# Cluster 1: 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.

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

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

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.

## Assessments

Sample 4 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

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

## Educational Game

All Things Being Equal:

In this game, learners strategize to win the most cards by building number equations. Learners practice operations (addition, subtraction, multiplication, and division) to construct their equations. This activity guide contains sample questions to ask, literary connections, extensions, and alignment to local and national standards.

Type: Educational Game

## Formative Assessments

Comparative Relational Thinking in a Multiplication Equation:

Students use comparative relational thinking to determine the value of an unknown number.

Type: Formative Assessment

Comparative Relational Thinking in a Division Equation:

Students are asked to use comparative relational thinking to determine the value of an unknown number.

Type: Formative Assessment

True and False Multiplication Equations:

Students are asked to determine if each of two equations is true without performing any operations.

Type: Formative Assessment

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.

Type: Formative Assessment

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.

Type: Formative Assessment

Are the Equations True?:

Students are asked to determine if each of two equations is true without performing any operations.

Type: Formative Assessment

Comparative Relational Thinking in an Addition Equation:

Students use comparative relational thinking to determine the value of an unknown number.

Type: Formative Assessment

Comparative Relational Thinking in a Subtraction Equation:

Students use comparative relational thinking to determine the value of an unknown number.

Type: Formative Assessment

Picking Strawberries:

Students are asked to solve a three-step word problem.

Type: Formative Assessment

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

Kate and Her Doll:

Students are given a context for a multiplicative comparison and asked to explain the comparison.

Type: Formative Assessment

Pet Snakes:

Students discuss the relationship between the lengths of two snakes in a multiplicative comparison problem that includes an equation.

Type: Formative Assessment

Writing an Equation to Match a Word Problem:

Students write an equation to match a given word problem.

Type: Formative Assessment

Animal Photographs:

Students read a multiplicative comparison word problem and are asked to write an equation that matches the problem.

Type: Formative Assessment

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.

Type: Formative Assessment

Roller Coaster Rides:

Students are given a multistep word problem to solve that requires interpreting remainders.

Type: Formative Assessment

Estimating the Solution:

Students are asked to use a mental estimation strategy to evaluate the solution of a multistep word problem.

Type: Formative Assessment

## Lesson Plans

I Love Leftovers!:

In the lesson, I Love Leftovers, students will learn to interpret the remainder through collaborative problem solving. Interpreting the remainder is a skill where students often struggle. When solving real world division problems, there are different ways to interpret the quotient and the remainder. It all depends on what the problem asks for and/or what you are trying to solve. In this lesson, students will explore situational problems that address the different ways to interpret the remainder.

Type: Lesson Plan

Can You Compare and Find the Missing Number In an Equation?:

Students will be able to compare and solve equations using comparative relational thinking. This lesson only addresses addition, not the other operations. Solving these equations will require the students to mentally evaluate to determine if it is true or false. The students will also determine the unknown number in some equations.

Type: Lesson Plan

Is my equation TRUE or FALSE?:

In this lesson, students will determine if equations are true or false and justify their reasoning using relational thinking.

Type: Lesson Plan

Gimme Two Steps!:

In this lesson, students are provided with opportunities to use different strategies to solve multi-step, real world problems using thinking maps and cooperative learning activities.

Type: Lesson Plan

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

Robotics on a Budget:

The P.T.A. President at ABC Elementary needs your students' help in selecting a robotics model that fits the needs of the students and the after school enrichment program. There is a budget of \$2,000 that the students must adhere to. Students will be asked rank 4 models based on criteria given to them and the budget. Students will be given a data set to help them develop a procedure for doing so. In their teams they will write a letter to the P.T.A President giving their procedures and explanation of the strategy they used. Students will practice adding, subtracting and multiplying numbers to the thousands in order to calculate the amount of models that can be bought of a certain model without going over the budget. Rubrics are included to help grade students.

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

Park Planning:

Students will be asked to plan a playground using no more than 30% of a park's area. They will analyze the best use of playground equipment using a data chart of area requirements, and making selections based on the least area used for the most amount of equipment (without exceeding 30% of total area of park).

Type: Lesson Plan

Pioneer City MEA:

This MEA is designed so that students can create a process of choosing the "Best Pioneer City" in Florida based on certain given criteria. The students will have to reformulate their process once provided with additional criteria on which to base their model.

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. The scenarios include preparing for a school field-day, purchasing stamps at the Post Office, and preparing for a wedding celebration. 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

Birthday Balloon Planner:

Students will develop a model for choosing a balloon party planner and rank them from best to worst.

The students will be able to use prior knowledge of addition of multi-digit whole numbers, multiplication and division facts and concepts, math calculations with money and time, understanding fractions, and problem solving skills to solve a non-routine MEA (Model Eliciting Activity) that requires real-world application of mathematical skills.

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

“Express Yourself!” with Math Story Chains:

Students work in small groups to write math story chains (multi-step real world problems) and write expressions or equations for their story chains.

Type: Lesson Plan

Yards to Yards:

In this MEA, students will work in collaborative groups to solve multistep word problems posed with whole numbers. The students will be asked to assist a landscaping company in deciding which hedges will be the best to use in replacing the existing hedges which are currently not thriving due to insect infestation. They will need to take into consideration factors such as height, cold, drought tolerance, price, and the client's comments. A twist is added to the problem when students are asked to consider if it would be a good idea to treat the existing hedge instead of replacing it.

Type: Lesson Plan

Tennis Lessons:

This MEA asks students to take on the job of a tennis pro and decide which factors are most important in choosing a facility to take tennis lessons. Students will perform math calculations, create a two-column table for hours and minutes, develop a procedure to rank facilities, and provide written feedback through letters to a parent whose child needs group tennis lessons and writes letters to ask for advice. They will rank their choices from "best to worst" tennis lesson facilities. Students will provide a detailed written explanation for how they decided to rank factors and their solution for rating tennis lesson facilities.

Type: Lesson Plan

Talented Divas MEA:

This Model Eliciting Activity (MEA) is written at a 5th grade level. This MEA asks the students to decide on a talent shirt that will provide Talented Divas with the best value for their money. Students are asked to rank order of Talent Shirt Company from best to worst. Students must provide a "Best Value"talent shirts to the Talented Divas and explain how they arrived at their solution.

Type: Lesson Plan

Walk This Way:

Students will be asked to rank the different floor tiles for the playrooms in activity centers throughout community parks. They will need to take certain factors into consideration when making their rankings. They will also need to calculate the costs of installing the floor tiles using the given measurement of the playroom and the floor tiles. The "twist" will be that the client now needs to include a storage room for some of the playroom's equipment. They will need to decide if to use the same floor tile or different from the playroom and the additional cost of the storage closet. After, they will add the total costs of the playroom and the storage closet. They will report their findings and reasons by writing letters to the client.

Type: Lesson Plan

Pickle Pick:

This Model Eliciting Activity (MEA) asks students to develop a procedure to select a pickle brand for a sandwich shop. Students will need to consider appearance, texture, price, flavor, length of shelf life, and estimating shipping costs. In the second portion of the problem statement, the students will need to trade off what they have previously considered and give more worth to the estimated shipping costs, while adding three more brands for consideration. The students will complete a culminating activity of making a commercial to advertise their selected brand. Student will need to work together and use the standard conventions of writing to write and perform their commercial for the other groups.

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

Fish Ahoy Fish:

Students will work in groups to assist a client in purchasing different fish for a fish pond. From a data table, they will need to decide which type of fish and how many fish to purchase according to the size of the each pond. After, they will need to revisit a revised data table to make different selection of fish and calculate costs for the purchase of the fish.

Type: Lesson Plan

Great Estimations!:

In this lesson, students will be strengthen their skills of estimation by using a benchmark number to aid in more accurate estimations. They will use problem-solving skills to identify relationships between given factors and products, i.e. 6 x 4 = 24 specifically means that 24 is 6 times as large as 4.

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

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 PowerPoint for direct instruction, word problem scenarios for small group work, individual practice, and student reflection form.

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. Fourth grade does not have to translate remainders to decimals or fractions.

Type: Lesson Plan

## Original Student Tutorials

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.

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 in this second interactive tutorial in the Field Trip Frenzy Series.

This is the second 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 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

## Perspectives Video: Teaching Idea

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.

Type: Perspectives Video: Teaching Idea

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 see identify that Student A is just looking at how many feet are being added on, while the 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 using four operations to solve problems.

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.

## 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

## Unit/Lesson Sequence

Reasonable Estimates:

Students are taught to estimate, to identify appropriate situations using estimation, to calculate estimated sums and differences, and to evaluate answers for reasonableness.

Type: Unit/Lesson Sequence

## Student Resources

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

## Original Student Tutorials

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.

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 in this second interactive tutorial in the Field Trip Frenzy Series.

This is the second 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 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

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 see identify that Student A is just looking at how many feet are being added on, while the 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 using four operations to solve problems.

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.

## Parent Resources

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

## Educational Game

All Things Being Equal:

In this game, learners strategize to win the most cards by building number equations. Learners practice operations (addition, subtraction, multiplication, and division) to construct their equations. This activity guide contains sample questions to ask, literary connections, extensions, and alignment to local and national standards.

Type: Educational Game

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 see identify that Student A is just looking at how many feet are being added on, while the 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.