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?
Take two or three hands-up answers, not open call-outs. You are fishing for the idea of splitting into tens and units (30 + 4, 20 + 6) — if nobody offers it, say 'what if we split each one into its tens and units?' and move straight on. Keep this to one minute; the splitting is built properly in the next step.
The interactive splits each multiplication into a grid of smaller boxes. Watch how each factor breaks apart along the sides, and how the boxes fill in. Each box is one partial product; we add them all for the total.
34 × 26: 30 and 4 down the side, 20 and 6 along the top, four boxes. Name each as you point: 30×20=600, 30×6=180, 4×20=80, 4×6=24, add to 884. Coin the term partial product here.
123 × 14: 100, 20, 3 and 10, 4. A three-digit factor just adds one more column of boxes, method unchanged.
256 × 23: 200, 50, 6 and 20, 3. Ask which box is biggest and why: 200×20=4,000, the biggest place-value parts give the biggest area. Pause for their reasoning.
Stress throughout: partial products always add back to the same total, partitioning never changes the number.
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. Fill in each of the four boxes with its partial product, then add them all for the total.
This round is for talking it through together — a pupil at the board fills one box at a time and the class agrees or corrects out loud.
The split is already into tens and units (40 + 7, 30 + 8). Before each box is confirmed, pose a quick question to the whole class — 'what does this box come to?' — take two hands-up answers, then revoice the agreed one so the back rows hear a classmate reason it out. Watch for the common slip of multiplying 40 × 30 as 120 instead of 1,200 — head it off by saying 'four tens times three tens is twelve hundreds'.
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.
Walk the room glancing at how the boxes are labelled and whether the partial products add up correctly — this is whole-class copybook practice, not marking. Look for pupils dropping a zero on the tens × tens box.
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.
These are the practice questions — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
For each product ask 'which partial product is the largest here, and why?' — it is always the box made by the two biggest place-value parts. With 263 × 35 and 318 × 46, watch for pupils forgetting one of the six boxes; count the boxes aloud before adding.
We split factors into place-value parts, but does a different split of the same factors still give the same total?
Take 34 × 26 two ways.
Way 1: 30 + 4 and 20 + 6. The four partial products add to 884.
Way 2: split 34 as 20 + 14 and keep 26 as 20 + 6. New partial products, same total 884.
Why does breaking a number into different 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? Talk with a partner, then we share.
Board both partitions of 34 × 26 side by side before the talk.
Way 1 (known): 30+4 and 20+6 → 600, 180, 80, 24 → 884.
Way 2 (new): 20+14 and 20+6 → 20×20=400, 20×6=120, 14×20=280, 14×6=84. Add: 400+120=520, 280+84=364, 520+364=884.
Point: parts always rebuild the same factors, so the whole area is unchanged. Slip to watch: pupils claiming a new split must change the total. Revoice a strong answer: the rectangle stays the same size however you slice it.
Next we use estimation alongside long multiplication, rounding first to check our answers are sensible.
Recap the three bullets quickly, pointing back at one of the area-model grids still on screen. Keep this under two minutes.
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