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

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

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

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

Students write an equation to match a given word problem.

Type: Formative Assessment

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

Type: Formative Assessment

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

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

Type: Formative Assessment

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

Type: Formative Assessment

In this lesson plan, students will solve problems with division, including interpreting remainders, as they identify how citizens can help solve local and state problems.

Type: Lesson Plan

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

Type: Lesson Plan

Students will determine if an equation is true or false based on using comparative relational thinking and knowledge of operations. The students will also determine the unknown number in some equations involving addition. 

Type: Lesson Plan

In this lesson, students will determine if equations are true or false and justify their reasoning. The lesson focuses on the meaning operations and properties.

Type: Lesson Plan

In this lesson, students will create representations for different multi-step word problems. One of these representations will be an expression with a variable.

Type: Lesson Plan

Students will apply multiplication, division and factor knowledge to word problems.

Type: Lesson Plan

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.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

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.

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

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

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

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.

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

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.

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

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

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.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

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.

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

This Model Eliciting Activity (MEA) is written at a 5th grade level. This MEA asks the students to decide on a t shirt that will provide the school’s Math club with the best value for their money. Students are asked to rank order the t shirt company options from best to worst. Students must explain how they arrived at their solution.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

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.

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

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.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

The Plant Package MEA provides students with an engineering problem in which they are asked to rank different plant containers using recycled materials.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

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.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

In this lesson, students will deepen their knowledge of using equal groups in multiplication and their ability to visualize the quantity of an item in a given object. They will use problem-solving skills and see the value in using benchmarks.

Type: Lesson Plan

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.

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

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.

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

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

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

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

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

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.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

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.

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

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

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

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

Type: Original Student Tutorial

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.

• Part 1: Think Fast! Comparative Strategies (Addition expressions on both sides of the equal sign)
• Part 2: Think Fast! Comparative Strategies (Subtraction expressions on both sides of the equal sign)

Type: Original Student Tutorial

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]

Type: Original Student Tutorial

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.

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.

• 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.

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.

• Part 1
• Part 2
• Part 3
• Part 4
  

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.

• Part 1
• Part 2
• Part 3
• Part 4
  

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.

• Part 1
• Part 2
• Part 3
• Part 4
  

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

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.

Type: Original Student Tutorial

Sideways or wayside, math word problems can be a ton of fun, no matter how you look at them.

Type: Perspectives Video: Teaching Idea

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

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.

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

The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.

Type: Problem-Solving Task

"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

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

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

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

Type: Text Resource

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

Type: Tutorial