Understand the idea.
Explain more than the next answer
A helpful pattern explanation gives the starting value and the change, so another person can continue it. The bead stages show , and beads: each new stage keeps the earlier beads and adds three.
Giving only the next total does not describe how it was found. Say which quantity changes and by how much. For a growing bead pattern, “three beads are added each stage” explains more than simply naming eleven.
Check before predicting
Check a suggested step against each shown change. Here and , so add-three fits both moves. If the task gives that rule, use it consistently for later stages.
A short list alone can fit more than one rule. When the question says the step stays constant, use that condition. Otherwise describe the rule you are using without claiming that checking a few numbers proves it is the only possibility.
See the method in action.
Growing beads
Continue the bead diagram's add-3 rule for 2 more stages.
Worked solution
- 1
Check the changes in the shown stages.
Both pictured increases match the given add-three rule.
- 2
Find the next stage.
The next stage adds three beads to the last shown total.
- 3
Apply the rule for one more stage.
The following stage adds another three, giving eleven and fourteen beads.
11 and 14 beads.
Shrinking ribbon
A ribbon starts at 30 cm. Each step removes 4 cm. Explain its lengths after 3 steps.
Worked solution
- 1
Remove four centimetres for the first step.
The starting thirty centimetres is the length before any removal.
- 2
Repeat for the second step.
Use the remaining length from the first step.
- 3
Repeat for the third step.
The lengths after the three removals are twenty-six, twenty-two and eighteen centimetres.
26 cm, 22 cm and 18 cm; 4 cm is removed each step.
Try it yourself.
Check your understanding
A constant-step sequence is 10, 15, 20. Explain the next number.
Show answer & reasoning
25, because each step adds 5.
The constant step is and also . Add that same five to the last number: .
Keep practising
6 worksheet questions
Read the questions online
- A constant-step pattern is . Explain the rule and give the next number.
- Start at 24 and subtract 5 each time. Explain the next 3 numbers.
- A pattern starts at 2 and doubles. A child writes . Explain the mistake.
- Separate tables each seat 4 children. Explain the totals for tables.
- The constant-step sequence is . A child says 17. Explain and correct it.
- Explain how you know stage 4 of this bead pattern has 11 beads.
Read the worked solutions
- A constant-step pattern is . Explain the rule and give the next number.
; ; .
Add 4 each time; next is 15. - Start at 24 and subtract 5 each time. Explain the next 3 numbers.
; ; .
. - A pattern starts at 2 and doubles. A child writes . Explain the mistake.
Double 4 is 8; double 8 is 16.
The child added 2 instead of doubling. It should be . - Separate tables each seat 4 children. Explain the totals for tables.
, , .
seats. Each extra table adds 4 seats. - The constant-step sequence is . A child says 17. Explain and correct it.
Each shown step adds 5. , not 17.
The next number is 16. - Explain how you know stage 4 of this bead pattern has 11 beads.
Check and , then add another 3.
The stages have beads, adding 3 each time. Stage 4 has .
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Number sequences; step-by-step rules; decisions; explaining resulting patterns.
Official curriculum source ↗