Number sequences | Year 3 | Ascent Library

01 / LEARN

The idea, step by step

A number sequence is an ordered list that follows a rule. Some sequences add the same amount each time. Others subtract the same amount each time.

Compare neighbours. In 4, 8, 12, 16, every change is add 4. Check more than one pair before choosing a rule.

A sequence starting at 20 and subtracting 3 continues 17, 14, 11. Use the same rule at every step.

A missing number in the middle must fit both sides. In 5, 10, __, 20 with an add-5 rule, the missing number is 15.

An add-4 sequence
Position	1	2	3	4	5
Number	3	7	11	15	19

Check only the first pair of numbers before choosing a rule.

Instead: A repeated rule must fit every shown step.

02 / WORKED EXAMPLES

Example 1

Start at 6 and add 4 each time. Write the first 4 numbers.

6, 10, 14, 18.

Example 2

The rule is subtract 3. Complete 22, 19, __, 13.

16.

The rule is add 6. What follows 2, 8, 14?

Show answer

20.

$14 + 6 = 20$ . Both earlier changes also add 6.

03 / WORKSHEET

6 questions · Work at your own pace.

Read the questions online

Start at 3 and add 3 each time. Write 5 numbers.
Start at 18 and subtract 2 each time. Write 4 numbers.
The rule is add 5. Fill the gap: 7, 12, __, 22.
The sequence 4, 8, 12, 16 has a constant step. Describe it.
The rule is add 3. Correct the error: 6, 9, 12, 16, 18.
A child saves 4 stickers each day. The total after day 1 is 4. Give the totals after days 2, 3 and 4.

Read the worked solutions

Start at 3 and add 3 each time. Write 5 numbers.
Add 3 four times after the starting number.
3, 6, 9, 12, 15.
Start at 18 and subtract 2 each time. Write 4 numbers.
Subtract 2 from each previous number.
18, 16, 14, 12.
The rule is add 5. Fill the gap: 7, 12, __, 22.
$12 + 5 = 17$ and $17 + 5 = 22$ .
17.
The sequence 4, 8, 12, 16 has a constant step. Describe it.
Each pair of neighbours differs by 4.
Add 4 each time.
The rule is add 3. Correct the error: 6, 9, 12, 16, 18.
$12 + 3 = 15$ and $15 + 3 = 18$ .
16 should be 15.
A child saves 4 stickers each day. The total after day 1 is 4. Give the totals after days 2, 3 and 4.
Add 4 for each extra day.
8, 12 and 16 stickers.

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Step-by-step rules

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Number sequences; step-by-step rules; decisions; explaining resulting patterns.