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

Multiplying Multi-digit Whole Numbers

Learn to multiply multi-digit whole numbers by splitting each factor into place-value parts, using an area model to find partial products, then adding them together for the total.

Teacher Class Feed

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    1 - Getting Started ~4 mins

    Here is a question to chew on: 34 × 26. That looks like a hard sum to do in one go. But what if we could break it into easier multiplications and then add them together?

    How could we split 34 and 26 into smaller, friendlier pieces?

    2 - Watch and Notice ~9 mins

    Illustration for Watch and Notice

    34 × 26

    Watch as the rectangle is split. 34 breaks into 30 and 4 down the side; 26 breaks into 20 and 6 along the top. That makes four boxes. Each box is one piece of the answer — we call it a partial product. We add all four partial products together for the total.

    123 × 14

    Now a three-digit number. 123 splits into 100, 20 and 3; 14 splits into 10 and 4. More boxes, so more partial products to add, but the same idea every time.

    256 × 23

    One more. 256 splits into 200, 50 and 6; 23 splits into 20 and 3. Look at which box is the biggest, and think about why.

    3 - Try It Together ~7 mins

    Now we build one together: 47 × 38. We split each factor into its tens and units — 47 becomes 40 and 7 down the side, 38 becomes 30 and 8 along the top. That makes four boxes, one partial product in each. Filling them in, the boxes are 40 × 30 = 1,200, then 40 × 8 = 320, then 7 × 30 = 210, then 7 × 8 = 56. Add all four partial products for the total.

    Build the area model: 47 × 38

    4 - Draw the Grid in Your Copy ~4 mins

    COPYBOOK MOMENT

    In your maths copy, draw the area-model grid for each of these products. Write each partial product inside its box, then add them for the total. Box the final answer.

    • 34 × 26
    • 47 × 38

    5 - Class Challenge ~11 mins

    Today we work through these four products together, each one a step harder: 47 × 38, then 152 × 24, then 263 × 35, then 318 × 46. Split both factors into their place-value parts, fill in every partial product, and add them for the total.

    Find the product by partial products

    6 - What Did We Notice? ~2 mins

    MATHS TALK

    Why does breaking a number into its place-value parts never change the answer? When you added all the boxes, did you ever get a different total from a friend who split the numbers a different way?

    7 - What's Next ~3 mins

    What we learned

    • Split each factor into its place-value parts to make easier multiplications.
    • Each box of the area model is one partial product.
    • Add all the partial products for the total — the answer is the same however you split.

    Coming up

    Tip

    Next we use estimation alongside long multiplication, rounding first to check our answers are sensible.

    Pupil practice
    Module 2 · Operations and Computational Fluency Number
    Lesson 15 · Multiplying Multi-digit Whole Numbers
    Download Activity Book page (PDF)
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