Mathematics · Grade 4

Active learning ideas

Multiplication as Scaling and Arrays

Active learning works for multiplication as scaling and arrays because students need to see the visual shift from repeated addition to dimensional change. When students manipulate physical or drawn arrays, they build mental models that bridge concrete and abstract thinking, which is essential for fluency with larger numbers and future fraction work.

• Ontario Curriculum Expectations
• CCSS.MATH.CONTENT.4.NBT.B.5
• CCSS.MATH.CONTENT.4.OA.A.1

• 15–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Gallery Walk
• 30 min · Whole Class

Gallery Walk: Array Architects

Students create different arrays or area models for the same product (e.g., 24) on large paper. They walk around the room to see how many different 'shapes' the same number can take, noting the relationship between factors.

Explain how an area model helps visualize partial products in multiplication.

Facilitation Tip

During the Gallery Walk, assign each student or pair a unique multiplication problem to model on grid paper so the variety of examples sparks connections.

What to look for

Present students with a multiplication problem, such as 4 x 13. Ask them to draw an area model and label the partial products. Then, have them write a sentence explaining how their model shows the total product.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Inquiry Circle
• 40 min · Small Groups

Inquiry Circle: The Great Decomposer

Give groups a large multiplication problem like 14 x 18. They must use grid paper to cut the area into four smaller rectangles (partial products), calculate each, and tape them back together to find the total.

Compare multiplication and repeated addition, highlighting their differences despite similar totals.

Facilitation Tip

For The Great Decomposer, provide grid paper and colored pencils so students can clearly differentiate each partial product section.

What to look for

Pose the question: 'How is multiplying 5 x 6 different from adding 6 five times?' Facilitate a discussion where students use arrays or area models to explain their reasoning, focusing on the concept of scaling versus repeated summation.

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

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Doubling and Halving

Present a problem like 5 x 16. Ask students to halve 16 and double 5 to get 10 x 8. They discuss with a partner why this works and try it with other pairs of numbers to find 'friendly' products.

Analyze how doubling and halving strategies simplify complex multiplication problems.

Facilitation Tip

In Doubling and Halving, explicitly model the strategy on the board first, then ask students to explain their thinking to a partner before sharing with the class.

What to look for

Give students a multiplication problem like 12 x 8. Ask them to solve it using a doubling and halving strategy, showing their steps. For example, they might halve 12 to 6, double 8 to 16, then solve 6 x 16.

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

A few notes on teaching this unit

Experienced teachers approach this topic by starting with hands-on tools like square tiles or grid paper to build area models. They avoid rushing to the standard algorithm, instead emphasizing the connection between the visual rectangle and the numerical partial products. Research shows that students who spend time decomposing and recomposing rectangles develop deeper multiplicative reasoning, which supports their work with fractions and algebra later.

Successful learning looks like students confidently breaking multiplication problems into partial products using area models and arrays. They should explain how the two factors create a rectangle and how the total area represents the product, using precise mathematical language to describe their process.

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Watch Out for These Misconceptions

• During the Gallery Walk, watch for students who describe multiplication as 'just adding the same number many times' instead of seeing the rectangle's dimensions.

  Prompt them to trace the rows and columns with their fingers, asking, 'How many squares are in each row? How many rows are there?' to refocus on the array's structure as scaling.

• During The Great Decomposer, watch for students who skip adding all the partial products, especially the 'cross' products like 10 x 5.

  Have them use a different colored pencil for each section and add them step-by-step, writing the sum next to each color to ensure all parts are included.

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Methods used in this brief

• Gallery Walk
• Inquiry Circle
• Think-Pair-Share