MA.4.AR.1.1

Solve real-world problems involving multiplication and division of whole numbers including problems in which remainders must be interpreted within the context.

Examples

A group of 243 students is taking a field trip and traveling in vans. If each van can hold 8 students, then the group would need 31 vans for their field trip because 243 divided by 8 equals 30 with a remainder of 3.

Clarifications

Clarification 1: Problems involving multiplication include multiplicative comparisons. Refer to Situations Involving Operations with Numbers (Appendix A).

Clarification 2: Depending on the context, the solution of a division problem with a remainder may be the whole number part of the quotient, the whole number part of the quotient with the remainder, the whole number part of the quotient plus 1, or the remainder.

Clarification 3: Multiplication is limited to products of up to 3 digits by 2 digits. Division is limited to up to 4 digits divided by 1 digit.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 4
Strand: Algebraic Reasoning
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.4.AR.1.AP.1: Solve one-step real-world problems involving multiplication and division of whole numbers. Multiplication may not exceed two-digit by one-digit and division must be related to one-digit by one-digit multiplication facts.

Related Resources

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

Formative Assessments

Making Necklaces:

The student is asked to solve a multiplicative comparison word problem comparing 6 inches of string to 24 inches of string.

Type: Formative Assessment

Roller Coaster Rides:

Students are given a multi-step word problem to solve that requires interpreting remainders.

Type: Formative Assessment

Lesson Plans

I Love Leftovers!:

In this lesson, students will explore situational problems that address the different ways to interpret the remainder.

Type: Lesson Plan

Slither Not in the Everglades! Python MEA:

This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.

Type: Lesson Plan

Park Planning:

Students are asked to plan a playground for a new park within a given budget and area limit. They will analyze the best use of playground equipment using a data table of area requirements and cost. Students will convert units within a single measurement system, calculate the area of a rectangle, and perform addition/subtraction calculations involving money using decimal notation.

Type: Lesson Plan

One Step at a Time: Word Problems:

In this lesson, students will use the four operations to solve multi-step word problems composed of whole numbers. Students will be asked to estimate, write equations, decide if their answers are reasonable, and explain their decision. Several problems include explaining the meaning of the remainder in a division problem.

Type: Lesson Plan

2-Digit Array Multiplication:

This lesson explores a conceptual approach to multiplying two 2-digit numbers. Students will create, explore, describe and record arrays built with place value pieces. The lesson supplies the understanding that will make multiplying multidigit numbers easy to do.

Type: Lesson Plan

Amazing Arrays 3X1 or 1X3:

This lesson is the third lesson in a unit beginning with Amazing Arrays and Amazing Arrays 2X1.

In this lesson students solve a multiplication problem by drawing arrays and segment the areas in several ways to solve the problem. Students will also apply the distributive property, explore rotations of area models to demonstrate the commutative property of multiplication, and match a word problem with its array.

Type: Lesson Plan

Cookies and Treats:

Fourth graders will help Cookies and Treats find cost-effective and eco-friendly packaging for its cookies. Students will organize data and compare prices using decimal notation in order to develop a procedure for choosing packaging for cookies.  Students will use multiplication and division of whole numbers to plan for how many packages to order.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

"Bar Model Math" - "Twice" as Nice:

In this lesson students will solve real world problems that have multiplicative comparisons in them. They will use the strategy of bar models to solve the problems.

Type: Lesson Plan

Amazing Arrays 2X1:

This is a hands-on lesson for extending and practicing drawing arrays using area models that show a 2-digit number times a 1-digit number. Students are also required to use the distributive property of multiplication and the equations they represent.

Type: Lesson Plan

Rockin' Remainders:

This is a lesson designed to teach interpreting remainders in division based on the context of the word problem. Included with the lesson plan is a PowerPoint for direct instruction and word problems for small group or individual practice.

Type: Lesson Plan

Those Pesky Remainders:

This is a lesson to help students understand how to interpret the remainder in a division problem. Real world problems are presented in a PowerPoint so students may visualize situations and discover the four treatments of a remainder. 

Type: Lesson Plan

Original Student Tutorials

Space: Division as Comparison:

Discover how multiplicative comparison problems, from outer space, can be solved using division in this online tutorial.

Type: Original Student Tutorial

Space: Multiplication as Comparison:

Launch into solving word problems that use multiplicative comparisons, drawings, and symbols in this space-themed interactive tutorial.

Type: Original Student 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.

Note: This tutorial extends beyond whole number quotients with whole number remainders to whole number quotients with fractional or decimal remainders.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

Multiplying Math Magic:

Learn how to write multiplication equations based on multiplication comparisons and story problems in this magical math online tutorial!

Type: Original Student Tutorial

Problem-Solving Tasks

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.

Type: Problem-Solving Task

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").

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Comparing Money Raised:

The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money. 

Type: Problem-Solving Task

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. 

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Tutorial

Division: Intro to remainders:

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial

STEM Lessons - Model Eliciting Activity

Cookies and Treats:

Fourth graders will help Cookies and Treats find cost-effective and eco-friendly packaging for its cookies. Students will organize data and compare prices using decimal notation in order to develop a procedure for choosing packaging for cookies.  Students will use multiplication and division of whole numbers to plan for how many packages to order.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Park Planning:

Students are asked to plan a playground for a new park within a given budget and area limit. They will analyze the best use of playground equipment using a data table of area requirements and cost. Students will convert units within a single measurement system, calculate the area of a rectangle, and perform addition/subtraction calculations involving money using decimal notation.

Slither Not in the Everglades! Python MEA:

This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.

MFAS Formative Assessments

Making Necklaces:

The student is asked to solve a multiplicative comparison word problem comparing 6 inches of string to 24 inches of string.

Roller Coaster Rides:

Students are given a multi-step word problem to solve that requires interpreting remainders.

Original Student Tutorials Mathematics - Grades K-5

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.

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.

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.

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.

Note: This tutorial extends beyond whole number quotients with whole number remainders to whole number quotients with fractional or decimal remainders.

Multiplying Math Magic:

Learn how to write multiplication equations based on multiplication comparisons and story problems in this magical math online tutorial!

Space: Division as Comparison:

Discover how multiplicative comparison problems, from outer space, can be solved using division in this online tutorial.

Space: Multiplication as Comparison:

Launch into solving word problems that use multiplicative comparisons, drawings, and symbols in this space-themed interactive tutorial.

Student Resources

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

Original Student Tutorials

Space: Division as Comparison:

Discover how multiplicative comparison problems, from outer space, can be solved using division in this online tutorial.

Type: Original Student Tutorial

Space: Multiplication as Comparison:

Launch into solving word problems that use multiplicative comparisons, drawings, and symbols in this space-themed interactive tutorial.

Type: Original Student 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.

Note: This tutorial extends beyond whole number quotients with whole number remainders to whole number quotients with fractional or decimal remainders.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

Multiplying Math Magic:

Learn how to write multiplication equations based on multiplication comparisons and story problems in this magical math online tutorial!

Type: Original Student Tutorial

Problem-Solving Tasks

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.

Type: Problem-Solving Task

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").

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Comparing Money Raised:

The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money. 

Type: Problem-Solving Task

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. 

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Tutorial

Division: Intro to remainders:

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial

Parent Resources

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

Problem-Solving Tasks

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.

Type: Problem-Solving Task

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").

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Comparing Money Raised:

The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money. 

Type: Problem-Solving Task

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. 

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Tutorial

Division: Intro to remainders:

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial