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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.
- Assessment Limits :
Items requiring precise or exact solutions are limited to:- addition and subtraction within 1,000.
- multiplication of 2-digit by 1-digit or a multiple of 10 by a 1-digit.
- division of 2-digit by 1-digit. Items may contain a maximum of 3 steps.
- Calculator :
No
- Context :
Required
- Test Item #: Sample Item 1
- Question: Jack bought 2 umbrellas. Each umbrella costs $13. He bought 3 hats, each costing $4. How much did Jack spend in all?
- Difficulty: N/A
- Type: EE: Equation Editor
- Test Item #: Sample Item 2
- Question: Jack wants to buy the same number of hats for 3 of his friends. He has $57 dollars, and each hat costs $5. What is the greatest number of hats that Jack can buy for each friend?
- Difficulty: N/A
- Type: EE: Equation Editor
- Test Item #: Sample Item 3
- Question: Jack bought 2 umbrellas and 3 hats and spent between $30 and $50. Each
umbrella costs the same amount. Each hat costs the same amount. The price of a
hat is $4.
A. What is the least amount Jack could have spent on an umbrella?
B. What is the greatest amount Jack could have spent on an umbrella?
- Difficulty: N/A
- Type: EE: Equation Editor
- Test Item #: Sample Item 4
- Question:
There are 27 players on a soccer team. They are traveling to a game in 7 cars. There are 4 players in each of the first 6 cars.
How many players on the soccer team will travel in the seventh car? - Difficulty: N/A
- Type: EE: Equation Editor
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Idea
Problem-Solving Tasks
Tutorial
STEM Lessons - Model Eliciting Activity
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.
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.
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
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
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.
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.
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.
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
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
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.
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.
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
MFAS Formative Assessments
Students are asked to use a mental estimation strategy to evaluate the solution of a multistep word problem.
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.
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.
Student Resources
Original Student Tutorials
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
Problem-Solving Tasks
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 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 help students gain a better understanding of fractions and the conversion of fractions into smaller units.
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 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 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 help students gain a better understanding of fractions and the conversion of fractions into smaller units.
Type: Problem-Solving Task
Tutorial
In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.
Type: Tutorial
