Mathematics
Intermediate
40 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen

Mental Addition Strategies: Partitioning and Compensating

Learn three mental addition strategies—partitioning, compensating, and bridging—and choose which one fits the numbers you're adding. Use number-line jump arcs to show your thinking.

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    1 - Getting Started ~4 mins

    Here is a sum: 47 + 38. No paper, no columns. How could you work this out in your head? There is more than one way, and some ways are quicker than others depending on the numbers.

    2 - Watch and Notice ~9 mins

    Illustration for Watch and Notice

    Partition: +30 then +8

    Watch 47 + 38 worked as two forward jumps. First jump +30 to land on 77, then +8 to land on 85. We split the 38 into its tens and ones.

    Compensate: +40 then take back 2

    This time we jump +40 to land on 87, which is a little too far, then jump back 2 to land on 85. Adding 40 is easier than adding 38, so we fix it afterwards.

    Bridge to fifty: +3 then +35

    Here we jump +3 first to land on the friendly number 50, then +35 to land on 85. Landing on a round ten first makes the next jump easier.

    Bigger numbers: 235 + 198

    Watch how compensating shines here. Jump +200 to land on 435, then jump back 2 to land on 433. Adding 200 is much easier than adding 198.

    3 - Try It Together ~11 mins

    Today we explore one sum together: 56 + 27. First we choose a strategy, then we draw the jump arcs to land on the answer — and once we pick a strategy, the label on the screen names the strategy we used. When we are finished we clear the line and start fresh for the next sum the class wants to try.

    Choose a strategy and jump

    4 - Work It Three Ways in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, take the sum 47 + 38 and work it three ways, one under the other: once by partitioning, once by compensating, once by bridging to fifty. Write the jumps you used beside each one. Then decide which way you would choose if you had to do it quickly.

    5 - Class Challenge ~8 mins

    Today we work through these sums and reach each target in the fewest jumps you can: 47 + 38, then 56 + 27, then 235 + 198, then 268 + 197. The numbers get bigger, so think about which strategy keeps your jumps to a minimum each time.

    Reach the target in the fewest jumps

    6 - What Did We Notice? ~3 mins

    MATHS TALK

    One pupil says partitioning is always best. Another says compensating is best for 235 + 198. Who is right, and how would you settle it? Which strategy fits 47 + 38, and which fits 235 + 198?

    7 - What's Next ~2 mins

    What we did today

    • We added two-digit and three-digit numbers in our heads using jump arcs
    • We learned three strategies: partition, compensate, and bridge to a friendly ten
    • We saw that the numbers decide which strategy is quickest

    Coming up

    Coming up

    Next we move from mental jumps to the written column method, where we line up the ones and add column by column with regrouping.

    Pupil practice
    Module 2 · Operations and Computational Fluency Number
    Lesson 17 · Mental Addition Strategies: Partitioning and Compensating
    Download Activity Book page (PDF)
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