Properties of Multiplication

Active learning helps Primary 3 students see how multiplication properties make their work faster and more accurate. Hands-on experiences with counters and arrays let students test ideas themselves, building confidence in their calculations. This approach moves beyond memorization to true understanding of why properties work.

• Primary 3
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Compare the products of multiplication when the order of factors is changed using arrays.
2. Explain how the commutative property of multiplication simplifies calculations.
3. Apply the distributive property to decompose one factor in a multiplication problem into a sum.
4. Calculate the product of a multiplication problem by applying the distributive property.
5. Verify multiplication answers by using the commutative and distributive properties for mental checks.

Concept Mapping

⏱ 25 min·Pairs

Counter Swap: Commutative Exploration

Give pairs bags of 24 counters. Students form groups of 3 then 8, then swap to 8 then 3, noting equal totals. Record sentences and discuss why products match. Extend to other factors.

Prepare & details

Why does changing the order of factors not change the product?

Facilitation Tip: During Counter Swap, circulate and ask pairs to explain why their two factor arrangements still give the same total.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 35 min·Small Groups

Array Split: Distributive Stations

Set up stations with grid paper. At each, draw a 7 × 6 array, then break into 7 × 5 + 7 × 1. Groups rotate, calculate both ways, and compare. Share strategies class-wide.

Prepare & details

How can breaking a multiplication into smaller parts make it easier to calculate?

Facilitation Tip: In Array Split, remind groups to label each smaller array with equations to show the distributive breakdown.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 30 min·Whole Class

Property Relay: Mental Math Race

Divide class into teams. Call a fact like 9 × 7; first student computes using commutative or distributive, tags next. Teams verify with calculators after. Debrief winning strategies.

Prepare & details

Can you use these properties to check your multiplication answers mentally?

Facilitation Tip: Set a timer for Property Relay so students practice quick mental calculations while reinforcing property use.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 20 min·Pairs

Fact Family Cards: Property Matching

Print cards with facts like 4 × 5 = 20 and commutative/distributive variants. Students in pairs sort into families, write missing facts, and explain property used.

Prepare & details

Why does changing the order of factors not change the product?

Facilitation Tip: Use Fact Family Cards to have students verbally connect multiplication and division facts during the matching game.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Teaching This Topic

Teach these properties by starting with concrete models students can manipulate. Avoid rushing to abstract symbols before students have built mental images of why properties hold. Research shows that when students first experience properties through hands-on work, they develop stronger number sense and flexibility. Be patient with repeated explanations, as some students need multiple exposures before the concept clicks.

What to Expect

Students will explain how the commutative and distributive properties help solve multiplication problems. They will use manipulatives to model these properties, justify their reasoning, and apply them to new situations up to 10 × 10. Peer discussions and written explanations show clear understanding.

Watch Out for These Misconceptions

Common Misconception

During Counter Swap, watch for students who believe swapping the order of factors changes the product.

What to Teach Instead

Have partners rebuild their arrays after swapping to see they still produce the same total. Ask each pair to write an equation pair on the board to reinforce the commutative property visually.

Common Misconception

During Array Split, watch for students who avoid breaking numbers apart in multiplication.

What to Teach Instead

Ask students to trace their fingers along the array lines to see how one big grid splits into smaller, easier-to-count sections. Have them write the matching equations below each section to connect the visual with the math.

Common Misconception

During Property Relay, watch for students who think properties only work with small numbers.

What to Teach Instead

After the race, gather students to solve 9 × 8 together using both properties. Have them compare which method they found simpler, then try one more larger fact like 7 × 12 to generalize the concept.

Assessment Ideas

Quick Check

After Counter Swap and Array Split, present students with multiplication facts like 4 × 9. Ask them to write the answer and another fact with the same product, explaining which property they used. Then present 7 × 5 and ask them to show how they broke it apart using the distributive property.

Exit Ticket

After Property Relay, give each student a small card with: '1. Explain why 5 × 8 equals 8 × 5. 2. Show how to use the distributive property to solve 3 × 7. Write your steps clearly.' Collect these to check for precise property language and correct equation breakdowns.

Discussion Prompt

During Fact Family Cards, pose the question: 'Imagine you need to calculate 9 × 6. How could you use the commutative property to make it easier? Now, how could you use the distributive property to solve it? Discuss your strategies with a partner before writing your preferred method on the back of your card.'

Extensions & Scaffolding

• Challenge early finishers to create their own multiplication fact cards showing both the commutative and distributive versions of a fact.
• For struggling students, provide pre-partitioned array mats with dotted lines to guide their breaking apart of numbers.
• Give extra time for students to explore larger facts like 12 × 8 using both properties, comparing which method feels easier for them.

Key Vocabulary

Commutative Property	This property states that changing the order of the numbers being multiplied does not change the answer. For example, 7 x 3 is the same as 3 x 7.
Distributive Property	This property allows us to break apart a multiplication problem by splitting one of the numbers into a sum. For example, 5 x 6 can be calculated as 5 x (2 + 4), which is 5 x 2 + 5 x 4.
Factor	A number that is multiplied by another number to get a product. In 7 x 3 = 21, both 7 and 3 are factors.
Product	The answer to a multiplication problem. In 7 x 3 = 21, 21 is the product.