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.

• Primary 6
• Mathematics
• 4 activities
• 25 min–40 min

Learning Objectives

1. Calculate the product of two negative integers using the concept of repeated addition or zero pairs.
2. Explain the rule for multiplying integers with different signs, demonstrating with examples.
3. Analyze patterns in multiplication tables to justify why the product of two negative integers is positive.
4. Construct a word problem involving the division of negative integers to represent a real-world scenario.
5. Compare the results of multiplying and dividing integers with same signs versus different signs.

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.

Prepare & details

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.

Setup: Standard classroom, flexible for group activities during class

Materials: Pre-class content (video/reading with guiding questions), Readiness check or entrance ticket, In-class application activity, Reflection journal

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

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.

Prepare & details

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.

Setup: Standard classroom, flexible for group activities during class

Materials: Pre-class content (video/reading with guiding questions), Readiness check or entrance ticket, In-class application activity, Reflection journal

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

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.

Prepare & details

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.

Setup: Standard classroom, flexible for group activities during class

Materials: Pre-class content (video/reading with guiding questions), Readiness check or entrance ticket, In-class application activity, Reflection journal

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

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.

Prepare & details

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.

Setup: Standard classroom, flexible for group activities during class

Materials: Pre-class content (video/reading with guiding questions), Readiness check or entrance ticket, In-class application activity, Reflection journal

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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

Common Misconception

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

What to Teach Instead

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

Common Misconception

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

What to Teach Instead

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

Assessment Ideas

Quick Check

After Chip Model: Sign Rules, present a short set of equations such as (-3) x (-4) = ?, 8 / (-2) = ?, and (-5) x 6 = ?. Ask students to write answers and explain the sign rule they used in one sentence each.

Discussion Prompt

During Number Line Relay: Operations, ask a volunteer to demonstrate their team’s solution on the number line and explain how the jumps match the equation. Invite peers to ask questions or propose alternative solutions using the same model.

Exit Ticket

After Scenario Creation: Real Problems, give each student a temperature change scenario, such as 'The temperature dropped 3 degrees every hour for 5 hours. What was the total change?' Ask them to write the multiplication problem with negative numbers and calculate the final change.

Extensions & Scaffolding

• Challenge students to create a three-step word problem using negative multiplication and division, then solve a peer’s problem and check their work together.
• For students who struggle, provide partially completed chip models or number lines with marked jumps to scaffold the process.
• Allow advanced students to explore how negative exponents follow the same sign rules by extending their integer grid patterns into powers.

Key Vocabulary

Integer	A whole number that can be positive, negative, or zero. Examples include -3, 0, and 5.
Product	The result of multiplying two or more numbers together.
Quotient	The result of dividing one number by another.
Zero pairs	A pair of numbers that add up to zero, such as a positive number and its negative counterpart (e.g., 3 and -3).