Here is a question to crack in your head: what is 6 × 13?
Don't reach for the column method yet. Could you split that 13 into 10 and 3 to make the multiplying easier? Have a go, then we'll find out together why that splitting trick always works.
This is a genuine first attempt, not a teaser. Give about ten seconds of quiet think-time, then take two or three hands-up answers and the route each pupil used. Do not reveal the rule yet — the next step builds it from the evidence.

Let's look at these together. Here is 6 × 13 drawn as a rectangle, 6 down and 13 across. A factor is one of the two numbers we are multiplying. Here we have split one factor, the 13, into a 10 piece and a 3 piece. What do you notice about the two smaller rectangles?
Same idea, different numbers. The 25 side splits into 20 and 5. Read off each smaller rectangle's area, then add them.
Once more, splitting at the tens. The 16 side splits into 10 and 6. Watch how the two rectangles tile together to make the one whole rectangle, with no gaps and no overlaps.
Every time, multiplying by a sum gives the same answer as multiplying each part and adding. In short: a × (b + c) = a × b + a × c. The brackets just mean do the adding inside first.
Walk each example one at a time, pointing at the two smaller rectangles.
After the second example, pause for a quick hands-up check before moving on: which two smaller rectangles will we get when we split 16 at the tens? Take two answers, then run the third example.
Only after the third example, point to the on-screen rule and let the class help finish it aloud: multiplying by a sum equals multiplying each part and adding. This naming is the pay-off, not the opener.
Now we work one product together on the area model: 8 × 14. We'll split one factor (one of the two numbers we are multiplying), the 14, into 10 and 4, fill in each smaller rectangle, and add the two parts to check the whole.
Where would you cut the 14 to make the multiplying easy? Let's find out together.
This round is for talking it through together — invite a pupil up to the board to choose the split while the class agrees or corrects out loud.
Now we test the rule we just named on fresh numbers — does it still hold? Most pupils will cut at the tens (10 + 4). Watch for a pupil who multiplies the two parts together instead of adding the two partial products; revoice: we add the two rectangles, we don't multiply them. Keep this to the single on-screen product; the further practice products are done in the copybook step that follows.
In your maths copy, write these three products and beside each show the distributive split, then work out both sides:
Work out both sides of each line and underline the two equal totals.
Walk the room glancing that each split adds back to the whole product and that the totals match — this is whole-class copybook practice, not marking. Watch for pupils who split into 10 + something but then forget the second partial product.
Today we work through these splits together, getting trickier each time: 7 × 13, then 6 × 24, then 8 × 35, then 9 × 27. Build each on the area model, fill both rectangles, and add the parts.
This round is the practice bank — 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.
The last two have larger tens parts, so the partial products are bigger; ask which rectangle is the largest each time and why. A fast finisher who is waiting can mouth the next product to themselves — no parallel desk task.
One pupil says the splitting trick also works for subtraction, so 6 × 18 should equal 6 × 20 − 6 × 2. Another pupil isn't sure. Look at the picture below: we start with the big 6 × 20 rectangle and cut off the extra 6 × 2 strip on the end.
What is left after we cut the strip off? So who is right, and how does the picture settle it without doing the full sum first?
Listen for pupils who reason from the area picture: take the big 6 × 20 rectangle and cut off the extra 6 × 2 strip. Revoice that as so the rule shares out over a minus the same way it shares out over a plus. Confirm 6 × 18 = 120 − 12 = 108 only after the class has reasoned it from the picture, not as the opener.
Today you learned that multiplying by a sum is the same as multiplying each part and adding the answers, and you saw why the area picture makes that true every time, for both plus and minus.
Next we'll meet letter-symbols: using a letter to stand for a number we don't know yet, the first step into writing things in algebra.
Recap the rule in one line and link forward: the splitting we did with numbers is exactly what lets us simplify expressions with letters later in the module.
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