T

Number Patterns

Maths · Y3 Patterns
Year 3
Lesson Guide
Explanation
A number pattern is a line of numbers following a secret RULE. Look at 3, 6, 9, 12, 15 — the jump between neighbours is +3 every time, so the rule is 'add 3'. To crack any pattern, subtract neighbours and see if the jump repeats. Same jump every time = rule found!
Your Turn
Find the rule: 5, 10, 15, 20 … and 40, 36, 32, 28 … Check: add 5; and subtract 4.
Watch Out
Check the jump at least TWICE. One matching jump could be luck; two or three prove the rule.
Explanation
Patterns go two ways. GROWING patterns climb — 7, 14, 21, 28 — their rules add. SHRINKING patterns fall — 50, 45, 40, 35 — their rules subtract. So before hunting the jump size, ask the easy question first: are the numbers going up or down? That instantly tells you whether the rule adds or subtracts.
Your Turn
Up or down, and what rule? 60, 54, 48, 42 … Check: down, subtract 6.
Watch Out
Don't just read the first two numbers and guess — a pattern like 2, 4, 8, 16 doubles rather than adds 2!
Explanation
Continuing a pattern is two steps: crack the rule, then apply it. 4, 9, 14, 19, ▢, ▢: the jump is +5 (check it twice!), so next comes 19 + 5 = 24, then 24 + 5 = 29. Careful at the roll-overs — 19 + 5 crosses into the twenties. Say it as a bridge: 19 + 1 = 20, + 4 = 24.
Your Turn
Continue: 8, 16, 24, 32, ▢, ▢ and 90, 80, 70, ▢, ▢. Check: 40, 48; and 60, 50.
Watch Out
Apply the rule to the LAST number, not to the first. Each new number grows from the one before it.
Explanation
Sometimes the gap is in the MIDDLE: 6, 12, ▢, 24, 30. Find the rule from the pairs you can see: 12 − 6 = 6 and 30 − 24 = 6 — the rule is add 6. The hole is 12 + 6 = 18. Best part: you can double-check from the other side, 24 − 6 = 18. When both neighbours agree, you know you're right.
Your Turn
Fill the hole: 15, 20, ▢, 30, 35 and 44, ▢, 36, 32. Check: 25; and 40.
Watch Out
Always confirm with BOTH neighbours — forward from the left one AND backward from the right one.
Explanation
Patterns are everywhere: odd house numbers climb by 2, clock minutes by 5, weekly savings by 4. And the superpower of patterns is PREDICTION: saving $4 a week means you can say exactly how much you'll have in week 6 (24 dollars!) before it happens. Crack the rule, predict the future. Quiz time!
Your Turn
You save $5 each week. Predict: how much after 4 weeks? Check: 5, 10, 15, 20 → $20.
Watch Out
A prediction is only as good as its rule — check the rule twice before trusting it far into the future.
Step 1: Introduction
Step 1 of 5
A pattern follows a RULE 3 6 9 12 15 +3+3+3+3 3, 6, 9, 12, 15 … the rule is "add 3 each time". To find a rule: look at the JUMP between neighbours. 6 − 3 = 3, 9 − 6 = 3, 12 − 9 = 3 — same jump every time!
Up the stairs, down the stairs Growing (add): 7, 14, 21, 28, 35 … numbers get bigger — the rule ADDS Shrinking (subtract): 50, 45, 40, 35, 30 … numbers get smaller — the rule SUBTRACTS First question to ask: going UP or going DOWN? Up → the rule adds. Down → the rule subtracts.
What comes next? 4 9 14 19 ? ? Step 1: find the rule. 9 − 4 = 5, 14 − 9 = 5 → add 5. Step 2: keep it going. 19 + 5 = 24, then 24 + 5 = 29. 4, 9, 14, 19, 24, 29 ✓ Watch the tens roll over: 19 + 5 = 24!
A hole in the middle 6 12 ? 24 30 Use the numbers you CAN see: 12 − 6 = 6, and 30 − 24 = 6. Rule: add 6. So the hole holds 12 + 6 = 18. Double-check from the other side: 24 − 6 = 18 ✓ Both neighbours agree — the answer is safe!
Where patterns live 🌿 🏠 house numbers on one side 1, 3, 5, 7 … add 2 🕐 minutes on a clock face 5, 10, 15 … add 5 💰 saving $4 every week 4, 8, 12, 16 … add 4 🎂 candles each birthday 6, 7, 8, 9 … add 1 Patterns let you PREDICT the future. Quiz and exercises now!
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