Sec 1 Maths Practice Page

Negative Numbers and Integer Operations

Learn how negative numbers work, how to compare integers, and how to add or minus negative integers using number lines and the elevator model.

This page is written for Secondary 1 students and teachers. Use it for class teaching, self-study, revision or printable practice.

Start learning Go to Practice 2A Go to Practice 2B Download PDF

Teri using an elevator to understand negative numbers and integer subtraction from B3 to Thinkel tuition

Learning goals

What you will learn

This page focuses on the first part of Chapter 2: negative numbers, integers, number lines, addition and minus with negative integers.

Understand negative numbersKnow that negative numbers are below zero and can represent basement floors, loss, debt or temperature below zero.

Compare integersUse the number line to decide which number is greater or smaller.

Add and minus integersUse movement: go up or right for add, and go down or left for minus.

Concept 1

Negative numbers

Negative numbers are numbers less than zero. They are useful when a value goes below a starting point or reference level.

Temperature

−4°C means 4 degrees below 0°C.

Basement floors

B1 means −1, B2 means −2, and B3 means −3.

Money

−$20 can mean a loss, debt or amount owed.

Important: 0 is the reference point. Positive numbers are above or to the right of 0. Negative numbers are below or to the left of 0.

Concept 2

Integers and the number line

Integers are whole numbers, zero and negative whole numbers. They do not include fractions or decimals.

−4

−3

−2

−1

Greater or smaller?

Numbers become greater as we move to the right. Numbers become smaller as we move to the left.

−2 is greater than −5 because −2 is to the right of −5.

−6 is smaller than −1 because −6 is to the left of −1.

Common trap

Do not compare negative numbers by only looking at the digit.

8 is greater than 3.

But −8 is smaller than −3.

That is because −8 is further left on the number line.

Concept 3

Elevator model: go up and go down

The elevator model helps students picture negative numbers clearly. Ground floor is 0. Floors above ground are positive. Basement floors are negative.

Teri starts at B3, goes up to Thinkel on Level 5, then goes down to B1 and B3.

Teaching rule

Go up = add

Go down = minus

B3 means −3Teri starts at the B3 carpark.

−3 + 8 = 5She goes up 8 floors to Level 5.

5 − 6 = −1She goes down 6 floors to B1.

−1 − 2 = −3She goes down 2 floors to B3.

Why −7 − 5 = −12

Start at −7. Minus 5 means go down 5 floors. You do not move towards 0. You reach −12.

−7 − 5 = −12

Concept 4

Adding integers

Adding a positive number moves right or up. Adding a negative number moves left or down.

Same direction

4 + 3 = 7

−4 + (−3) = −7

If both numbers move in the same direction, continue in that direction.

Different direction

5 + (−2) = 3

−5 + 2 = −3

When the signs are different, think about which side has the stronger movement.

Concept 5

Minusing integers

For this page, think of minus as movement down or left. This helps with examples such as −7 − 5.

Positive starting point

5 − 2 = 3

5 − 6 = −1

Start at 5. If you go down 6 floors, you pass 0 and reach −1.

Negative starting point

−1 − 2 = −3

−7 − 5 = −12

When you are already below zero, going down takes you to a lower number.

Teacher note: avoid saying “more” when explaining minus. Use “go down”, “move down”, “lower” and “reach”.

Practice Set 2A

Negative numbers, integers and number line

Try these questions first. They focus on recognising negative numbers, comparing integers and using number-line thinking.

Write the integer represented by B4.

Think of basement floors below ground.

Which is greater: −2 or −6?

Use their positions on the number line.

Arrange in ascending order: 3, −1, −5, 0, 2.

Arrange in descending order: −4, 1, −2, 5, 0.

A temperature changes from 2°C to −3°C. Did it go up or down?

A carpark level is labelled B2. What integer can represent this level?

Which number is smaller: −8 or −3?

Fill in the blank: −6, −5, −4, ___, −2.

Practice Set 2B

Adding and minusing negative integers

These questions focus on integer operations. Picture movement up, down, left or right.

Evaluate: 6 + (−4)

Evaluate: −3 + 8

Evaluate: −5 + (−7)

Evaluate: 4 − 9

Evaluate: −1 − 2

Evaluate: −7 − 5

Teri starts at B2. She goes up 5 floors. Which level does she reach?

Teri starts at Level 4. She goes down 7 floors. Which level does she reach?

A lift starts at −3 and goes up 6 floors. Write the calculation and answer.

A lift starts at −4 and goes down 3 floors. Write the calculation and answer.

Mixed practice

Mixed questions

Use these questions to check whether students can switch between comparison, number lines and operations.

Arrange in ascending order: −7, −2, 4, 0, −5.

Evaluate: −9 + 4

Evaluate: −2 − 6

Evaluate: 3 − 8 + 2

A diver is at −6 m. He moves up 4 m. What is his new position?

A lift is at Level 2. It goes down 5 floors, then up 3 floors. Where does it stop?

Explain why −10 is smaller than −4.

Explain why −6 − 4 = −10 using the elevator model.

Download printable PDF

Answers

Answers and explanations

Use these answers after students have attempted the questions.

Practice Set 2A answers

1. B4 = −4

2. −2 is greater

3. −5, −1, 0, 2, 3

4. 5, 1, 0, −2, −4

5. It went down

6. B2 = −2

7. −8 is smaller

8. −3

Practice Set 2B answers

1. 2

2. 5

3. −12

4. −5

5. −3

6. −12

7. B2 = −2. −2 + 5 = 3. She reaches Level 3.

8. 4 − 7 = −3. She reaches B3.

9. −3 + 6 = 3

10. −4 − 3 = −7

Mixed practice answers

1. −7, −5, −2, 0, 4

2. −5

3. −8

4. −3

5. −6 + 4 = −2 m

6. 2 − 5 + 3 = 0. It stops at ground floor.

7. −10 is further left on the number line than −4.

8. Start at −6. Minus 4 means go down 4 floors. You reach −10.

Teacher notes

Teaching notes and common misconceptions

Common misconceptions

Thinking −8 is greater than −3Use the number line. −8 is further left, so it is smaller.

Thinking minus always moves towards zeroUse −7 − 5. Start at −7, go down 5 floors, reach −12.

Confusing add and minus movementKeep repeating: go up = add, go down = minus.

Suggested classroom flow

Start with the elevator imageLet students point to 0, positive floors and basement floors.

Move to the number lineShow that the same idea appears left and right on the number line.

Then practise calculationsAsk students to say the movement before writing the answer.

Next step

After students are confident with negative numbers and integer operations, continue with multiplication, division, fractions, decimals and real numbers.

Go to Practice Page 2 Back to Chapter 2 Overview