Additive/multiplicative rules | Year 4

01 / LEARN

Understand the idea.

Look at each jump

Read a sequence from left to right and compare neighbouring terms. In $7, 12, 17, 22$ , each jump adds $5$ . An additive rule uses the same increase or decrease each time. Describe both the starting number and the repeated change.

Check every jump before continuing a pattern. Subtracting can also give a fixed change: $36, 30, 24, 18$ subtracts $6$ each time. When a question asks for five terms, the starting value counts as the first term.

Compare adding with multiplying

A multiplicative rule scales each term by the same factor. In $3, 6, 12, 24$ , the increases are different, but each term is twice the previous term. Adding three fits only the first jump and fails on the next one.

A short list may fit more than one possible rule. Here, look for a simple repeated operation that fits every given transition. State that rule, test it on the whole list, then use it to predict another term.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Continue an additive pattern

The rule is subtract 7. Start at 50. Write five terms.

Worked solution

1
Write the starting value as term one.
$50$
Five terms include the given starting term, so only four subtractions are needed.
2
Find terms two and three.
$\begin{aligned} 50 - 7 & = 43 \\ 43 - 7 & = 36 \end{aligned}$
Apply the same subtraction once for each move to a new term.
3
Find terms four and five.
$\begin{aligned} 36 - 7 & = 29 \\ 29 - 7 & = 22 \end{aligned}$
Two more moves complete four jumps from the first term.
4
Check the number of terms.
$50, 43, 36, 29, 22$
The list has five terms, and every neighbouring pair differs by seven.

Answer

50, 43, 36, 29, 22.

EXAMPLE 02

Check the type of rule

Describe a simple rule for 4, 12, 36, 108. Find the next term.

Worked solution

1
Test whether the increases are equal.
$\begin{aligned} 12 - 4 & = 8 \\ 36 - 12 & = 24 \\ 108 - 36 & = 72 \end{aligned}$
Different increases rule out one fixed-addition rule.
2
Check multiplication by three.
$\begin{aligned} 4 \times 3 & = 12 \\ 12 \times 3 & = 36 \\ 36 \times 3 & = 108 \end{aligned}$
The same multiplication fits every given transition.
3
Apply that rule to the final term.
$108 \times 3 = 324$
Continuing the multiply-by-three rule predicts 324 next.

Answer

Multiply by 3; next term 324.

03 / YOUR TURN

Try it yourself.

Check your understanding

The rule is add 8. What follows 11, 19, 27?

Show answer & reasoning

The next term is $27 + 8 = 35$ . The earlier moves, $11 + 8 = 19$ and $19 + 8 = 27$ , confirm that the same rule is being continued.

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

Continue 9, 15, 21, 27 with two more terms, using a constant addition rule.
2 marks
Start at 48 and halve each time. Write the first five terms.
2 marks
Fill the gap in 5, 10, __, 40, 80. Use a multiply-by-2 rule.
1 mark
Does add 4 fit every jump in 6, 10, 14, 19? Explain.
2 marks
A club saves 6 dollars each week. It has 13 dollars now. How much will it have after three more weeks?
2 marks
Create four terms starting at 7 using a multiply-by-3 rule.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Continue 9, 15, 21, 27 with two more terms, using a constant addition rule.
2 marks
Each jump adds 6.
$27 + 6 = 33$ ; $33 + 6 = 39$ .
33, 39
Start at 48 and halve each time. Write the first five terms.
2 marks
Include the starting number.
Divide by 2 four times.
48, 24, 12, 6, 3
Fill the gap in 5, 10, __, 40, 80. Use a multiply-by-2 rule.
1 mark
$10 \times 2 = 20$ .
$20 \times 2 = 40$ .
20
Does add 4 fit every jump in 6, 10, 14, 19? Explain.
2 marks
$10 - 6 = 4$ and $14 - 10 = 4$ .
$19 - 14 = 5$ , so add 4 does not fit all terms.
No. The last jump adds 5.
A club saves 6 dollars each week. It has 13 dollars now. How much will it have after three more weeks?
2 marks
Three weeks add $3 \times 6 = 18$ dollars.
$13 + 18 = 31$ dollars.
31 dollars
Create four terms starting at 7 using a multiply-by-3 rule.
2 marks
$7 \times 3 = 21$ ; $21 \times 3 = 63$ ; $63 \times 3 = 189$ .
7, 21, 63, 189

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics 2026

Additive/multiplicative rules; steps/decisions; predicting and explaining patterns.

Official curriculum source ↗

In this lesson

Understand the idea.

Look at each jump

Compare adding with multiplying

See the method in action.

Continue an additive pattern

Write the starting value as term one.

Find terms two and three.

Find terms four and five.

Check the number of terms.

Check the type of rule

Test whether the increases are equal.

Check multiplication by three.

Apply that rule to the final term.

Try it yourself.

Check your understanding

Keep practising