Mathematics · Class 1 · Number Systems and Operations · Term 1

Multiplying Integers

Students will learn and apply the rules for multiplying integers, including understanding the sign of the product.

• CBSE Learning Outcomes
• NCERT: Class 7, Chapter 1, Integers

About This Topic

Multiplying integers requires students to master rules for determining the sign of the product based on the factors involved. A positive times a positive gives positive, positive times negative or negative times positive gives negative, and negative times negative gives positive. Students practise these with two or more integers, counting negative factors to predict the sign: even number results in positive, odd in negative.

This topic appears in the CBSE Class 7 NCERT Chapter 1 on Integers, within Number Systems and Operations for Term 1. It extends prior knowledge of integer addition and subtraction, addressing key questions like justifying why two negatives multiply to positive, predicting signs for multiple factors, and constructing real-world scenarios such as profit-loss calculations or temperature drops below zero. These skills strengthen number sense and prepare for algebraic operations.

Active learning suits this topic well because abstract sign rules gain meaning through visual models and discussions. When students manipulate integer chips, draw number line jumps, or role-play debt scenarios in groups, they connect rules to patterns they discover themselves. This approach reduces errors, boosts confidence, and makes justification intuitive.

Key Questions

1. Justify why multiplying two negative integers results in a positive product.
2. Predict the sign of the product when multiplying multiple integers.
3. Construct real-world scenarios that require integer multiplication.

Learning Objectives

• Calculate the product of two or more integers, applying the rules for signs.
• Explain the rule for determining the sign of a product involving multiple negative integers.
• Compare the sign of a product when the number of negative factors changes.
• Construct word problems that require the multiplication of integers to solve.

Before You Start

Addition and Subtraction of Integers

Why: Students need a foundational understanding of how to add and subtract positive and negative numbers before they can effectively multiply them.

Multiplication of Whole Numbers

Why: Students must be proficient in basic multiplication facts and the process of multiplication before applying it to integers.

Key Vocabulary

Integer	A whole number (not a fraction) that can be positive, negative, or zero. Examples include -3, 0, 5.
Product	The result obtained when two or more numbers are multiplied together.
Positive Integer	An integer greater than zero. Multiplying two positive integers results in a positive product.
Negative Integer	An integer less than zero. Multiplying two negative integers results in a positive product.

Watch Out for These Misconceptions

Common Misconception

The product of two negative integers is negative.

What to Teach Instead

Students often extend subtraction logic incorrectly. Pair discussions with repeated addition on number lines show two negative jumps from zero land positive, revealing the pattern. Group chip models reinforce this visually.

Common Misconception

The sign of the product depends only on the first integer.

What to Teach Instead

This ignores factor pairs. Collaborative card games prompt students to test multiple examples, leading them to discover both signs matter. Class sharing corrects isolated thinking.

Common Misconception

You cannot multiply negative numbers meaningfully.

What to Teach Instead

Real-world scenarios like debts show relevance. Role-play activities in small groups build context, helping students justify rules through stories they create and debate.

Active Learning Ideas

Pairs: Sign Rule Card Game

Prepare cards with pairs or triples of integers. Pairs draw a card, predict the product's sign, state the rule, and verify by calculating. Switch roles after five rounds and discuss surprises as a class.

25 min·Pairs

Small Groups: Chip Multiplication Model

Provide two-colour chips for positive and negative values. Groups model multiplication as repeated addition, flip chips for negatives, and count final positives or negatives. Record patterns on charts and share with class.

35 min·Small Groups

Whole Class: Scenario Storytelling

Project a real-world prompt like bank debts or elevator floors. Class brainstorms integer multiplications, votes on signs, then justifies with rules. Teacher facilitates group presentations of solutions.

40 min·Whole Class

Individual: Number Line Jumps

Students draw number lines and mark jumps for multiplication, like -2 times 3 as three jumps of -2. Shade regions to visualise sign and magnitude, then explain in journals.

20 min·Individual

Real-World Connections

• Accountants use integer multiplication to calculate changes in company finances. For example, multiplying a daily loss (negative integer) by the number of days in a month shows the total monthly loss.
• Scientists tracking the temperature in polar regions might use integer multiplication. A drop of 2 degrees Celsius per hour (negative integer) over 5 hours would result in a total temperature change of -10 degrees Celsius.

Assessment Ideas

Quick Check

Present students with a series of multiplication problems on the board, such as (-3) x 4, 5 x (-2), and (-6) x (-7). Ask students to write down the answer and the sign for each problem on a mini-whiteboard or paper.

Discussion Prompt

Ask students: 'If you multiply -2 by itself three times, what will the sign of your answer be? Explain your reasoning using the rules we learned.' Facilitate a class discussion where students share their predictions and justifications.

Exit Ticket

Give each student a card with a scenario. For example: 'A diver descends 5 metres every minute. What is their position after 3 minutes?' Ask them to write the multiplication expression and its answer, including the correct sign.

Frequently Asked Questions

Why does multiplying two negative integers give a positive product?

Consider -3 times -2 as adding -3 twice to zero, but reverse direction for negatives: from zero, add +3 twice, reaching +6. This repeated addition model, explored via number lines in class, clarifies the rule. Students grasp it best when they draw jumps themselves and discuss patterns with peers.

What are real-world examples of multiplying integers?

Examples include owing Rs 5 daily for 3 days: -5 times 3 equals -15. Or rising 4 degrees below zero twice: -2 times -4 equals +8. Classroom storytelling activities let students invent and solve such problems, connecting abstract rules to daily life like banking or weather.

How can active learning help teach multiplying integers?

Active methods like chip models and group games make sign rules tangible. Students manipulate materials to see patterns, discuss predictions, and justify answers, shifting from rote memory to understanding. This reduces misconceptions and improves retention, as peer explanations solidify concepts during collaborative tasks.

How to predict the sign when multiplying multiple integers?

Count negative factors: even number gives positive product, odd gives negative. Practice with card sorts in pairs builds fluency. Students quickly apply this to triples like -2, 3, -4 by tallying two negatives for positive result, confirmed through class verification.