Mathematics · 3rd Year

Active learning ideas

Multiplication as Repeated Addition

Active learning works for multiplication as repeated addition because it moves students from abstract symbols to concrete, spatial understanding. Arrays and area models make the relationship between rows, columns, and totals visible, which helps students internalize multiplication as efficient counting rather than isolated facts.

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

• 15–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 25 min · Small Groups

Inquiry Circle: Array Scavenger Hunt

Students work in small groups to find 'natural' arrays around the classroom or school grounds (e.g., a tray of paints, a window pane, a muffin tin). They must record the array as a multiplication sentence and then 'rotate' it to show the commutative property.

Explain how repeated addition is connected to multiplication.

Facilitation Tip

During Array Scavenger Hunt, have students physically move along rows and columns to feel the directional difference before recording their findings.

What to look for

Present students with an image of 4 bags, each containing 5 apples. Ask them to write the repeated addition sentence and the corresponding multiplication sentence that represents the total number of apples.

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

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Array Switch

Give one student a multiplication fact (e.g., 4 x 5) and have them draw the array on a whiteboard. They then pass it to their partner, who must turn the board 90 degrees and write the new multiplication sentence (5 x 4) and the total, discussing why the answer stayed the same.

Construct a multiplication sentence from a given set of equal groups.

Facilitation Tip

In The Array Switch, ask pairs to verbalize their thinking about why the total remains the same when they swap rows and columns before writing anything.

What to look for

Give each student a card with a multiplication sentence, e.g., 5 x 3. Ask them to write the equivalent repeated addition sentence and draw a picture showing equal groups to represent the problem.

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

Activity 03

• Stations Rotation
• 30 min · Small Groups

Stations Rotation: Building Blocks of Area

Set up stations where students build arrays using different materials: one with LEGO bricks, one with square tiles, and one with digital grid tools. Each station has a 'target number' (e.g., 12), and students must find as many different arrays as possible that equal that number.

Compare the efficiency of repeated addition versus multiplication for large numbers.

Facilitation Tip

At Building Blocks of Area, circulate with scissors ready to help students cut arrays into smaller rectangles when they show signs of struggling to visualize the distributive property.

What to look for

Pose the question: 'Imagine you need to count 100 items arranged in groups. Would it be faster to use repeated addition or multiplication? Explain why, using an example with smaller numbers to illustrate your point.'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Experienced teachers approach this topic by starting with objects students can group, then moving to drawn arrays on grid paper before introducing area models. They avoid rushing to abstract symbols too soon, as students need repeated exposure to the grid structure to build automaticity. Research shows that students who physically manipulate arrays develop stronger mental models for multiplication facts and properties.

Successful learning looks like students confidently describing arrays using rows and columns, switching between repeated addition and multiplication sentences without hesitation, and explaining why 3 x 4 equals 4 x 3 using visual evidence from their work.

---

Watch Out for These Misconceptions

• During Array Scavenger Hunt, watch for students confusing rows and columns in their written descriptions.

  Ask students to stand at the edge of the array and walk along one row while saying, 'This is one row,' then walk down one column while saying, 'This is one column.' Have them repeat the mnemonic 'row across, column down' before recording their findings.

• During Building Blocks of Area, watch for students thinking multiplication only works with numbers that fit neatly in an array.

  Provide grid paper and scissors, then model cutting an 8 x 5 array into a 5 x 5 and a 3 x 5. Have students repeat this with their own arrays and write the equivalent equations to show the totals stay the same.

---

Methods used in this brief

• Inquiry Circle
• Think-Pair-Share
• Stations Rotation