Explaining resulting patterns | Year 3

01 / LEARN

The idea, step by step

Explain more than the next answer

“The next number is 11” gives a result. “Start at 2 and add 3 each time” explains how someone else can continue the pattern.

In the bead pattern, stages have 2, 5 and 8 beads. Each new stage keeps the earlier beads and adds 3.

Check before predicting

Check the change at more than one stage. Here, $5 - 2 = 3$ and $8 - 5 = 3$ , so adding 3 fits both changes.

A short list can fit more than one rule. If a question gives a rule or says the step is constant, use that information. State your assumption rather than pretending a short list proves there is only one rule.

A common trap

Giving the next answer is a full explanation.

Instead: Include the starting value, the change and a check showing how the rule fits.

02 / WORKED EXAMPLES

See the thinking

Example 1

Growing beads

Continue the bead diagram's add-3 rule for 2 more stages.

Both shown increases are 3.
$8 + 3 = 11$ , then $11 + 3 = 14$ .

11 and 14 beads.

Example 2

Shrinking ribbon

A ribbon starts at 30 cm. Each step removes 4 cm. Explain its lengths after 3 steps.

$30 - 4 = 26$ cm.
$26 - 4 = 22$ cm, then $22 - 4 = 18$ cm.

26 cm, 22 cm and 18 cm; 4 cm is removed each step.

Check your understanding

A constant-step sequence is 10, 15, 20. Explain the next number.

Show answer

25, because each step adds 5.

$15 - 10 = 5$ and $20 - 15 = 5$ , so $20 + 5 = 25$ .

03 / WORKSHEET

Your turn

6 questions · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

A constant-step pattern is 3, 7, 11. 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 2, 4, 6, 8. Explain the mistake.
Separate tables each seat 4 children. Explain the totals for 1, 2 and 3 tables.
The constant-step sequence is 1, 6, 11, __. 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 3, 7, 11. Explain the rule and give the next number.
$7 - 3 = 4$ ; $11 - 7 = 4$ ; $11 + 4 = 15$ .
Add 4 each time; next is 15.
Start at 24 and subtract 5 each time. Explain the next 3 numbers.
$24 - 5 = 19$ ; $19 - 5 = 14$ ; $14 - 5 = 9$ .
19, 14, 9.
A pattern starts at 2 and doubles. A child writes 2, 4, 6, 8. Explain the mistake.
Double 4 is 8; double 8 is 16.
The child added 2 instead of doubling. It should be 2, 4, 8, 16.
Separate tables each seat 4 children. Explain the totals for 1, 2 and 3 tables.
$1 \times 4 = 4$ , $2 \times 4 = 8$ , $3 \times 4 = 12$ .
4, 8 and 12 seats. Each extra table adds 4 seats.
The constant-step sequence is 1, 6, 11, __. A child says 17. Explain and correct it.
Each shown step adds 5. $11 + 5 = 16$ , not 17.
The next number is 16.
Explain how you know stage 4 of this bead pattern has 11 beads.
Check $5 - 2 = 3$ and $8 - 5 = 3$ , then add another 3.
The stages have 2, 5 and 8 beads, adding 3 each time. Stage 4 has $8 + 3 = 11$ .

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Number sequences; step-by-step rules; decisions; explaining resulting patterns.

Official curriculum source ↗

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