Practice: Sequence Drills

Complete the next three terms in each sequence.

Part A: Addition & Subtraction

1. 5, 10, 15, ___, ___, ___
2. 3, 6, 9, ___, ___, ___
3. 50, 45, 40, ___, ___, ___
4. 12, 20, 28, ___, ___, ___
5. 100, 98, 96, ___, ___, ___

Part B: Multiplication & Division

1. 2, 4, 8, ___, ___, ___
2. 3, 9, 27, ___, ___, ___
3. 100, 50, 25, ___, ___, ___
4. 5, 25, 125, ___, ___, ___
5. 88, 44, 22, ___, ___, ___

Part C: Mixed & Tricky

1. 1, 4, 9, 16, ___, ___, ___ (Hint: Square numbers)
2. 1, 1, 2, 3, 5, ___, ___, ___ (Hint: Fibonacci)
3. A, C, E, ___, ___, ___
4. Z, Y, X, ___, ___, ___
5. O, T, T, F, F, S, S, ___, ___, ___ (Hint: Think of numbers)

🔑 Kaiako answer key

Part A — Addition & Subtraction

20, 25, 30 — add 5 each time
12, 15, 18 — add 3 each time
35, 30, 25 — subtract 5 each time
36, 44, 52 — add 8 each time
94, 92, 90 — subtract 2 each time

Part B — Multiplication & Division

16, 32, 64 — double each time
81, 243, 729 — multiply by 3 each time
12.5, 6.25, 3.125 — halve each time
625, 3125, 15 625 — multiply by 5 each time
11, 5.5, 2.75 — halve each time

Watch for: Q3 and Q5 leave the whole numbers — halving 25 gives 12.5, and halving 11 gives 5.5. Both answers are correct. Ākonga who stop at 12.5 or 11 and say “it doesn’t work any more” have spotted something real: the rule keeps working, the whole numbers run out. That is worth two minutes of class discussion. If you want the set to stay whole-number, ask for the rule in words instead of three more terms.

Part C — Mixed & Tricky

25, 36, 49 — the square numbers, n²
8, 13, 21 — Fibonacci: each term is the sum of the two before it
G, I, K — every second letter of the alphabet
W, V, U — the alphabet backwards
E, N, T — first letters of One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten

📋 Teacher Planning Snapshot

Ngā Whāinga Ako — Learning Intentions

Fluency practice for Lesson 1: continuing sequences and stating their rules.

Ngā Paearu Angitū — Success Criteria

✅ I can work out what a sequence is doing and write the next three terms.
✅ I can say the rule in words — "add 8 each time", "halve it each time".
✅ I can keep going when a sequence stops being whole numbers, and say why that happened.

Differentiation & Inclusion

Part A is the entry point and Part C the extension; there is no need for every ākonga to reach Part C. Ākonga who find Part B hard can use a calculator for the halving questions — the skill being practised is spotting the rule, not the arithmetic. Part C questions 3–5 are language patterns rather than number patterns and suit ākonga who read well but find number work heavy.