Mathematics
Intermediate
50 mins
Teacher/Student led
+65 XP
What you need:
IWB/Projector/Large Screen
Estimate-working-compare template

Long Multiplication Strategies and Estimation

Learn to estimate products by rounding, then carry out long multiplication accurately. Use your estimate to spot place-value errors in your working.

Teacher Class Feed

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    1 - Getting Started ~4 mins

    Example

    Illustration for Getting StartedHere is a scoreboard sum someone worked out on the board: a club added up the points scored across a whole season of matches, 384 × 27, and got 1,363. Is that right? Before we check with a pencil, roughly how big should the answer to 384 × 27 actually be?

    2 - Watch and Notice ~10 mins

    Illustration for Watch and NoticeWe will work three multiplications on the board, each in two parts: first a rounded estimate, then the real working row by row. Watch what happens to the second row each time, and keep an eye on where the real answer lands compared to the estimate.

    3 - Estimate Then Work It in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, for this product write your rounded estimate first, then the full long-multiplication working underneath. When you have the total, compare the two and note in one line how close your estimate was.

    • 412 × 23 (this is how many programmes a club printed for each of 23 matches — how many altogether?)

    4 - Try It Together ~11 mins

    Today we estimate first, then work it out, and check each result against the estimate. We'll do the written long multiplication together on the board, and use the screen only for the estimate check. Our products come from a GAA weekend: 245 × 32 (tickets for 32 matches), then 517 × 26, then 683 × 45. For each one we say the rounded estimate aloud before anyone touches the working, so we always know roughly where the answer should land. Remember what a place-value slip looks like: if the tens row lands one column too far right, the answer comes out much too small, so 517 × 26 giving 4,136 (far too small) would be a slipped row.

    Estimate the size, then check against the board

    5 - Class Challenge ~9 mins

    Key point

    Today we work out these products, estimating first and then working them out to check: 478 × 36, then 815 × 29, then 364 × 52, and finally the stretch, 926 × 47 (points scored across a full club fixture list).

    For each one we predict roughly how big the answer will be before we work it out on the board. The screen is just for the estimate; the long multiplication is written out by hand. If there is time, see whose estimate landed within five hundred of the real answer.

    Estimate, then check within 500

    Pupil practice
    Module 2 · Operations and Computational Fluency Number
    Lesson 16 · Long Multiplication Strategies and Estimation
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