Mathematics · Primary 6 · Integers and Rational Numbers · Semester 2

Multiplying and Dividing Integers

Applying rules for multiplication and division of positive and negative integers.

• MOE Syllabus Outcomes
• MOE: Integers - S1

About This Topic

Multiplying and dividing integers builds on students' understanding of positive and negative numbers by introducing sign rules. A positive times a positive or negative times a negative gives a positive result, while mixed signs produce negative. Division follows the same pattern: same signs yield positive quotients, different signs yield negative. Primary 6 students justify these rules, examine patterns in multiplication tables, and construct real-world problems such as calculating net gains from debts or temperature changes across zero.

In the MOE Integers and Rational Numbers unit, this topic develops computational accuracy and pattern recognition, key for rational numbers and algebra. Students analyze why (-2) × (-3) equals 6 through repeated addition or zero pairs, connecting operations to addition on number lines. Real contexts like bank transactions or elevations reinforce relevance in Singapore's data-driven curriculum.

Active learning benefits this topic greatly because rules feel arbitrary without visualization. Hands-on tools like two-color counters or number line relays let students discover patterns collaboratively, reducing errors and building confidence through peer explanations and tangible models.

Key Questions

1. Justify the rules for multiplying two negative integers resulting in a positive product.
2. Analyze the patterns that emerge when multiplying or dividing integers with different signs.
3. Construct a real-world problem that requires multiplication or division of negative numbers.

Learning Objectives

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

Before You Start

Understanding Positive and Negative Numbers

Why: Students must be able to identify and represent positive and negative numbers on a number line before performing operations with them.

Multiplication and Division of Whole Numbers

Why: Students need a solid foundation in the basic operations of multiplication and division before applying sign rules.

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).

Watch Out for These Misconceptions

Common Misconception

Two negatives always multiply to negative.

What to Teach Instead

Students often extend positive rules without pattern checks. Use chip pairing to show zero pairs cancel, leaving positives; active group discussions reveal the repeated addition logic, shifting mental models.

Common Misconception

Division sign rules differ from multiplication.

What to Teach Instead

Confusion arises from ignoring quotient signs. Number line relays demonstrate consistent patterns across operations; peer teaching in relays corrects this as students explain jumps to teammates.

Common Misconception

Signs can be ignored if absolute values match.

What to Teach Instead

This overlooks direction in negatives. Real-world scenario swaps force sign checks in solutions; collaborative verification highlights errors and reinforces rules through context.

Active Learning Ideas

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.

35 min·Small Groups

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.

25 min·Whole Class

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.

40 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.

30 min·Pairs

Real-World Connections

• Accountants use multiplication and division of negative numbers to track financial losses or debts. For example, if a company loses $500 each month for 3 months, the total change in their account is (-$500) x 3 = -$1500.
• Meteorologists use negative numbers to represent temperatures below freezing. Calculating the average temperature change over several days, especially across the freezing point, requires multiplying or dividing negative values.

Assessment Ideas

Quick Check

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.

Discussion Prompt

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.

Exit Ticket

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.

Frequently Asked Questions

How do you justify why negative times negative is positive?

Link to repeated addition: (-2)×(-3) as adding -2 three times equals adding +2 three times since negatives 'undo' each other. Use zero pairs in chips: each negative pair makes zero, even count leaves positive. Patterns in tables confirm across examples, building student-owned proofs.

What real-world examples work for integer operations?

Debts and credits: owing $5 twice is -10, but forgiving two $5 debts nets +10. Temperatures: dropping 3 degrees from -2 reaches -5; dividing rise by negatives models wind chill. Elevations or scores in games provide relatable Singapore contexts for practice.

How can active learning help with integer signs?

Manipulatives like counters visualize cancellations, while relays and pair swaps make rules experiential. Students discover patterns through movement and talk, not memorization. This cuts errors by 30-40% in MOE-aligned classes, as peers correct each other in real time.

What patterns emerge in integer multiplication tables?

Tables show quadrants: positive-positive positive, mixed negative, negative-negative positive. Diagonals mirror positives; rows flip signs predictably. Students spot these via color-coding grids, then predict divisions, solidifying rules for multi-step problems.