Mathematics · Primary 6

Active learning ideas

Multiplying and Dividing Integers

Students learn integer multiplication and division best by seeing and touching patterns, not just hearing rules. Active tasks let them test sign rules with physical models and real numbers, building confidence before abstract calculation.

• MOE Syllabus Outcomes
• MOE: Integers - S1

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Flipped Classroom
• 35 min · Small Groups

Chip Model: Sign Rules

Provide red chips for negatives and yellow for positives. Students pair chips to model multiplication, such as three pairs of red for (-2)×(-3). For division, group chips and remove pairs. Groups record results and signs on charts.

Justify the rules for multiplying two negative integers resulting in a positive product.

Facilitation Tip

During Chip Model: Sign Rules, circulate to ensure students pair red and yellow chips to create zero pairs and observe how cancellation leads to positive or negative totals.

What to look for

Present students with a series of equations, such as (-4) x (-5) = ?, (-6) x 7 = ?, and 12 / (-3) = ?. Ask them to write the answer and briefly explain the sign rule they applied for each.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Activity 02

• Flipped Classroom
• 25 min · Whole Class

Number Line Relay: Operations

Mark a class number line on the floor. Teams send one student at a time to jump for each factor or divisor, noting landing sign. Rotate roles and discuss patterns after five rounds.

Analyze the patterns that emerge when multiplying or dividing integers with different signs.

Facilitation Tip

In Number Line Relay: Operations, set clear jump directions and distances so students physically experience how repeated subtraction or addition aligns with division or multiplication by negatives.

What to look for

Ask students to explain why (-2) x (-3) = 6. Encourage them to use a method like repeated addition (adding -2 three times) or the concept of zero pairs to justify their answer. Facilitate peer discussion on different explanations.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Activity 03

• Flipped Classroom
• 40 min · Pairs

Scenario Creation: Real Problems

Give cards with contexts like debts or temperatures. Pairs write and solve multiplication or division problems, swap with another pair to check signs and justify answers.

Construct a real-world problem that requires multiplication or division of negative numbers.

Facilitation Tip

For Scenario Creation: Real Problems, model one example aloud to show how to translate a real situation into an equation and solve it step by step.

What to look for

Give each student a scenario: 'A diver descends 10 meters every minute. What is their position after 4 minutes?' Ask them to write the multiplication problem using negative numbers and calculate the final depth.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

Activity 04

• Flipped Classroom
• 30 min · Pairs

Pattern Table: Integer Grids

Pairs construct 5×5 multiplication tables for integers from -4 to 4. Highlight sign patterns in colors, then extend to division. Share findings in a class gallery walk.

Justify the rules for multiplying two negative integers resulting in a positive product.

Facilitation Tip

In Pattern Table: Integer Grids, guide students to highlight rows where products stay positive or switch signs to reinforce the sign rule through visual patterns.

What to look for

Present students with a series of equations, such as (-4) x (-5) = ?, (-6) x 7 = ?, and 12 / (-3) = ?. Ask them to write the answer and briefly explain the sign rule they applied for each.

• Understand
• Apply
• Analyze
• Self-Management
• Self-Awareness

A few notes on teaching this unit

Teachers should avoid teaching the sign rules as isolated facts. Instead, use concrete models first so students see the logic behind the rules through repeated actions and patterns. Research shows that when students reason from models before abstract calculations, they retain understanding longer and make fewer sign errors.

Students can confidently apply sign rules to multiply and divide integers, explain their reasoning with models or examples, and connect calculations to real-world contexts with accuracy.

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Watch Out for These Misconceptions

• During Chip Model: Sign Rules, watch for students pairing chips without forming zero pairs or canceling correctly.

  Have them rebuild each model slowly, counting red and yellow pairs aloud and removing matched sets to see why negative times negative gives positive.

• During Number Line Relay: Operations, watch for students ignoring direction when jumping left or right.

  Ask them to mark each jump with a plus or minus sign and explain how the sign affects the landing position before moving on.

• During Scenario Creation: Real Problems, watch for students ignoring signs when translating words into equations.

  Prompt them to highlight all negative words in the problem and match them to negative numbers in the equation before solving.

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Methods used in this brief

• Flipped Classroom