Mathematics · 3rd Year

Active learning ideas

Arrays and Area Models for Multiplication

Active learning lets students see how multiplication and division connect through equal grouping. When students manipulate objects or draw models, they build mental images that make abstract facts concrete. This topic needs movement and visuals because the inverse relationship between operations is easier to grasp when students can rearrange or split quantities with their hands.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Algebra

• 15–25 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Role Play
• 25 min · Small Groups

Role Play: The Fair Share Café

Students act as servers who must divide 'food items' (counters) equally among a set number of guests at a table. They must then write the division sentence and the 'check' multiplication sentence (e.g., 15 / 3 = 5 because 5 x 3 = 15) to prove the sharing was fair.

Analyze how an array shows that 3 times 4 is the same as 4 times 3.

Facilitation Tip

During The Fair Share Café, circulate with counters so you can immediately correct misplaced items when students confuse divisor and dividend.

What to look for

Give students a blank grid and ask them to draw an array for 5 x 7. Then, ask them to draw a second array for 7 x 5 and write one sentence explaining why the total number of squares is the same in both.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Fact Family Houses

Give pairs a set of three numbers (e.g., 2, 5, 10). They must work together to draw a 'house' and fill it with the four related facts (two multiplication, two division). They then explain to another pair how knowing one fact helps them solve the other three.

Explain the relationship between the rows in an array and the total count.

Facilitation Tip

When students work on Fact Family Houses, ask each pair to use one color for multiplication and another for division to make the inverse relationship visually clear.

What to look for

Present students with a multiplication problem, such as 6 x 8. Ask them to draw an area model for it. Then, ask them to show how they could split this area model into two smaller area models (e.g., 6 x 4 and 6 x 4) to find the same product.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Inquiry Circle
• 20 min · Small Groups

Inquiry Circle: The Remainder Riddle

Provide groups with sets of objects that don't divide evenly (e.g., 13 counters to share among 4 people). Students must decide what to do with the 'leftover' and debate whether it should be ignored, rounded up, or kept as a remainder, depending on the context provided.

Design a method to use an array to split a large multiplication into two smaller ones.

Facilitation Tip

For The Remainder Riddle, provide grid paper cut into strips so students can physically rearrange models to test different grouping strategies.

What to look for

Pose the question: 'How does an array help us understand that multiplication is the same no matter which number comes first?' Facilitate a discussion where students use their drawings and vocabulary to explain the commutative property.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

A few notes on teaching this unit

Teachers start with physical objects so students feel the ‘split’ in division before they write symbols. Avoid rushing to abstract notation; let students name their groups and record only after they can explain their actions. Research shows that students who draw arrays before writing equations retain the connection between operations longer, so model this process repeatedly.

Students will confidently use arrays and area models to show that multiplication and division are two sides of the same process. They will explain why 12 divided by 3 equals 4 by referencing their drawings of 3 groups of 4 items each. They will also use the commutative property to justify why 5 x 7 and 7 x 5 both total 35.

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Watch Out for These Misconceptions

• During The Fair Share Café, watch for students who assume dividing always makes the total smaller because they finish with fewer items on their plates.

  Have the class recount the total plates before and after sharing to show the quantity stays the same, just rearranged. Ask students to point to the original pile of counters to reinforce that division is splitting, not reducing.

• During Fact Family Houses, watch for students who write the divisor before the dividend in division sentences.

  Remind students to place the total counters on the table first, then build the groups. Label the house with ‘Total / Groups = Items per group’ so the order is always visible.

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Methods used in this brief

• Role Play
• Think-Pair-Share
• Inquiry Circle