The idea, step by step
Count each stage
A growing pattern adds objects in a planned way. If stage 1 has 2 tiles, stage 2 has 4 and stage 3 has 6, the number pattern is 2, 4, 6. Draw stage 4 by adding another pair, not by changing the size of each tile.
Shapes can repeat or grow
A repeating pattern repeats a unit such as circle, square, square. A growing pattern changes its amount, such as a row gaining 2 counters. Say which kind of pattern you see and describe its rule.
| Stage | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Tiles | 2 | 4 | 6 | 8 |
A common trap
Making the pictures larger instead of adding the stated number of objects.
Instead: The rule describes the number of tiles. Keep each tile the same size and add the next group.
See the thinking
Grow by one row
A tile pattern has 1 row of 3 at stage 1, 2 rows of 3 at stage 2 and 3 rows of 3 at stage 3. How many tiles at stage 4?
- Each new stage adds one row of 3.
- Four rows of 3 give 3 + 3 + 3 + 3 = 12.
Find the repeating unit
Continue: circle, square, square, circle, square, square. What are the next three shapes?
- The repeated unit is circle, square, square.
- Start the same unit again.
Check your understanding
Stages have 3, 5, 7 and 9 counters. How many at the next stage?
Show answer
11 counters.
Each stage adds 2 counters.
Your turn
6 questions · Work at your own pace.
Read the questions online
- A row grows from 2 to 4 to 6 counters. How many at the next stage?
- A pattern has 5, 10 and 15 tiles in its first three stages. How many in stage 4?
- Continue: triangle, circle, triangle, circle. Name the next two shapes.
- Stage 1 has 4 tiles. Each next stage adds 3 tiles. How many tiles in stage 3?
- Draw three stages starting with 1 dot and adding 2 dots each stage. Give the totals.
- A pattern goes square, square, circle, square, square, circle. Is it repeating or growing? Explain.
Read the worked solutions
- A row grows from 2 to 4 to 6 counters. How many at the next stage?
The row gains 2 counters each time.
8 counters. - A pattern has 5, 10 and 15 tiles in its first three stages. How many in stage 4?
Add 5 again.
20 tiles. - Continue: triangle, circle, triangle, circle. Name the next two shapes.
The two-shape unit repeats.
Triangle, circle. - Stage 1 has 4 tiles. Each next stage adds 3 tiles. How many tiles in stage 3?
Stage 2 has 7; stage 3 has 10.
10 tiles. - Draw three stages starting with 1 dot and adding 2 dots each stage. Give the totals.
Add 2 dots to the previous stage; many neat layouts are possible.
1, 3, 5 dots. - A pattern goes square, square, circle, square, square, circle. Is it repeating or growing? Explain.
The same three-shape unit starts again; the unit itself does not gain objects.
Repeating.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Constant increases/decreases; describing rules; missing terms; shape/number patterns.
Official curriculum source ↗