Mathematics
Intermediate
50 mins
Teacher/Student led
+65 XP
What you need:
IWB/Projector/Large Screen

Subtraction Strategies: Counting on, Take Away, Decomposition

Explore three strategies for subtraction — counting on, take away, and decomposition — and learn when each one works best by representing them as jumps on a number line.

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    1 - Getting Started ~4 mins

    Look at this: 7328.

    If you had to do it in your head right now, would you count up from 28 until you reach 73, or would you start at 73 and take 28 away?

    Note

    Hands up — which feels easier? There is no wrong answer. We will meet both ways, and a third way, before the end of the lesson.

    2 - Watch and Notice ~10 mins

    Illustration for Watch and NoticeWatch three subtractions on the number line. The same subtraction can be done two different ways — and a bigger subtraction tells us when one way fits better than another.

    Counting on: 7328 = 45

    Start at 28. Jump forward to 30 (+2), then to 70 (+40), then to 73 (+3). The forward jumps total 45 — that is the answer.

    Counting-on works best when the two numbers are close together — the gap is small enough to hop across in a few friendly jumps.

    Take away: 7328 = 45

    Start at 73. One single back-jump of 28 lands you on 45. Same answer, completely different picture.

    Take-away works best when the number you are subtracting is small and easy to hold in your head as one back-jump.

    Decomposition: 305178 = 127

    Now the numbers are bigger. Break 178 into 100 + 70 + 8 and take each chunk away in its own back-jump.

    Decomposition works best when the numbers are bigger or messier — breaking the subtraction into place-value chunks is friendlier than one massive back-jump.

    3 - Try It Together ~13 mins

    Today's exploration on the number line: for each subtraction called out, pick a strategy that you think fits — counting-on, take-away, or decomposition. Sometimes more than one works, and that is fine — be ready to say why you chose yours.

    One pupil at a time comes to the board, names their chosen strategy out loud, and drags the jumps. Before they touch the screen, think which strategy you would choose — you might pick a different one.

    Starters

    Starters to work through: 6539, 8427, and 412246.

    Pick a strategy and jump

    4 - Work It Three Ways in Your Copy ~6 mins

    COPYBOOK MOMENT

    In your maths copy, work each subtraction below using a different strategy (count-on, take-away, decomposition) and label which strategy you used next to your answer.

    • 7328
    • 9047
    • 305178

    5 - Class Challenge ~10 mins

    Today's bank: subtraction-bonds fact-race. Four rounds, one minute each. One pupil at a time comes to the board to type the answer; the rest of us call out the answer together before they type.

    • Round 1 — bonds to 20 (warm-up).
    • Round 2 — bonds to 100 (the friendly ones).
    • Round 3 — bonds to 100 again, harder pairs.
    • Round 4 — mixed two-digit subtractions.

    Subtraction-bonds fact-race

    Pupil practice
    Module 2 · Operations and Computational Fluency Number
    Lesson 20 · Subtraction Strategies: Counting on, Take Away, Decomposition
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