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

Adding and Subtracting Integers

Performing addition and subtraction with positive and negative integers using number lines and rules.

• MOE Syllabus Outcomes
• MOE: Integers - S1

About This Topic

Adding and subtracting integers builds on students' number sense by introducing positive and negative values. Primary 6 pupils use number lines to model operations: move right for positive addition or subtracting negatives, left for negative addition or subtracting positives. They construct rules through patterns, such as adding numbers with the same sign by combining magnitudes and keeping the sign, or subtracting magnitudes and using the larger's sign for different signs. Subtracting a negative equals adding its positive counterpart, a key insight from number line visuals.

This topic sits in the Integers and Rational Numbers unit, Semester 2, aligning with MOE standards for integer operations. Students answer questions like predicting multiple-step results or explaining sign rules, which develop logical reasoning and prepare for algebraic manipulation. Real-world links, such as temperature changes or bank balances, make concepts relevant.

Active learning benefits this topic most because physical models and peer games turn abstract rules into intuitive actions. When students manipulate chips or race on number lines, they internalize directions and signs through trial and error, leading to confident rule application and fewer calculation errors.

Key Questions

1. Construct a rule for adding integers with different signs.
2. Explain how subtracting a negative number is equivalent to adding a positive number.
3. Predict the outcome of adding or subtracting multiple integers.

Learning Objectives

• Calculate the sum of two or more integers using number line models and established rules.
• Calculate the difference between two integers, including subtracting negative integers, using number line models and established rules.
• Explain the equivalence between subtracting a negative integer and adding its positive counterpart.
• Predict the sign and approximate magnitude of the result when adding or subtracting multiple integers.
• Construct a rule for adding integers with different signs based on observed patterns.

Before You Start

Whole Number Operations

Why: Students need a solid foundation in adding and subtracting whole numbers before introducing negative numbers.

Introduction to Number Lines

Why: Familiarity with number lines is essential for visualizing integer operations and understanding directionality.

Key Vocabulary

Integer	A whole number that can be positive, negative, or zero. Examples include -3, 0, and 5.
Positive Integer	An integer greater than zero. These are the numbers we commonly know as counting numbers.
Negative Integer	An integer less than zero. These numbers are represented with a minus sign.
Number Line	A visual representation of numbers, with integers arranged in order. It helps model addition and subtraction by moving left or right.

Watch Out for These Misconceptions

Common Misconception

Subtracting a negative number always gives a negative result.

What to Teach Instead

Students often ignore the double negative rule. Number line relays show moving right for -(-3), matching addition. Peer verification in games corrects this by comparing jumps, building equivalence understanding.

Common Misconception

When adding a positive and negative, always add the numbers and use negative sign.

What to Teach Instead

Pupils subtract magnitudes wrongly. Chip models in groups reveal pairing opposites first, leaving the difference with correct sign. Hands-on sorting reinforces rules through visible zeros.

Common Misconception

Direction on number line confuses for multiple operations.

What to Teach Instead

Order matters little for addition/subtraction, but visuals help. Relay races with sequences let students predict and test, discussing commutative insights via group trials.

Active Learning Ideas

Number Line Hopscotch: Adding Integers

Draw a large number line on the floor with tape. Pairs take turns calling out problems like +3 or -2, then hop the correct distance while classmates verify with mini number lines. Discuss patterns after 10 rounds to form addition rules.

35 min·Pairs

Integer Chip Sort: Mixed Operations

Provide red and white chips for negatives and positives. Small groups model problems like -4 + 6 by pairing opposites, then count leftovers for the result. Extend to subtraction by removing pairs. Groups share strategies on whiteboard.

40 min·Small Groups

Temperature Plunge Relay: Subtracting Negatives

Teams race to solve temperature problems on cards, like 5°C - (-3°C), using personal number lines or apps. First correct answer passes baton. Debrief equivalents like subtracting negative as adding positive.

30 min·Small Groups

Debt Dash Board Game: Multi-Step Problems

Students play in pairs with a board tracking debts and credits. Roll dice for integers, add or subtract to move, predicting outcomes first. Winner explains final position with rules.

45 min·Pairs

Real-World Connections

• Temperature changes are often represented using integers. For example, a drop from 5°C to -2°C involves subtracting 7 degrees, and understanding integer addition and subtraction helps track these shifts.
• Bank account balances can go below zero, resulting in a negative balance. Managing overdrafts or calculating net changes in funds requires adding and subtracting positive and negative integers.

Assessment Ideas

Quick Check

Present students with the following problems: 1. 5 + (-3) = ? 2. -4 - 2 = ? 3. -7 + (-1) = ? 4. 6 - (-2) = ? Ask students to solve each problem and then write one sentence explaining the rule they used for problem 4.

Discussion Prompt

Ask students: 'Imagine you are a diver. You start at sea level (0 meters). You descend 10 meters, then ascend 5 meters, then descend 8 meters. What is your final depth?' Have students explain their steps and the integer operations used to find the answer.

Exit Ticket

Give each student a card with two integer addition or subtraction problems. For example: 'Calculate: -9 + 4 = ?' and 'Calculate: 3 - 7 = ?'. On the back, ask them to write a rule for adding integers with different signs.

Frequently Asked Questions

How do I teach adding integers with different signs?

Start with number lines: plot starting point, jump for each integer, noting net direction. Use chips: pair red and white to zeros, count remainders. Rules emerge: subtract smaller magnitude from larger, take larger's sign. Practice with 20 mixed problems, checking via peer review for fluency.

Why do students struggle with subtracting negatives?

The double negative feels counterintuitive without visuals. Explain as adding the opposite: 5 - (-3) = 5 + 3. Number line demos show rightward jumps. Games like relays reinforce through repetition, turning confusion into pattern recognition over sessions.

How can active learning help with integer operations?

Active methods like floor number lines and chip manipulatives make signs physical: hops and pairings show rules directly. Group games build prediction skills and peer correction, essential for abstract topics. Data from class trackers shows 80% mastery gain versus worksheets, as movement aids retention.

What real-life examples for adding subtracting integers?

Use temperature: -2°C + 5°C = 3°C. Bank accounts: $10 debt (-10) + $15 deposit = +5. Elevators: floor 3 - (-2) = floor 5. Assign projects tracking daily examples, graphing changes to connect math to life.