Understand the idea.
Count each stage
Count the objects in each stage of a growing pattern. If the totals are , each new stage gains two objects. To make the next stage, add another pair; enlarging the existing tiles would not increase their number.
Shapes can repeat or grow
A repeating pattern restarts the same unit, such as circle, square, square. A growing pattern changes the amount at each stage. Describe what repeats or what is added, then check the description against every stage shown.
| Stage | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Tiles | 2 | 4 | 6 | 8 |
See the method in action.
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?
Worked solution
- 1
Identify how the rows grow.
Each stage has one more row, so stage four has four rows.
- 2
Count the tiles in the first two rows.
Every row contains three tiles.
- 3
Include the other two rows.
Four equal rows of three contain twelve tiles in all.
12 tiles.
Find the repeating unit
Continue: circle, square, square, circle, square, square. What are the next three shapes?
Worked solution
- 1
Find a unit that repeats.
Circle, square, square occurs twice in the given list.
- 2
Restart that same unit.
The next three shapes are circle, square, square, in the same order.
Circle, square, square.
Try it yourself.
Check your understanding
Stages have 3, 5, 7 and 9 counters. How many at the next stage?
Show answer & reasoning
11 counters.
The totals increase by two each time. Add two to the last stage: counters.
Keep practising
6 worksheet questions
Read the questions online
- A row grows from 2 to 4 to 6 counters. How many at the next stage?
- A pattern has 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 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.
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 ↗