# MA.3.AR.1.2

Solve one- and two-step real-world problems involving any of four operations with whole numbers.

### Examples

A group of students are playing soccer during lunch. How many students are needed to form four teams with eleven players each and to have two referees?

### Clarifications

Clarification 1: Instruction includes understanding the context of the problem, as well as the quantities within the problem.

Clarification 2: Multiplication is limited to factors within 12 and related division facts. Refer to Situations Involving Operations with Numbers (Appendix A).

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 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.3.AR.1.AP.2a: Solve one- and two-step addition and subtraction real-world problems within 100.
MA.3.AR.1.AP.2b: Solve one-step multiplication and division real-world problems. Multiplication may not exceed two single-digit whole numbers and their related division facts.

## Related Resources

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

## Formative Assessments

Writing a Problem With a Quotient:

Students are asked to solve a division equation and then interpret the quotient by writing a word problem that can be modeled by the equation.

Type: Formative Assessment

Finding the Number of Groups:

Students are asked to model an equal groups and an array problem in which the number of groups is unknown with multiplication or division equations and then solve each problem.

Type: Formative Assessment

Finding an Unknown Product:

Students are asked to model an equal groups and an array problem in which the product is unknown with multiplication or division equations and then solve each problem.

Type: Formative Assessment

Finding the Group Size:

Students are asked to model an equal groups and an array problem in which the group size is unknown with multiplication or division equations and then solve each problem.

Type: Formative Assessment

Zoo Field Trip:

Students solve a two-step word problem involving subtraction and division and then choose an equation that represents the word problem.

Type: Formative Assessment

Party Beverages:

Students solve a two-step problem requiring multiplication and addition and then write an equation to represent the problem.

Type: Formative Assessment

Bake Sale:

Students solve a two-step word problem involving addition and division and then write an equation to represent the problem.

Type: Formative Assessment

Books at the Book Fair:

Students solve a two-step word problem involving multiplication and subtraction and then write an equation to represent the problem.

Type: Formative Assessment

## Lesson Plans

Chess Wish List:

The 3rd grade chess club members will make two wish lists on how to spend \$75 on chess related materials. Then they have to make two new wish lists on how to spend \$750 on chess related materials.

Type: Lesson Plan

Best Vegetable Garden:

The students will plan a vegetable garden, deciding which kinds of vegetables to plant, how many plants of each kind will fit, and where each plant will be planted in a fixed-area garden design. Then they will revise their design based on new garden dimensions and additional plant options.  Students will explore the concept of area to plan their garden and they will practice solving 1 and 2-step real-world problems using the four operations to develop their ideas.

Type: Lesson Plan

Science Space Camp:

This MEA asks the students to compare information provided on various Science Space Camps to be attended by a student during the summer. They will take into account past attendee's reviews of the camps which should create interesting student discussions.

Type: Lesson Plan

Water Park Fun Day:

This third grade MEA asks students to work as a team to figure out which activities they would like to do at the water park with a given amount of tickets and time. Students will make informed decisions about which activities and food and beverage items on which to spend their allotted tickets.

Type: Lesson Plan

Same Perimeter, Different Area:

In this lesson, students are presented with a problem that requires them to create rectangles with the same perimeter but different areas.  Students also search for relationships among the perimeters and areas of different rectangles and find which characteristics produce a rectangle with the greatest area.

Type: Lesson Plan

Students will solve multiplication and division word problems by drawing arrays and writing the related equation.

Type: Lesson Plan

Kites for Education MEA:

Kites for Education is a Modeling Eliciting Activity which presents students with an engineering challenge in which they must analyze data sets and develop a procedure for ranking different kite models. The product ranked as best by the students will hypothetically be sold to customers and the profit used to purchase school textbooks and supplies for school age children impacted by Haiti's devastating earthquake.

Type: Lesson Plan

Hungry Zero:

The definition of the Zero Property of Multiplication will be analyzed, modeled and practiced.

Type: Lesson Plan

Subtraction Attraction:

In this lesson, students will demonstrate fluency in using a standard algorithm to complete story problems involving subtraction with regrouping using multi-digit whole numbers.

Type: Lesson Plan

Pet Store Partitive Division:

In this lesson students will model partitive division through the real-world activity of a pet store owner.

Type: Lesson Plan

Chip Chip Array!:

Students work together to create arrays to represent given numbers.

Type: Lesson Plan

Tasty Algebra: Using toasted O cereal to find the missing factor in a multiplication equation.:

In this lesson students will use Cheerios to solve multiplication equations relating 3 whole numbers from word problems that include missing factors ranging from one through ten. Students will also argue the validity of multiplication equations that include missing factors and products with corresponding word problems.

Type: Lesson Plan

Apples, Oranges, and Bananas of Math?:

In this lesson, the students will work in independently or in small groups to write equations to represent situations as well as their own math riddles around the concepts of multiplication. The teacher will use the book, The Grapes of Math by Greg Tang, to support this lesson.

Type: Lesson Plan

How Many Seeds in a Pumpkin?:

In this hands-on math exploration, students will use knowledge of estimation and multiplication to develop strategies for estimating how many seeds are in a medium-sized pumpkin.

Type: Lesson Plan

Way Too Much!:

In this lesson, students will learn that in some word problems too much information is given. They will learn to identify what information is needed to solve a single digit multiplication problem and what is "additional information" or way too much! With this information, they will represent their answers using arrays and explain their thinking. This is a good lesson to use after students have become comfortable with multiplication and prior to introducing multi-step problems.

Type: Lesson Plan

## Original Student Tutorial

Protect the Turtles: Solve Two-Step Word Problems:

Solve some two-step word problems and write equations about sea turtles and how pollution created by people is impacting their survival in this interactive tutorial.

Type: Original Student Tutorial

## STEM Lessons - Model Eliciting Activity

Best Vegetable Garden:

The students will plan a vegetable garden, deciding which kinds of vegetables to plant, how many plants of each kind will fit, and where each plant will be planted in a fixed-area garden design. Then they will revise their design based on new garden dimensions and additional plant options.  Students will explore the concept of area to plan their garden and they will practice solving 1 and 2-step real-world problems using the four operations to develop their ideas.

Chess Wish List:

The 3rd grade chess club members will make two wish lists on how to spend \$75 on chess related materials. Then they have to make two new wish lists on how to spend \$750 on chess related materials.

Kites for Education MEA:

Kites for Education is a Modeling Eliciting Activity which presents students with an engineering challenge in which they must analyze data sets and develop a procedure for ranking different kite models. The product ranked as best by the students will hypothetically be sold to customers and the profit used to purchase school textbooks and supplies for school age children impacted by Haiti's devastating earthquake.

Science Space Camp:

This MEA asks the students to compare information provided on various Science Space Camps to be attended by a student during the summer. They will take into account past attendee's reviews of the camps which should create interesting student discussions.

Water Park Fun Day:

This third grade MEA asks students to work as a team to figure out which activities they would like to do at the water park with a given amount of tickets and time. Students will make informed decisions about which activities and food and beverage items on which to spend their allotted tickets.

## MFAS Formative Assessments

Bake Sale:

Students solve a two-step word problem involving addition and division and then write an equation to represent the problem.

Books at the Book Fair:

Students solve a two-step word problem involving multiplication and subtraction and then write an equation to represent the problem.

Finding an Unknown Product:

Students are asked to model an equal groups and an array problem in which the product is unknown with multiplication or division equations and then solve each problem.

Finding the Group Size:

Students are asked to model an equal groups and an array problem in which the group size is unknown with multiplication or division equations and then solve each problem.

Finding the Number of Groups:

Students are asked to model an equal groups and an array problem in which the number of groups is unknown with multiplication or division equations and then solve each problem.

Party Beverages:

Students solve a two-step problem requiring multiplication and addition and then write an equation to represent the problem.

Writing a Problem With a Quotient:

Students are asked to solve a division equation and then interpret the quotient by writing a word problem that can be modeled by the equation.

Zoo Field Trip:

Students solve a two-step word problem involving subtraction and division and then choose an equation that represents the word problem.

## Original Student Tutorials Mathematics - Grades K-5

Protect the Turtles: Solve Two-Step Word Problems:

Solve some two-step word problems and write equations about sea turtles and how pollution created by people is impacting their survival in this interactive tutorial.

## Student Resources

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

## Original Student Tutorial

Protect the Turtles: Solve Two-Step Word Problems:

Solve some two-step word problems and write equations about sea turtles and how pollution created by people is impacting their survival in this interactive tutorial.

Type: Original Student Tutorial

## Parent Resources

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