Here is a question to crack in your head: what is 6 × 13?

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?

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.

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.

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?

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.