# 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

U.S. Symbols Construction:

Students will interpret and make comparisons of construction start and end dates and heights of U.S. symbols. Students will solve one- and two-step word problems based on the data.

Type: Lesson Plan

How Many Years?:

Students will discuss what they know about individuals who represent the U.S. or Florida and interpret data including important dates in the lives of these individuals. Students will use the data to solve one and two-step word problems in this integrated lesson.

Type: Lesson Plan

School Food Drive- Word Problems:

Students will solve one- and two-step word problems using a given set of data of collected food items from a school food drive. Students will use the word problems to identify roles volunteers have in a food drive in this integrated lesson plan.

This lesson is Part 2 of 3 math lesson integrating the importance of volunteering in a food drive.

Type: Lesson Plan

Sightseeing the U.S. Symbols:

Students will review the details of various trips to landmark destinations in the U.S. and rank the trips from most to least preferred, in this model eliciting activity.

Type: Lesson Plan

Representing Symbols Using Perimeter and Area:

In this integrated lesson, students will create Uncle Sam cards encouraging responsible citizenship, find the dimensions of their card, and then use measurement, addition, and multiplication to solve a real-world task requiring calculation of perimeter and area of a larger space to display all of the student-created Uncle Sam cards.

Type: Lesson Plan

Feeding the Community:

Students analyze various proposed sites to determine which site would be best for a group of volunteers to construct and maintain a community garden in this model eliciting activity.

Type: Lesson Plan

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

Partial Products with Arrays:

In this inquiry-based lesson, students will use the distributive property to find partial products of arrays to solve multiplication problems. They will also move from a concrete representation of arrays using manipulatives to a pictorial representation.

Type: Lesson Plan

Students will solve real-world addition problems within 1,000 using strategies and an algorithm and justify their solutions.

Type: Lesson Plan

Candy Apple Fun:

Students will learn how to solve one-digit by two-digit multiplication problems using the distributive property.

Type: Lesson Plan

Party Planning: Using Multiplication:

As the end of the year approaches, and your students have already learned several multiplication strategies, this party planning activity can help put all of that hard work into action. Students will be asked to use a menu and catalog to purchase food, decorations and goody bag items for an upcoming party. (I use this right before our end of the year 3rd Grade Luau Party, and have students purchase items that correlate with that theme. However, it can be used to plan an ideal birthday party, 4th of July Celebration, family reunion, etc.) After working together as a whole group, children will work with a partner and, ultimately independently, to solve one and two-digit multiplication and addition problems. Your students will get a chance to be creative and apply multiplication strategies to real world scenarios.

Type: Lesson Plan

Getting the hang of two-step word problems:

Students will solve two-step word problems involving any of the four operations and represent these problems using equations.

Type: Lesson Plan

From Array to Van De Walle 100-Dot Matrix:

This lesson builds upon student knowledge of arrays to using the Van de Walle 100-Dot Matrix model to solve multiplication problems involving rows and columns.

Type: Lesson Plan

Bridging Multiplication with Word Problems:

This introductory lesson uses word problems to help students make connections between arrays and multiplication with single and two-digit factors within 100.

Type: Lesson Plan

The Array Frame, your best friend:

In this lesson, students will learn to use the structure of array frames to build familiarity and fluency with the array as a tool. Students will explore multiplication by solving several multiplication word problems involving rows and columns situations using the array as a representation.

Type: Lesson Plan

The Distributive Property, Revealed! with a 100-dot matrix:

This lesson is designed as an introduction to the Distributive Property by using a 100-dot matrix. The lesson addresses one-digit x one-digit multiplication challenges as a precursor to one-digit x two-digit multiplication.

Type: Lesson Plan

Circles and Stars:

This is an introductory lesson to prepare students to move from using repeated addition to using multiplication to represent equal groups situations.

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

Table Top Problem:

In this Model Eliciting Activity, MEA, The Junior League needs the students' help to determine which table rental company to use for their Charity Auction. With a tight budget, limited time, and a mistake in the order, students must create a procedure for determining the best rental company, write an explanation about their procedure, and present their recommendations to the class.

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 work as a team to figure out which candidate is the best possible choice for the 8th grade boys' basketball coach. They will have to analyze data, decide on a procedure, and create a ranking system to choose the best candidate. They are also given multiplication and division problems based on the data.

Type: Lesson Plan

Sweet Donut Shop:

In this Model Eliciting Activity, MEA, students will help the Sweet Donut Shop determine what the newest donut will be. Students are given the cost to make each batch along with the selling price and are asked to determine the profit for each batch. Students create a procedure for ranking the donuts and write a letter explaining the procedure and the ranking. In the “twist” students are provided the starting and finishing times for each batch. They must determine the total amount of time, decide if their procedure should change based on the new information, and write a letter explaining whether the procedure changed and the new ranking of the donuts.

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

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

In this model eliciting activity students use data about the temperature and water requirements of plants to figure out when the plants should be planted. They also use data such as space requirements and time until harvest to make judgments about which plants would best suit the needs of students planning a school garden in Florida.

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

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

Pick a Pet:

In this MEA, students will rank pets from most family-friendly to least family-friendly by considering data such as purchase price, cost to feed, cleanliness, etc. as well as notes regarding the physical description of the pet. In the twist, students will be given information on additional pets as well as information on cleanliness and life expectancy. Students may need to make trade-offs in regards to cost to adopt, feed, and house along with life expectancy, ease of clean up, etc.

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

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.

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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Hungry Zero:

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

Type: Lesson Plan

Great Estimations!:

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

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

Area Architects, Lesson 4:

In this 5-lesson unit on area, students explore geometric measurement by becoming "Area Architects" in order to learn the concepts of area and relate area to multiplication and addition. In this 4th lesson, students will use tiling to show in a concrete case that the area of a rectangle can be found using the distributive property of multiplication. This lesson is focused on single-digit x single-digit dimensions using proper units for dimensions (e.g. ft, yd, m) and square units for the area (e.g. sq. ft, sq. yd, sq. m).

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

Lunchroom Logistics:

The principal needs help planning the school lunch schedule! Students will plan a lunch schedule to accommodate all of the students in the school. However, there can only be 100 students in the cafeteria at a time and only 20 students can sit at a table. Students will figure out how to arrange the lunch schedule so that every class eats together and so that certain grade levels are not together at the same time.

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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

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

## Perspectives Video: Teaching Ideas

Representing Remainders as Fractions:

Unlock an effective teaching strategy for representing remainders as fractions in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Making Connections with the Area Model:

Unlock an effective teaching strategy for making connections in area models in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

The Van de Walle Dot Matrix: A tool to support concepts from counting to multiplying polynomials:

Unlock an effective teaching tool that can help students all the way from basic counting principles to multiplying polynomials.

Dot Matrix sheet is available for dowload here.

Type: Perspectives Video: Teaching Idea

The Stamp Collection:

For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

Classroom Supplies:

The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.

## 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

The Stamp Collection:

For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity.

Classroom Supplies:

The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.

## Parent Resources

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