# 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.
General Information
Subject Area: Mathematics
Domain-Subdomain: Operations and Algebraic Thinking
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Use the four operations with whole numbers to solve problems. (Major Cluster) -

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.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Multiplication situation must be a comparison (e.g., times as many). Limit multiplication and division to 2-digit by 1-digit or a multiple of 10 by a 1-digit.
• Calculator :

No

• Context :

Required

Sample Test Items (1)
• Test Item #: Sample Item 1
• Question:

Johnny has 17 marbles. Mitchell has 3 times as many marbles as Johnny. How many marbles does Mitchell have?

• Difficulty: N/A
• Type: EE: Equation Editor

## Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
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.2b: Determine the number of sets of whole numbers, ten or less, that equal a dividend.

## Related Resources

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

## Assessments

Sample 3 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 2 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 1 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

## 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

Dogs as Pets:

Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems.

Type: Formative Assessment

Books and Yarn:

Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems.

Type: Formative Assessment

Throwing Footballs:

Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems.

Type: Formative Assessment

## Lesson Plans

Aaron and Anya's Quilt Challenge: Problem Solving and Interpreting Remainders:

In this situational story, Aaron and Anya find a large piece of brightly colored fabric. They decide to cut it into squares to make a quilt. Students will find the area of the fabric by multiplying two digits by two digits. They will explore factors as they figure out the largest quilt square that can be cut for 25 students. There will be fabric left over; students will have to determine and justify remainders based on several different scenarios. Finally, students will create their own quilt square using grid paper.

Type: Lesson Plan

Take Time to Tile - MEA:

In this MEA, students will work in collaborative groups to solve multistep problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and division. The students will be asked to assist a property owner, who is planning to retile his kitchen and family room floors, with purchasing the best quality tiles for the least amount of money. Students will need to read a data table, rank the tile companies from best to worst, calculate the amount of tiles needed according to the area, and determine the total cost to retile the kitchen and family room. A twist is added to the problem when one of the tile companies goes out of business, but two new companies are added. An additional twist will be that the homeowner has decided to tile his bathroom as well. The students will need to reevaluate the tile companies as well as recalculate the total costs to include tile for the bathroom.

Type: Lesson Plan

Party Planners Wanted:

In this MEA, students will work in collaborative groups to solve multistep problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and division. The students will be asked to assist a businessman who is planning a party for his employees. They will need to read several ads and decide which company offers the best deal in renting tables, chairs, and tablecloths for the client. They will need to take into consideration the amount of guests attending the party and the budget allowed. A twist is added to the problem when the students are asked to consider an additional ad and the fact that the guest list is now slightly larger.

Type: Lesson Plan

Plant Package:

The Model Eliciting Activity (MEA) is written at a 4th grade level. The Plant Package provides students with an engineering problem in which they are asked to rank different plant packaging designs using recycled materials.

Type: Lesson Plan

Hotels: Where to Stay:

This MEA allows students to explore the creation of a model to rank hotels. Students are presented with the first part of the problem and the data which includes cost, meals served, pet friendly, and closeness to highway. They will determine which hotel will receive their highest recommendation. The second part of the task adds two hotels and additional data related to discounts. Students need to apply and test their model and make modifications as needed. All findings are submitted to the client in writing. Students may use this information to plan a family vacation researching which hotels they might stay in as they travel.

Type: Lesson Plan

Travels and More MEA:

In this Model Eliciting Activity (MEA), students will be need to help a travel agent come up with the best vacation hotel package for a family of four. They need to take into consideration all the amenities, prices, perks, and reviews into consideration. A twist comes in when the travel agent will need to provide vacation hotel packages for families of 5 members.

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

Cruising for a Great Value:

This MEA allows students to explore the creation of a model to rank cruise ships. Students are presented with the first part of the problem and the data which includes cost, meals served, child care, and airfare. They will determine which ship will receive their highest recommendation. The second part of the task adds two ships and additional data related to time of the year. Students need to apply and test their model and make modifications as needed. All findings are submitted to the client in writing. Students may use this information to plan a family vacation researching which cruise ship they might stay in as they travel

Type: Lesson Plan

Light It Up:

In this MEA, students will work in collaborative groups to solve real-world, multi-step problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and/or division. The students will be asked to assist a business/property owner in purchasing holiday lights for his property. They will need to read several ads and decide which product would be the best for the property. They will be provided with an office plan to calculate the perimeter of the building to then calculate how many holiday lights will need to be purchased and its total cost for each. They also need to take into consideration the owner's primary concerns. In the twist, the owner finds different holiday lights made from another material.

Type: Lesson Plan

New Coat of Paint:

In this MEA, students will work in collaborative groups to solve multistep problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and division. The students will be asked to assist a property owner, who is planning to repair his new property, in purchasing the right exterior paint. They will need to read a data table, rank the paints from highest to lowest, calculate the amount of gallons needed according to the surface area, and the total cost of each paint. A twist is added to the problem when one of the paints is not available but two others are added, and also the owner wants to paint the dividing walls outside.

Type: Lesson Plan

## 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

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").

Comparing Money Raised:

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

## Teaching Ideas

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.

Type: Teaching Idea

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.

Type: Teaching Idea

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.

Type: Teaching Idea

## Text Resource

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

Type: Text Resource

## STEM Lessons - Model Eliciting Activity

Cruising for a Great Value:

This MEA allows students to explore the creation of a model to rank cruise ships. Students are presented with the first part of the problem and the data which includes cost, meals served, child care, and airfare. They will determine which ship will receive their highest recommendation. The second part of the task adds two ships and additional data related to time of the year. Students need to apply and test their model and make modifications as needed. All findings are submitted to the client in writing. Students may use this information to plan a family vacation researching which cruise ship they might stay in as they travel

Hotels: Where to Stay:

This MEA allows students to explore the creation of a model to rank hotels. Students are presented with the first part of the problem and the data which includes cost, meals served, pet friendly, and closeness to highway. They will determine which hotel will receive their highest recommendation. The second part of the task adds two hotels and additional data related to discounts. Students need to apply and test their model and make modifications as needed. All findings are submitted to the client in writing. Students may use this information to plan a family vacation researching which hotels they might stay in as they travel.

Light It Up:

In this MEA, students will work in collaborative groups to solve real-world, multi-step problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and/or division. The students will be asked to assist a business/property owner in purchasing holiday lights for his property. They will need to read several ads and decide which product would be the best for the property. They will be provided with an office plan to calculate the perimeter of the building to then calculate how many holiday lights will need to be purchased and its total cost for each. They also need to take into consideration the owner's primary concerns. In the twist, the owner finds different holiday lights made from another material.

New Coat of Paint:

In this MEA, students will work in collaborative groups to solve multistep problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and division. The students will be asked to assist a property owner, who is planning to repair his new property, in purchasing the right exterior paint. They will need to read a data table, rank the paints from highest to lowest, calculate the amount of gallons needed according to the surface area, and the total cost of each paint. A twist is added to the problem when one of the paints is not available but two others are added, and also the owner wants to paint the dividing walls outside.

Party Planners Wanted:

In this MEA, students will work in collaborative groups to solve multistep problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and division. The students will be asked to assist a businessman who is planning a party for his employees. They will need to read several ads and decide which company offers the best deal in renting tables, chairs, and tablecloths for the client. They will need to take into consideration the amount of guests attending the party and the budget allowed. A twist is added to the problem when the students are asked to consider an additional ad and the fact that the guest list is now slightly larger.

Plant Package:

The Model Eliciting Activity (MEA) is written at a 4th grade level. The Plant Package provides students with an engineering problem in which they are asked to rank different plant packaging designs using recycled materials.

Take Time to Tile - MEA:

In this MEA, students will work in collaborative groups to solve multistep problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and division. The students will be asked to assist a property owner, who is planning to retile his kitchen and family room floors, with purchasing the best quality tiles for the least amount of money. Students will need to read a data table, rank the tile companies from best to worst, calculate the amount of tiles needed according to the area, and determine the total cost to retile the kitchen and family room. A twist is added to the problem when one of the tile companies goes out of business, but two new companies are added. An additional twist will be that the homeowner has decided to tile his bathroom as well. The students will need to reevaluate the tile companies as well as recalculate the total costs to include tile for the bathroom.

Travels and More MEA:

In this Model Eliciting Activity (MEA), students will be need to help a travel agent come up with the best vacation hotel package for a family of four. They need to take into consideration all the amenities, prices, perks, and reviews into consideration. A twist comes in when the travel agent will need to provide vacation hotel packages for families of 5 members.

## MFAS Formative Assessments

Books and Yarn:

Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems.

Dogs as Pets:

Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems.

Making Necklaces:

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

Throwing Footballs:

Students are asked to write equations to represent two multiplicative comparison problems and to then solve the problems.

## Original Student Tutorials Mathematics - Grades K-5

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 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

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").

Comparing Money Raised:

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

## Parent Resources

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