Here is a row of squares built from matchsticks. One square takes 4 sticks. Two squares side by side take 7 sticks, because the middle stick is shared. Three squares take 10.
How many sticks will the fourth square row need? Have a guess before we build it.
Take three hands-up guesses, not open call-outs. Don't confirm yet — the fun is in whether the rule they sense ("about 3 more each time") holds. What made you say that number? is the question to press on.
Here are two growing patterns marked out along the number line. Each mark shows a count, and the gap between one mark and the next is the jump.
Here is a second pattern. Look at how big each gap is.
One of these grows by the same jump every time. The other grows by a jump that gets bigger. See if you can tell which is which from the gaps.
First line: point at the gap 4→7→10 and hold out for a pupil to name it as three. The rule is start at 4, add 3. Ask what the fourth mark would be before revealing it.
Second line: the gaps are 2, then 3, then 4 — growing by one each time. The on-screen line names those jumps, but still ask what pupils notice about the gaps first. This is the one that catches people who assume every pattern adds the same amount.
Say the rule in plain words a 10-year-old would use: how much more each time, and where it started.
Now we work two growing patterns together on the board. One pupil comes up to mark a count while the rest of the class watches and agrees or corrects out loud. The teacher re-sets the line for each new pattern.
First the matchstick squares. The counts so far are 4, 7, 10. Find the jump, mark the next counts, and say the rule. Keep going on the line to reach step 6 without laying out six rows.
Then a shrinking pattern starting 20, 16, 12. Find how the jump changes and mark what comes next.
Each time, mark the next count and say the rule out loud before we check it.
Talk this one through together — a pupil marks while the class agrees or corrects out loud.
Named order: matchstick squares 4 → 7 → 10 → 13 (rule: start at 4, add 3), then keep adding 3 on the line to reach 16, 19 for step 6 so the class sees the skip-ahead happen; then a shrinking pattern 20 → 16 → 12 (rule: take away 4). Reset the line between the two patterns.
Listen for pupils naming the starting count as well as the jump — a rule needs both. Show the count carrying on past step 4 so nobody thinks they must build every row.
In your maths copy, draw the first four steps of the "add 3 sticks" square pattern — one square, then two joined, then three, then four. Beside your drawing, make a pattern record table: one column for the step number and one column for the stick count. Fill in 4, 7, 10, 13. Then write the rule you found underneath.
This pattern record table is the one we keep using for the rest of the lesson. Walk the room glancing at the tables — check pupils are counting shared sticks once, not twice, at the joins. No individual marking; this is whole-class copybook practice, not assessment.
Now we investigate the "add 3 sticks" pattern all the way through, using the pattern record table you drew in your copy.
How many matchsticks does the row of squares need at each step, and what rule lets you predict a step you have not built?
Check counts 4, 7, 10, 13 in the pattern record table; write the rule in words; keep adding 3 to reach step 6 (19); continue the table to step 10 (31) and notice the count is 3 × step number + 1; explain how the table helped.
Record: the pattern record table (step number in one column, stick count in the other) plus a written rule and two predictions
Share back: one group reads its rule and its prediction for step 10, and the class checks it against the table
This is the practice round — groups work through the four parts and the class confirms each stage before moving on. Keep it brisk.
Look for:
If a group is stuck predicting step 10, point them back at the table: the counts already tell you the jump — keep adding 3 down the column.
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