3.OA.3 - About the Math, Learning Targets, and Rigor

Grade 3 Multiplication and Division

3.OA.A.3

About the Math

Full Standard

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

**2nd Grade Students Learning 3rd Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
	Report Card Measurement Topic: Adds and subtracts to solve word problems.

About the Math

Skills and concepts below are learning goals for this standard.

To solve problems, we must understand the problem, select a strategy, and assess if our solution is reasonable. It is critical for students to develop these skills through practice and conversation. As teachers, we must be careful not to highlight or modify a singular approach to solving any one problem.

Represent a multiplication or division word problem with models, drawings, and equations.

Students should consistently represent problems. At first, physical models are necessary. In time, students should shift to drawings as appropriate. In all cases, students should connect an equation to their models or drawings. Note that representations should match the problem type. For example, baskets of apples should not be represented with an array or area model.

Working with Representations:

There are many ways that students can represent problems to solve them. We should be sure to encourage diverse representations. We also should be sure to connect representations. For example, it is important to connect drawingsand equations or physical models and equations. Bar diagrams are highly useful representations that help students develop an understanding of the relationships within a problem. Thinking Blocks Links to an external site. (pictured to the right) is an online resource that helps students develop an understanding of different problem solving situations by modeling them with bar diagrams.

Key Words:

Key words are not a viable strategy for solving word problems. Instead, we want students to make sense of problems and make use of their understanding to solve the problems. Moreover, research tells us that the use of key words as a strategy for solving problems adds to our students inability to solve problems.

Solve word problems with multiplication or division.

The chart to the right shows the different problem types for multiplication and division. It is important to note that students do not learn about multiplicative comparison until 4th grade.

Use estimation or related facts to determine if answers are reasonable.

We can help students develop a sense of reasonableness of their answers. One way to do this it to estimate the approximate solution of the problem before finding the exact solution.

Essential vocabulary for this standard includes: arrays, unknown, multiplication, division, array, product, factor, quotient, repeated addition, and repeated subtraction.

Progression of Standard within Grade 3

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Represent a multiplication or division word problem with models, drawings, and equations. Solve word problems with multiplication or division. Use estimation or related facts to determine if answers are reasonable.	Represent a multiplication or division word problem with models, drawings, and equations. Solve word problems with multiplication or division. Use estimation or related facts to determine if answers are reasonable.	Reinforce through work with problem solving with all operations.	Reinforce through work with problem solving with all operations.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade	Grade 4
This concept is not taught prior to grade 3.	Multiply/divide to solve multiplicative comparison word problems (4.OA.2)

Instructional Tasks

Tasks

These tasks can be used with small group or whole group instruction.

Give each student some color tiles. Pose the problem: Mr. Jarvis has 20 chairs and he wants to put 5 chairs in each row, how many rows will he make? Ask students to model the scenario using the color tiles and write what division equation is represented (20 ÷ 5). The model shows 4 rows to be the answer. Point out to students when looking at the expression 20 ÷ 5, they could think multiplication 5 x ? = 20 to also find the solution of 4. Collect the color tiles and pose a new scenario: Daquan is donating 30 books to the library. He will pack 5 books into each box. How many boxes will he need? Ask students to determine what operation this story problem represents. Ask students to write the division equation that matches the story. Finally ask students to practice "think multiplication" to find the answer. Repeat with other division scenarios, making the connection between using multiplication to find an unknown in a division equation.
Provide students with counters (cubes, two-sided counters, lima beans, etc.). Pose word problems involving multiplication or division (within 100). Just as with 3OA1 and 3OA2, ask students to represent the problem with the materials as well as with equations. Some examples include: There are 8 students in the dance club at school. Juan brought a bowl of 48 cherries to share among the members. How many cherries will each student get? In gym class, there are 5 teams with 5 players on each team. How many students are in the gym?
We need 52 juice boxes for our class party. Juice boxes come in packs of 6 or 8. How many packs of each do you need to have enough for each student?
Jim purchased 5 packages of muffins. Each package contained 3 muffins. Describe another situation where there would be 5 groups of 3 or 5 x 3.
The monkey keeper at the zoo needs 7 apples a day to help feed the monkeys. She has 50 apples at the start of the week. Will she have enough apples for the entire 7 day week ? Explain your reasoning.
Lisa has 30 shoes and says that she owns 12 pairs. Explain why she is correct or incorrect.
Write a word problem that the number sentence 72 ÷ 9 could be used to solve. Note: This is a way to increase rigor but is not required for demonstrating proficiency with this standard.
Write a word problem with the product of 35. Note: This is a way to increase rigor but is not required for demonstrating proficiency with this standard.

Slide-Based Tasks

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 6 • Multiplication & Division

Solve Multiplication and Division Word Problems:

Additional Tasks

These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.]

Analyzing Word Problems Involving Multiplication Links to an external site. (Illustrative Math)
Bikes and Trikes Links to an external site. (Inside Mathematics)
Two Interpretations of Division Links to an external site. (Illustrative Math)
Gifts from Grandma, Variation 1 Links to an external site.(Illustrative Math)
Fruit & Nut Links to an external site. (3 Act Task, G.Fletcher)
Seesaw Links to an external site. (3 Act Task, G.Fletcher)
A Squadron of Bugs Links to an external site. (NCTM Illuminations Lesson)
Ice Cream Scoops Links to an external site. (Georgia Department of Education, pages 174-179)
More Ideas Inspired by Teaching Student-Centered Mathematics

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Hands On Standards	1-2 3-4	56-57 (Repeated Subtraction) 58-59 (Equal Sharing) 24 (Multiplying with Arrays) 28 (Multiplying by 5) 34 (Finding Factor Pairs) 98 (Square Numbers)
Fundamentals	3	36 (Multiplication Mania) 40 (Climb the Ladder)
Problem Driven Math	3	124 - 126 (Mosquito Munch) 29 - 30 (Big Rigs) 90 - 92 (Keeping the Beat)
Brain-Compatible Activities for Mathematics	2-3	40-43 44-47
Developing Mathematics with Base Ten		44-46 67-70
Math Intervention: Building Number Power	3-5	82-84
Developing Number Concepts	Book 3	169-175 182-210
SuperSource: Pattern Blocks	K-2	34-37
NumberSense	3-4	59-61
Roads to Reasoning	2 3	66 (Pencil Put Away ) 20, 25, 51
Math In Practice Teaching Third-Grade Math	3	Module 1

Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Arranging Chairs Download Arranging Chairs
(HCPSS-adapted resource)

Independent Practice/Homework/Assessment

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

Solve Multiplication Word Problems:

Solve Division Word Problems:

Solve Multiplication and Division Word Problems:

Assessment

Full Standard

Measurement Topic

The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.

2nd Grade Students Learning 3rd Grade Standards by Measurement Topic

Adds and subtracts to solve word problems

Quarter 2

Represent a multiplication or division word problem with models, drawings, and equations.
Solve word problems within 100 with multiplication or division.

3OA3 Anecdotal Data Collection Tool Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) page in Course Essentials for more information and clarification.