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.
Each rectangle is one multiplication, with one side split at the tens into two smaller rectangles. Watch how the two pieces fit together to make the whole, and find each smaller area as we go. What stays true every time we split?
6 × 13: split 13 into 10 and 3. Factor means one of the numbers being multiplied. Pieces are 60 and 18; ask the class to add to 78.
4 × 25: split into 20 and 5. Pieces 80 and 20 make 100 — a clean one for confidence.
Before the third, hands-up check: which two rectangles when we split 16 at the tens? Take two answers.
9 × 16: split into 10 and 6, pieces 90 and 54. Stress the two rectangles tile with no gap and no overlap.
Only now point to the rule and let them finish it aloud: multiplying by a sum equals multiplying each part and adding, a × (b + c) = a × b + a × c. This naming is the key moment, 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.
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.
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. Imagine the big 6 × 20 rectangle with the extra 6 × 2 strip cut off the end.
What is left after we cut the strip off? So who is right, and how does this 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.
You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.