Math · Stage 4
Find the rule (nth term) of a growing pattern and extend it
Every growing pattern hides a rule. Spot the constant jump, write it as a times-rule, and you can leap straight to any term — even the 100th.
✦ Math📘 Stage 4 · S4⏱ ~12 min🧒 Ages 8–9★ Free to start
I can find the rule (nth term) of a growing pattern and extend it.
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Kavi and the Leaping Rule 🦉
Kavi spots a pattern growing: 4, 7, 10, 13… "Each step jumps the same amount," hoots Kavi. "If I find that jump, I don't have to count one-by-one — I can leap straight to the 100th shape!"
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What your child will learn
1A growing pattern climbs by the same jumpLook at the staircase. Step 1 has 4, step 2 has 7, step 3 has 10, step 4 has 13. Each bar is 3 taller than the one before. That steady jump is the common difference — the heartbeat of the pattern.
2The jump builds the times-tableA jump of 3 makes the pattern 3, 6, 9, 12… — the 3 times table. So the pattern is 3 × n plus a little adjustment. Tap Hop +3 to watch term 1, term 2, term 3 land.
3Rule = (jump × n) + the start-fixThe hops give 3, 6, 9, 12… but our pattern is 4, 7, 10, 13… — every term is 1 more. So the rule is 3 × n + 1. Check it: n=1 → 3+1 = 4 ✓, n=2 → 6+1 = 7 ✓. The lit numbers below are the 3-times hops.
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A peek inside
Find the rule of 5, 8, 11, 14…
jump = +3, so 3×n; term 1 is 5 but 3×1 = 3, so +2
Try this at home: What is the common difference (the steady jump)? 3, 7, 11, 15, …
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 4 · S4 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.