---
title: "Adding and subtracting integers"
subtitle: "Number Foundations · Integers · Lesson 2"
---

# Adding and subtracting integers

**Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}}

> **Key question:** A temperature that rises 9 degrees from −4 °C, a lift that goes down 5 floors from level 2, a bank balance below zero: all of them are moves along a number line.


:::teacher-note

**In one sentence:** Students add and subtract integers as moves on a number line, find that adding a negative moves left and that subtracting moves the opposite way to adding, so 5 − (−3) = 8 (AC9M7N07, node 2).

**Students should be able to say:** I can add and subtract integers by moving along a number line. I can explain why adding a negative number moves left. I can explain why 5 − (−3) is 8, not 2.

**Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet.

:::


## Predict

Start at 5. Which way does subtracting move you? Which way does the minus sign on $-3$ point?

:::keep-together

**What is $5 - (-3)$?**

☐ $-8$

☐ $2$

☐ $8$

☐ $-2$

My prediction, and why:

{{lines-3}}

:::


:::teacher-note

**What happens:** 5 − (−3) = 8. Adding −3 would move left 3; subtracting goes the opposite way, so it moves right 3, from 5 to 8.

:::


## Run

Try it on the board in the tutorial. Was your prediction right? What was different?

{{lines-2}}

## Which way to move


:::keep-together

### Moves on the line

Here is how to use the line for each kind of sum.

1. $-2 + 5$ — Start at the first number, $-2$.
2. $-2 + 5 = 3$ — Adding a positive moves right: 5 to the right lands on 3.
3. $4 + (-6) = -2$ — Adding a negative moves left: from 4, left 6 lands on $-2$.
4. $5 - (-3)$ — Subtracting moves the opposite way to adding.
5. $\text{adding } {-3} \text{ is left 3, so subtracting it is right 3}$ — Find the way adding would go, then turn round.
6. $5 - (-3) = 8$ — From 5, right 3 lands on 8. Subtracting $-3$ is the same as adding 3.

**Work out $4 + (-6)$.**

Answer: {{field-15}}

:::


:::teacher-note

**Answer:** -2

Start at 4. Adding −6 moves left 6: 3, 2, 1, 0, −1, −2.

:::


:::keep-together

### Find the mistake

**Mia works out $5 - (-3)$. Click the line where her working goes wrong.**

```
 1  Work out 5 − (−3) on a number line.
 2  Start at 5.
 3  The number is −3, so move 3 to the left.
 4  I land on 2, so 5 − (−3) = 2.
```

Line: {{field-15}}

Why is it wrong?

{{lines-2}}

:::


:::teacher-note

**Answer:** line 3

Line 3: adding −3 would move left 3, but this is subtracting, so the move is the opposite way: right 3. 5 − (−3) = 8.

:::


:::keep-together

### Right or left?

**From the first number, does each sum move right or left?**

Groups: Moves right, Moves left

- 2 + 3: {{field-15}}
- 2 + (−3): {{field-15}}
- 2 − 3: {{field-15}}
- 2 − (−3): {{field-15}}
- −5 + 4: {{field-15}}
- −2 − 4: {{field-15}}

:::


:::teacher-note

**Answer:** 2 + 3 → Moves right; 2 + (−3) → Moves left; 2 − 3 → Moves left; 2 − (−3) → Moves right; −5 + 4 → Moves right; −2 − 4 → Moves left

:::


:::typical

## One change at a time


**Adding across zero.** Each task changes one thing. First: start below zero and add a positive.

**Adding a negative.** Now the number you add is negative.

**Subtracting past zero.** A positive subtracted from a smaller number.

**Subtracting a negative.** The move from the Predict step.

**A number minus itself.** 

Work in the tutorial. Plan first: what will you change, and how will you test it?

{{box-4}}

:::


## Mixed sums


:::keep-together

### Adding

**Work out $-7 + 3$.**

Answer: {{field-15}}

:::


:::teacher-note

**Answer:** -4

From −7, right 3 lands on −4.

:::


:::keep-together

### Subtracting

**Work out $3 - 8$.**

Answer: {{field-15}}

:::


:::teacher-note

**Answer:** -5

From 3, left 8 lands on −5.

:::


:::keep-together

### A negative subtracted

**Work out $-2 - (-6)$.**

Answer: {{field-15}}

:::


:::teacher-note

**Answer:** 4

Subtracting −6 moves right 6: from −2 to 4.

:::


:::keep-together

### Temperature

**At 6 am it is $-4$ °C. By noon it is 9 degrees warmer. What is the temperature at noon?**

Answer: {{field-15}}

:::


:::teacher-note

**Answer:** 5

−4 + 9 = 5 °C.

:::


:::keep-together

### Review

**Review: which is greater, $-3$ or $-8$?**

☐ $-3$

☐ $-8$

:::


:::teacher-note

**Answer:** $-3$

−3 > −8: −3 is to the right of −8.

:::


## Make: a subtraction that grows

Use the + and − buttons and both sliders. The answer must be 10, and you must subtract a negative number.

Stretch: find two different subtractions that give $-3$, one subtracting a positive and one subtracting a negative.

Work in the tutorial. Plan first: what will you change, and how will you test it?

{{box-4}}

## Exit ticket

:::keep-together

**Work out −3 + 7, 2 − 9 and 4 − (−5).**

{{lines-3}}

:::


:::teacher-note

**Answer:** 4, −7 and 9.

:::