both sides of an equal sign by using comparative relational thinking and a number line in this interactive tutorial. This is part 3 in a 3-part series. Click below to open the other tutorials in the series on comparative strategies. Think Fast! Comparative Strategies: Part 2: Learn how to think fast to find a missing value when there are subtraction expressions on both sides of an equal sign by using using comparative relational thinking and a part-whole board in this interactive tutorial. This is part 2 in a 3-part series. Click below to open the other tutorials in the series on comparative strategies. Part 1: Think Fast! Comparative Strategies (Addition expressions on both sides of the equal sign) Part 3: Think Fast! Comparative Strategies [COMING SOON] Think Fast: Comparative Strategies: Part 1: Learn how to think fast and compare the parts in addition expressions on different sides of the equal sign to find an unknown number with this interactive tutorial. Space: Multiplication as Comparison: Launch into solving word problems that use multiplicative comparisons, drawings, and symbols in this space-themed interactive tutorial. Field Trip Frenzy (Part 4): Learn when to write the remainder of a multi-step division process as a fraction or decimal in this interactive tutorial. This is the final tutorial in the Field Trip Frenzy Series about remainders. Click below to open the other tutorials in this series. Part 1 Part 2 Part 3 Part 4 Note: This tutorial extends beyond whole number quotients with whole number remainders to whole number quotients with fractional or decimal remainders. Field Trip Frenzy (Part 3): Learn how to interpret remainders in multi-step division problems in this interactive tutorial This is the third tutorial in the Field Trip Frenzy Series about remainders. Click below to open the other tutorials in this series. Part 1 Part 2 Part 3 Part 4 Field Trip Frenzy (Part 2): Learn how to interpret remainders in multi-step division problems related to a field trip in this interactive tutorial. This tutorial is Part 2 in a four-part series about remainders. Click below to open the other tutorials in this series. Part 1 Part 2 Part 3 Part 4 Field Trip Frenzy (Part 1): Take a field trip while learning how to interpret remainders in multi-step division word problems. This is part 1 of a four-part series of interactive tutorials. Click below to open the other tutorials in this series. Part 1 Part 2 Part 3 Part 4 Multiplying Math Magic: Learn how to write multiplication equations based on multiplication comparisons and story problems in this magical math online tutorial!

 Title Description Comparing Growth, Variation 2: The purpose of this task is to assess students’ understanding of multiplicative and additive reasoning. We would hope that students would be able to identify that Student A is just looking at how many feet are being added on, while  Student B is comparing how much the snakes grew in comparison to how long they were to begin with. Comparing Growth, Variation 1: The purpose of this task is to foster a classroom discussion that will highlight the difference between multiplicative and additive reasoning. Some students will argue that they grew the same amount (an example of "additive thinking"). Students who are studying multiplicative comparison problems might argue that Jewel grew more since it grew more with respect to its original length (an example of "multiplicative thinking"). Carnival Tickets: The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases. Comparing Money Raised: The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money. Karl's Garden: The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication. Since addition is both commutative and associative, we can reorder or regroup addends any way we like. Students often believe the same is true for multiplication. What is 23 ÷ 5?: When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them. Comparing Products: The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades. It builds on applying properties of operations as strategies to multiply and divide and interpreting a multiplication equation as a comparison. Converting Fractions of a Unit into a Smaller Unit: The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.

#### Tutorial

 Title Description Division: Intro to remainders: In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

#### Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.