MA.5.AR.1.1

Solve multi-step real-world problems involving any combination of the four operations with whole numbers, including problems in which remainders must be interpreted within the context.

Clarifications

Clarification 1: Depending on the context, the solution of a division problem with a remainder may be the whole number part of the quotient, the whole number part of the quotient with the remainder, the whole number part of the quotient plus 1, or the remainder.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 5
Strand: Algebraic Reasoning
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.5.AR.1.AP.1: Solve one- and two-step real-world problems involving any combination of the four operations with whole numbers. Explore problems in which remainders must be interpreted within the context.

Related Resources

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

Formative Assessment

Picking Strawberries:

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

Type: Formative Assessment

Lesson Plans

Blessings in a Bag!!:

In this MEA, the students will help a charitable organization select 5 snack items from a list to provide nutritious snacks for children in low-income communities.  Students will practice using the four operations to solve real-world problems and use decimal notation to make calculations involving money.  Additionally, they will be asked to compare multi-digit numbers to the thousandths.

Type: Lesson Plan

Getting the Top Mini-Fridge not a Small Deal:

In this MEA, students will create a procedure to rank five mini-refrigerators to determine which one should be purchased for the school by the PTA based on size, type, features, energy usage, and cost.  In the process, students will solve real-world problems involving the multiplication of multi-digit numbers with decimals to the hundredths, including using money.  Students will also determine the volume of a rectangular prism using a formula.

Type: Lesson Plan

Museum Dilemma:

In this MEA, students evaluate the contributions of various explorers to help a museum select the subject who provided the most impact on Western development for a new exhibit. Students will need to convert units to have the necessary information to help come up with a solution to the problem.

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. 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

Diving deeper into division:

This lesson introduces students to dividing with 2 digit divisors.  Students are asked to apply strategies that they learned in dividing with 1 digit divisors such as partial quotients or breaking numbers apart using the distributive property.

Type: Lesson Plan

Wallpaper Woes Money Math: Lessons for Life:

Students hear a story about a middle-school student who wants to redecorate his bedroom. They measure the classroom wall dimensions, draw a scale model, and incorporate measurements for windows and doors to determine the area that could be covered by wallpaper. Students then hear more about the student's redecorating adventure and learn about expenses, budget constraints, and tradeoffs.

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 a PowerPoint for direct instruction and word problems for small group or individual practice.

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. 

Type: Lesson Plan

Problem-Solving Tasks

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.

Type: Problem-Solving Task

What is 23 ÷ 5?:

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

Converting Fractions of a Unit into a Smaller Unit:

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

STEM Lessons - Model Eliciting Activity

Blessings in a Bag!!:

In this MEA, the students will help a charitable organization select 5 snack items from a list to provide nutritious snacks for children in low-income communities.  Students will practice using the four operations to solve real-world problems and use decimal notation to make calculations involving money.  Additionally, they will be asked to compare multi-digit numbers to the thousandths.

Getting the Top Mini-Fridge not a Small Deal:

In this MEA, students will create a procedure to rank five mini-refrigerators to determine which one should be purchased for the school by the PTA based on size, type, features, energy usage, and cost.  In the process, students will solve real-world problems involving the multiplication of multi-digit numbers with decimals to the hundredths, including using money.  Students will also determine the volume of a rectangular prism using a formula.

Museum Dilemma:

In this MEA, students evaluate the contributions of various explorers to help a museum select the subject who provided the most impact on Western development for a new exhibit. Students will need to convert units to have the necessary information to help come up with a solution to the problem.

MFAS Formative Assessments

Picking Strawberries:

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

Student Resources

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

Problem-Solving Tasks

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.

Type: Problem-Solving Task

What is 23 ÷ 5?:

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

Converting Fractions of a Unit into a Smaller Unit:

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

Parent Resources

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

Problem-Solving Tasks

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.

Type: Problem-Solving Task

What is 23 ÷ 5?:

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

Converting Fractions of a Unit into a Smaller Unit:

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