**Integers on number lines** *KS3 Revision*

## What you need to know

**Things to remember:**

- Compare the difference between multiple pairs of numbers to see if it is going up by the same amount.
- We need to be careful numbers, especially when finding the difference between a pair of numbers where one is positive, and the other is negative.

Here we are going to be looking at sequences of integers and finding missing numbers.

*Find the missing number in the following sequence:*

5 10 15 ___ 25

We can do this in two steps:

**Step 1: **Choose two pairs of numbers that are next to each other and subtract the smallest from the biggest.

10-5=5

15-10=5

So, the difference is 5.

**Step 2: **Add or subtract the difference found in **Step 1 **to the number before the missing number.

Our numbers are increasing, so we want to add this difference.

15 + 5=20

So, the missing number is 20.

**Check: **We can use this number in Step 1 to check that the difference is the same.

25-20=5

This is the same difference, so our check tells us that our answer is correct!

How about when the number are decreasing? We can use the same steps.

** **

*Find the missing number in the following sequence:*

** **

5 1 -3 -7 ___

**Step 1: **Choose two pairs of numbers that are next to each other and subtract the smallest from the biggest.

*Hint: **When we subtract a negative number, it becomes an add!*

*Hint: **The “bigger” the number part of a negative number, the smaller it is.*

* *

5-1=4

-3- -7=-3+7=4

So, the difference is 4.

**Step 2: **Add or subtract the difference found in **Step 1 **to the number before the missing number.

Our numbers are decreasing, so we want to subtract this difference.

-7 -4 =-11

So, the missing number is -11.

**Check: **We can use this number in Step 1 to check that the difference is the same.

-7--11=-7+11=4

This is the same difference, so our check tells us that our answer is correct!

## Example Questions

**Question 1:** Find the missing number in the following sequence:

6 ___ 18 24

**Step 1: **Choose two pairs of numbers that are next to each other and subtract the smallest from the biggest.

30-24=6

24-18=6

So, the difference is 6.

**Step 2: **Add or subtract the difference found in **Step 1 **to the number before the missing number.

Our numbers are increasing, so we want to add this difference.

6 + 6=12

So, the missing number is 12.

**Check: **We can use this number in Step 1 to check that the difference is the same.

18 - 12=6

This is the same difference, so our check tells us that our answer is correct!

**Question 2:** Find the missing number in the following sequence:

-1 -3 -5 ___ -9

**Step 1: **Choose two pairs of numbers that are next to each other and subtract the smallest from the biggest.

*Hint: **When we subtract a negative number, it becomes an add!*

*Hint: **The “bigger” the number part of a negative number, the smaller it is.*

* *

-3--5=-3+5=2

-1--3=-1+3=2

So, the difference is 2.

**Step 2: **Add or subtract the difference found in **Step 1 **to the number before the missing number.

Our numbers are decreasing, so we want to subtract this difference.

-5 -2 =-7

So, the missing number is -7.

**Check: **We can use this number in Step 1 to check that the difference is the same.

-5--7=-5+7=2

This is the same difference, so our check tells us that our answer is correct!