Predicting and explaining patterns | Year 4

01 / LEARN

Understand the idea.

Make a table before predicting

Keep the step number separate from the amount at that step. In the tile table, step $1$ already has $4$ tiles. Each move to the next step adds $3$ , giving $7$ at step $2$ , then $10$ at step $3$ .

Count the jumps from the starting step to the target step. Moving from step $1$ to step $5$ takes four jumps. Either list all intervening values or multiply the increase by four, then include the starting amount.

A growing tile display
Step	Tiles
1	4
2	7
3	10
4	13

Explain and check a prediction

Explain a prediction with three pieces of information: the starting amount, the repeated change and the number of changes. Check your method against an earlier step from the table. This catches the common error of adding one extra increase.

A prediction uses the stated rule for as long as the situation allows. Read for a capacity or other limit before extending a practical pattern. Also distinguish a numbered step from a round of additions: five completed rounds mean five changes after the start.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Count the jumps

A display has 4 tiles at step 1 and adds 3 each step. Find step 6.

Worked solution

1
Count the moves after step one.
$6 - 1 = 5$
Step one already contains four tiles, so reaching step six takes five increases.
2
Find the total increase.
$5 \times 3 = 15$
Each of the five jumps adds three tiles.
3
Include the starting four tiles.
$4 + 15 = 19 tiles$
The final display contains both the original tiles and those added.
4
Check the method at step two.
$4 + 1 \times 3 = 7 tiles$
One jump from step one agrees with the earlier table value.

Answer

19 tiles.

EXAMPLE 02

Check a practical limit

A box holds 40 counters. It starts with 5 and gains 7 each round. Is it exactly full after five rounds?

Worked solution

1
Count the additions made in five rounds.
$5 \times 7 = 35 counters$
Each completed round adds seven counters after the initial five.
2
Include the counters already in the box.
$5 + 35 = 40 counters$
The final amount is the starting amount plus all five additions.
3
Compare with the capacity.
$40 = 40$
The final count equals the capacity, so the box is exactly full after five rounds.

Answer

Yes, 40 counters.

03 / YOUR TURN

Try it yourself.

Check your understanding

Step 1 has 6 tiles. Each new step adds 4. How many are at step 4?

Show answer & reasoning

18 tiles

From step $1$ to step $4$ there are $4 - 1 = 3$ jumps. These add $3 \times 4 = 12$ tiles, giving $6 + 12 = 18$ tiles in total.

Keep practising

6 worksheet questions · 13 marks

Open worksheet Worked solutions

Read the questions online

A pattern starts with 8 at step 1 and adds 5 each step. Find step 5.
2 marks
Complete the table for a rule that doubles each time.
2 marks
Step Value
1 3
2 6
3 ?
4 ?
Linked tables seat 4 people at step 1. Each extra table adds 2 seats. How many seats do 7 linked tables provide?
2 marks
A learner predicts that 21 follows 2, 6, 10, 14, 18. Check using the constant-addition rule.
2 marks
A tank starts with 10 litres. Each round adds 6 litres. It holds 40 litres. How many complete rounds fill it exactly?
2 marks
Make a constant-addition pattern with 9 at step 1 and 21 at step 4. State the rule and all four terms.
3 marks

Step	Value
1	3
2	6
3	?
4	?

Read the worked solutions

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

A pattern starts with 8 at step 1 and adds 5 each step. Find step 5.
2 marks
There are four jumps.
$8 + 4 \times 5 = 28$ .
28
Complete the table for a rule that doubles each time.
2 marks
Step Value
1 3
2 6
3 ?
4 ?
$3 \times 2 = 6$ ; $6 \times 2 = 12$ ; $12 \times 2 = 24$ .
Step 3: 12; step 4: 24
Linked tables seat 4 people at step 1. Each extra table adds 2 seats. How many seats do 7 linked tables provide?
2 marks
Seven tables are six additions after the first.
$4 + 6 \times 2 = 16$ .
16 seats
A learner predicts that 21 follows 2, 6, 10, 14, 18. Check using the constant-addition rule.
2 marks
Each jump adds 4.
$18 + 4 = 22$ .
22, not 21.
A tank starts with 10 litres. Each round adds 6 litres. It holds 40 litres. How many complete rounds fill it exactly?
2 marks
$40 - 10 = 30$ litres are needed.
$30 \div 6 = 5$ .
5 rounds
Make a constant-addition pattern with 9 at step 1 and 21 at step 4. State the rule and all four terms.
3 marks
There are three equal jumps.
$21 - 9 = 12$ ; $12 \div 3 = 4$ .
Add 4: 9, 13, 17, 21.

Step	Value
1	3
2	6
3	?
4	?

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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.

Make a table before predicting

Explain and check a prediction

See the method in action.

Count the jumps

Count the moves after step one.

Find the total increase.

Include the starting four tiles.

Check the method at step two.

Check a practical limit

Count the additions made in five rounds.

Include the counters already in the box.

Compare with the capacity.

Try it yourself.

Check your understanding

Keep practising