### 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.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**4

**Strand:**Algebraic Reasoning

**Standard:**Represent and solve problems involving the four operations with whole numbers and fractions.

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Tutorial

## STEM Lessons - Model Eliciting Activity

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.Â 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 studentsâ€™ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

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.

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

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

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

## Original Student Tutorials Mathematics - Grades K-5

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.

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.

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.

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.

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

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

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

## Student Resources

## Original Student Tutorials

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

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

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

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

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

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

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

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

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

Type: Problem-Solving Task

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

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

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

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

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

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

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

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

Type: Problem-Solving Task

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

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

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

Type: Tutorial