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

Mental Addition Strategies: Partitioning and Compensating

Develop three mental addition strategies — partitioning, compensating, and bridging — and learn when to choose each one for two- and three-digit addition problems.

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    1 - Getting Started ~4 mins

    Take a look at 47 + 38. No pencil, no paper, no column method. Could you work it out in your head?

    There's more than one way to do it. Today we'll look at three of them, and by the end of the lesson you'll be able to pick the one that best suits the numbers in front of you.

    2 - Watch and Notice ~10 mins

    Watch four worked examples on the number line. Same answer every time, but the route across the line is different. Notice how each strategy uses the numbers in a slightly different way.

    Example 1: 47 + 38 by partitioning

    Split the 38 into 30 + 8. Jump +30 first to land on 77, then jump +8 to land on 85.

    Example 2: 47 + 38 by compensating

    40 is friendlier than 38. Jump +40 to land on 87, then take back the extra 2 to land on 85.

    Example 3: 47 + 38 by bridging through fifty

    50 is the friendliest landing place near 47. Jump +3 to land on 50, then jump +35 in one go to land on 85.

    Example 4: 235 + 198 by compensating

    198 is almost 200. Jump +200 to land on 435, then take back the extra 2 to land on 433. Compensating shines when one number is just below a round hundred.

    3 - Try It Together ~13 mins

    Today's problem: 38 + 27. Three pupils in turn will come to the board — one for each strategy — and drag the jump arcs onto the number line to reach the answer. The strategy-hint label confirms which one they used.

    Tip

    While one pupil drags at the board, watch the route take shape and think about which strategy it is — partition, compensate, or bridge.

    38 + 27: your strategy

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

    COPYBOOK MOMENT

    In your maths copy, work each mental example three ways — partition, compensate, and bridge — so you can decide which strategy fits which numbers best.

    For each problem below, set up three short lines underneath it. Label each line with the strategy and write the two jumps you took. Use these examples:

    • 47 + 38
    • 235 + 198

    At the end, circle the strategy on each problem that you found cleanest for those numbers.

    5 - Class Challenge ~11 mins

    Today's bank: four rounds of fact-race, building from bonds to 20 right through to bonds to 1000. These are the friendly numbers your mental strategies will lean on for the rest of the year — speed and accuracy both count.

    How it runs

    One pupil at a time comes to the board to type the missing number. While they type, the rest of the class works out the answer too, then we check it together once it's on the board.

    Bonds fluency: 20 to 1000

    Pupil practice
    Module 2 · Operations and Computational Fluency Number
    Lesson 17 · Mental Addition Strategies: Partitioning and Compensating
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