Sequences & Instructions
Sequences and instructions form the foundation of computational thinking in KS2 and KS3 maths. When pupils trace through step-by-step processes—whether counting by 3s or following repeated doubling patterns—they develop logical reasoning skills essential for GCSE problem-solving.
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Why it matters
Sequential thinking appears everywhere in Year 6 SATs questions, from following number patterns to calculating compound interest at GCSE level. When pupils trace through a sequence like 'start at 2, add 5 each time for 4 steps', they're building the same logical skills needed for algorithm design in computing lessons. Real-world applications include calculating bus fares (£2.50 initial charge plus £1.20 per zone), compound savings growth (£100 doubling annually over 5 years reaches £3,200), and following recipe scaling instructions. Primary teachers find these skills transfer directly to times table patterns, whilst secondary colleagues use sequence tracing for quadratic formula applications and geometric progressions in GCSE Foundation papers.
How to solve sequences & instructions
Sequences in Code
- A sequence is a set of instructions executed one after another.
- Order matters: changing the order changes the result.
- Variables store values that can be updated.
- Trace through the code line by line to find the output.
Example: x = 3, x = x + 2, print(x) → outputs 5.
Worked examples
Collecting coins: start at 0, get 2 coins each turn for 3 turns. Total coins?
Answer: 6
- Execute each step → 0 -> 2 -> 4 -> 6 — Get 2 coins each turn.
- Final value → 6 — After 3 additions of 2: 0 + 2 x 3 = 6.
A piece of paper is folded in half 3 times. Starting with 1 layer, how many layers after folding?
Answer: 8
- Double each fold → 1 -> 2 -> 4 -> 8 — Each fold doubles the layers: multiply by 2, 3 times.
A counter starts at 1. A loop adds 4 each time, 6 repetitions. Result?
Answer: 25
- Trace the loop → 1 -> 5 -> 9 -> 13 -> 17 -> 21 -> 25 — The counter increases by 4 each step.
- Or calculate directly → 1 + 4 x 6 = 25 — Start + (step x repeats).
Common mistakes
- Pupils often confuse the number of steps with the final answer, writing 4 instead of 14 when tracing 'start at 2, add 3 four times'
- Students miscalculate repeated multiplication, getting 2×2×2×2 = 32 instead of 16 when folding paper 4 times from 1 layer
- Many forget the starting value in loop calculations, writing 3×5 = 15 instead of 2 + 3×5 = 17 for 'start at 2, add 3 five times'
- Pupils reverse operation order in compound formulas, calculating x+1×2 = 7 instead of (x+1)×2 = 8 when x = 3