Year 6 · Algebra & Patterns

Pattern Detective's Toolkit

How to crack pattern questions — find the rule, use it, and never lose marks on your working. 🦘

5-step plan Exam working checklist Double-check habit Trap alerts Print & keep
"Line them up, find the gap, write the rule, check the map — then DOUBLE-CHECK, it's the winning wrap!"Remember the motto — it is the whole method in one line. 💡

🧭 The 5-Step Pattern Plan

Every pattern question is solved the same way. Follow the steps IN ORDER — never jump straight to guessing the answer, and never skip the final double-check.

Step 1 · 👀 See

Line them up

Write the numbers (or shapes) in a neat row, and label each one with its position: 1st, 2nd, 3rd…

Example: 8, 13, 18, 23, …
Label it: 1st:8  2nd:13  3rd:18  4th:23
Step 2 · 🔍 Diff

Find the gap

Subtract neighbours. Same gap every time? → it's add/subtract. Gaps growing? → check the gap's own pattern.

8 → 13 is +5, 13 → 18 is +5, 18 → 23 is +5. Same gap! ✅
Step 3 · ✏️ Rule

Write the rule

Rule = first number + gap × (position − 1). Or spot the times-table plus a leftover.

8 + 5 × (position − 1). For position 12: 8 + 5 × 11 = 63
Step 4 · ✅ Check & answer

Test it, then answer

Test the rule at position 1 and 2. Then write the answer as a full sentence with units.

Check: pos 1 → 8 + 5 × 0 = 8 ✓  pos 2 → 13 ✓
"The 12th number is 63."
Step 5 · 🔄 Double Check

Check it twice!

Finished? Not yet! Re-read the question, put your answer back into the pattern, and work backwards to prove it fits.

63 − 5 = 58 → that's term 11? ✅ So term 12 = 63 is right!

🔎 One Pattern, Four Steps — Watch It Work

The rule "first + gap × (position − 1)" is your best friend. Here is the whole method on one question:

🦘 Kangaroo counting: 2, 6, 10, 14, … What is the 20th number?

"The gap is +4 every time, so I write the rule: 2 + 4 × (position − 1)."
1
See: 2, 6, 10, 14 labelled 1st, 2nd, 3rd, 4th.
2
Diff: +4 each time — same gap. ✅
3
Rule: 2 + 4 × (position − 1). For position 20: 2 + 4 × 19 = 78
4
Check: pos 1 → 2 ✓; pos 2 → 6 ✓. Answer: the 20th number is 78.

📋 Exam Working Checklist — Don't Lose Marks!

In a test, you get marks for the WORKING, not just the answer. Tick every box before you move on.

Show your working so you never lose a mark ✔

Tick each one as you do it — this is exactly what the marker is looking for.

Label the positions. Write 1st, 2nd, 3rd… above the terms.Why: it proves you know which term is which — and makes "position − 1" make sense.
Show at least TWO gaps. e.g. "13 − 8 = 5 and 18 − 13 = 5".Why: one gap could be a coincidence — two gaps prove the rule.
Write the rule. "8 + 5 × (position − 1)" or "start at 8, add 5".Why: this is usually where the marks are — the rule, not the final number.
Substitute and check. Test the rule at position 1 and position 2.Why: a wrong rule caught early is a wrong rule not carried into the answer.
Answer in a full sentence with units. "The 12th term is 63." Not just "63".Why: worded questions give a mark for the sentence and units (shells, dollars, flags…).
Reverse questions: set it up, don't guess. "5 + 4 × (day − 1) = 41" then solve.Why: guessing eats time and usually misses; writing the equation turns it into easy arithmetic.
Re-read the question once. Did they ask "next term", "12th term", or "which position"?Why: these are three different answers — the number, the value, or the position.

🔄 Double Check — Check It Twice

Finishing is not the end! The last 60 seconds of checking can rescue 2–3 marks. Do ALL four checks every time — no careless marks lost!

🔄 Double-check before you hand it in

The rule is found — now prove it's right. Tick all four, then move on.

1
Re-read the question. Did they ask "next term", "the 12th term", or "which position"? Each needs a different answer — the number, the value, or the position.
2
Substitute back. Put your answer into the rule and confirm it fits the pattern: 8 + 5×11 = 63, and 63 − 5 = 58 is term 11 — so 63 must be term 12.
3
Work backwards. Reverse the rule from your answer: undo the jumps one by one. If you land back on the first term, the rule and the answer both check out.
4
Sanity check. Is the answer sensible? A growing pattern must give a BIGGER number for a later term. Then re-check the units and the full sentence.
Check once, check twice — that's how you make every mark nice! 🔄

⚠️ Trap Alerts — Where Marks Are Lost

These four traps catch most students. Now they won't catch you!

🚩 The "one jump too many" trap

The 12th term needs only 11 jumps, because term 1 is already given. ✔ Count (position − 1) jumps, not position jumps.

🚩 The "forgot the leftover" trap

7, 12, 17 is +5 each time — but the rule is 5b + 2, not 5b. ✔ Always test your rule at position 1 before using it.

🚩 The "remainder 0" trap

In a repeating cycle of 3 (green, gold, red), term 27 has remainder 0 — that's red (the LAST colour), not green. ✔ Remainder 0 = the last item of the cycle.

🚩 The "shape counting" trap

For joined shapes, count what's newly shown, not everything. 2 hexagons show 10 sides, not 12. ✔ Draw the picture and count the visible bits.

Year 6 · Algebra & Patterns — Pattern Detective's Toolkit · Print this page and keep it with your homework! 📌