# Standard 1: Solve multiplication and division problems.

General Information
Number: MA.3.AR.1
Title: Solve multiplication and division problems.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.3.AR.1.AP.1
Apply the commutative property of multiplication to find a product of one-digit whole numbers.
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 topic.

## 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

Using the Associative Property of Multiplication:

Students are asked to find the product of three numbers and are observed to see if they use the Associative Property to find the product more easily.

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

Break Apart and Put Together:

Students are given two arrays, one representing the equation 7 x 9 = 63 and the other representing the equation (5 + 2) x 9 = 63, to see if they recognize a relationship between the two.

Type: Formative Assessment

Students are given two problems to solve, one represented by the equation 4 x 6 = 24 and the other by the equation 6 x 4 = 24, to see if they recognize the answer to the second problem based on the Commutative Property.

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

Making Sense of Multiplication to Build Fluency of 6's, 7's, 8's, and 9's:

This lesson will help students multiply numbers with factors of 6, 7, 8, or 9 through decomposing numbers in an array and applying the distributive property. Many times, these factors are difficult for students to recall from memory. Teaching students how to use an array can give them a visual representation of the final product. This visual can also help students to make the connection that multiplying whole numbers is a sum of equal groups. Decomposing the numbers and using the distributive property is a strategy for students to use who are having trouble solving these higher factor multiplication facts.

Type: Lesson Plan

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

Zero on a Hero (Exploring the Zero Property of Multiplication):

Students will explore the Zero Property of Multiplication using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication facts, and identify patterns in a set of multiplication facts to develop understanding of the Zero Property of Multiplication.

Type: Lesson Plan

One with a Bun (Exploring the Multiplicative Identity Property of 1):

In this lesson students will explore the Multiplicative Identity Property of 1, using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication equations, and identify patterns in a set of multiplication facts to develop understanding of the Multiplicative Identity Property of 1.

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

Multiply by Multiples of 10 with Number Cubes:

In this lesson students will use various strategies to multiply one-digit numbers by multiples of 10 within the range of 10-90. The strategies will encompass the Distributive, Commutative, and Associative properties, place value, number lines, base-ten blocks, diagrams, hundreds chart. Students will play a game with number cubes to practice this multiplication.

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

Efficient Multiplication:

Students will engage with questions to evaluate the students' abilities to select and apply multiplication strategies with fluency and efficiency. The focus of the lesson is decomposing numbers to multiply using the Distributive property and understanding and applying the Commutative property. Then, students will reinforce decomposing of factors while playing Decomposition of Factors. The lesson concludes with a real world application problem on an Exit Slip.

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

Fall Fun and Games! (Exploring the Commutative Property of Multiplication):

In this lesson, students will build and manipulate a variety of arrays in the context of creating games for a Fall Festival. They will practice using the Commutative Property of Multiplication to find related multiplication facts.

Type: Lesson Plan

Amazing Arrays:

This is a hands-on lesson for introducing and practicing building arrays to create models that represent the distributive property of multiplication, and then using those arrays to draw models of the equations they represent.

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 Tutorials

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

Monkeying Around with Multiplication: Commutative Property:

Learn strategies, like the commutative property, to help you become better at multiplying in this interactive tutorial.

Type: Original Student Tutorial

## Student Resources

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

## Original Student Tutorials

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

Monkeying Around with Multiplication: Commutative Property:

Learn strategies, like the commutative property, to help you become better at multiplying 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 topic.