3.OA.5 - About the Math, Learning Targets, and Rigor

Grade 3 Multiplication and Division

3.OA.5

About the Math

Full Standard

Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Measurement Topic

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

**3rd Grade Students Learning 3rd Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of multiplication.	Report Card Measurement Topic: Demonstrates understanding of multiplication.

Learning Targets

Explain and represent the commutative property (quarter 1).
Explain and represent the associative property (quarter 2)
Explain and represent distributive property (quarter 2)
Apply properties to recall basic facts or multiply with multiples of 10.

About the Math

distributive property Properties of arithmetic provide the conceptual foundations for computational strategies and the underpinnings of algebraic thinking. It can be effective to introduce these properties at a basic fact level so that students can apply them easily and understand the concept behind them. Students are not to simply recognize the properties in their algebraic form (e.g, a x b = b x a). Properties should be identified correctly. Created names for properties (e.g "flip flop") should not be used to describe the property. Students should use physical models and drawings to prove that the properties are true. Understanding of these properties is critical for fluency with basic facts and multi-digit computation in later grades.

Explain and represent the commutative property (quarter 1).

Commutative Property of multiplication states that two factors can be multiplied in either order and still have the same product. Students can make an array for 4 x 5 and then turn the array to see 5 X 4. The product is still 20. Understanding the commutative property helps students when learning the basic facts. They need to see that if they know 4 X 6 they also know 6 X4.

Explain and represent the associative property (quarter 2)

Associative Property of multiplication states that the way in which three or more factors are grouped before multiplying does not affect the product. Students often compute numbers based on the order in which they are given. Encourage students to look for friendly numbers when multiplying. For example 2 x 7 x 5, think 2 x 5 = 10 and 10 times 7 = 70. That is easier than saying 2 x 7 = 14 and 14 x 5 = 70.

Explain and represent distributive property (quarter 2)

Distributive property allows you to separate numbers into parts so that the numbers are easier to work with. The Distributive property tells you that you can multiply a sum by multiplying each addend separately and then adding the products. So, 4 x 7 = (4 x 2) + (4 x 5). As students progress to 4th grade, this will help with understanding of partial products such as 3 X 12 = (3 x 10) + (3 x 2).

Apply properties to recall basic facts or multiply with multiples of 10.

Multiplying by multiples of 10 is more than just adding a zero. Students need to understand why it works. 4 x 50 can be thought of as 4 x 5 x 10. The order can be arranged so that 5 x 4 is multiplied first and then 20 x 10.

See more about the distributive property Links to an external site.. Essential vocabulary for this standard includes: Commutative Property, Associative Property, and Distributive Property.

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.

Quarter 1	Quarter 2	Quarter 3	Quarter 4
Apply properties of operations as strategies to multiply and divide. If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.)	Apply properties of operations as strategies to multiply and divide. If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)	Commutative property as related to area.	Distributive property as related to area.

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.

Grade 2	Grade 4
	Multiplication with multi-digit factors (4.NBT.5) Division with multi-digit dividends (4.NBT.6)

Instructional Tasks

TASKs

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

Given a multiplication fact (i.e. 3x7), students work in pairs to represent the fact. Materials could include counters/cubes to make arrays and/or using the visual model of a number line. Discussion should focus on the commutative property and how representations may look differently (rows and columns, jumps on the number line) based on the interpretation of the order of the factors, but the product remains the same.
Melisha and Liz are working on a multiplication problem: 4x2x5, and Melisha says the answer is 8x5=40 and Liz says it is 4x10=40. Ask students to discuss and determine who they think is right and prove it (using physical or drawn models). The associative property should be the focus of the follow up debrief and instruction.
Thinking about 7x6, can you use counters/cubes to model this multiplication fact and show how you could break up the array in a way to use basic facts you already know to help you solve? Students can work in pairs/triads and record their thinking in their math journals as they work with the counters/cubes. The debrief and following explicit instruction should represent many different options for using the distributive property to help.
Eric says he has more donuts because his mom bought six boxes of four donuts each. Samantha says that she has more donuts because her mom bought four boxes, each with six donuts. Who is correct? Explain your thinking.
Melissa needs to solve 24 x 4 in her head. What strategy should she use?
Danielle is trying to multiply a strand of numbers (6 x 3 x 5) in her head but is having trouble keeping them organized in her head. Describe a strategy that she can use to solve the problem.
Malcolm multiplied 3 numbers together and got 24. What 3 numbers could he have multiplied? What strategy did you use to figure the numbers out?
Solve 8 x 7 using the distributive property. Could you distribute a different factor or distribute the same factor a different way?

Slide-BASED Tasks

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. When selected, a copy of the file is added to your drive for classroom use. 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 4 • Multiplication (Meaning and Representations) and Basic Facts (Multiply by 2)

Commutative Property:

Module 6 • Multiplication and Division

Associative Property:

The Great Debate Links to an external site.

Module 7 • Distributive Property & Multiples of Ten

Distributive Property:

Additional Tasks

These links provide instructional ideas connected to this standard.

Valid Equalities? (Part 2) Links to an external site. (Illustrative Math)
The Commutative Cookie Links to an external site. (Utah Education Network lesson)
Seating Arrangements Links to an external site. (Georgia Department of Education, pages 61-64)
Family Reunion Links to an external site. (Georgia Department of Education, pages 48-57)

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.

Book Title	Grade	Pages
Teaching Student-Centered Mathematics	K-3	86 (Slice It Up, Activity 3.8)
Hands On Standards	3-4	104-105 116 - 117 108-109 120 -121 122 -123
Math Intervention: Building Number Power	3-5	85-88 95-98 113-117 139-143
Math In Practice Teaching Third-Grade Math	3	Module 2

More Ideas

More Ideas Inspired by Teaching Student-Centered Mathematics

Independent Work

Centers

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

Turn Around Arrays Download Turn Around Arrays
(HCPSS-adapted resource )
How Low Can You Go? Associative Property Links to an external site. (HCPSS-adapted resource)
Array Cards Download Array Cards
(for Turn Around Arrays)

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.

Assessment

Learning Targets

Explain and represent the commutative property (quarter 2).
Explain and represent the associative property (quarter 2)
Explain and represent distributive property (quarter 2)
Apply properties to recall basic facts or multiply with multiples of 10.

Learning targets identify what students should be able to do. The resources below can be used to measure student understanding of the standard. This rubric can be applied to tasks and observations for assessment and/or grading.

Rubric for Tasks Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.