The idea, step by step
Make a table before predicting
Write the step number beside each value. This stops you mixing up the number of steps with the amount at a step. A display with 4 tiles at step 1 and 3 more tiles each new step has 7 at step 2 and 10 at step 3.
To reach step 5 from step 1, make four jumps, not five. List the intervening values or count the extra groups. Both methods should agree.
| Step | Tiles |
|---|---|
| 1 | 4 |
| 2 | 7 |
| 3 | 10 |
| 4 | 13 |
Explain and check a prediction
Name the start, the change and the number of changes. I added 3 four times to 4 is clearer than I guessed 16. Check your method on a value already in the table.
A prediction assumes the stated rule continues. A table does not prove that a real quantity will grow forever. Read for limits such as a full box or a maximum number of seats.
A common trap
Step 6 means adding the increase six times to the step-1 value.
Instead: There are five jumps from step 1 to step 6. List the step numbers to count.
See the thinking
Count the jumps
A display has 4 tiles at step 1 and adds 3 each step. Find step 6.
- There are five jumps from step 1 to step 6.
- Five jumps add 5 × 3 = 15 tiles.
- 4 + 15 = 19. Check step 2: 4 + 3 = 7.
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?
- Five rounds add 5 × 7 = 35 counters.
- 5 + 35 = 40 counters.
- 40 is the capacity, so the box is exactly full.
Check your understanding
Step 1 has 6 tiles. Each new step adds 4. How many are at step 4?
Show answer
18 tiles
Three jumps add 12 tiles; 6 + 12 = 18.
Your turn
6 questions · 13 marks · Work at your own pace.
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
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 × 5 = 28.
28 - Complete the table for a rule that doubles each time.2 marks
Step Value 1 3 2 6 3 ? 4 ? 3 × 2 = 6; 6 × 2 = 12; 12 × 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 × 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 ÷ 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 ÷ 3 = 4.
Add 4: 9, 13, 17, 21.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics 2026
Additive/multiplicative rules; steps/decisions; predicting and explaining patterns.
Official curriculum source ↗