Area and the distributive property
Use tiling to demonstrate the distributive property: the area of a rectangle with sides a and (b+c) equals a×b + a×c; use area models to represent the distributive property
What a learner can do afterwards
- Tile a 3×(4+2) rectangle and show it decomposes into 3×4 and 3×2
- Use an area model to compute 6×13 as 6×10 + 6×3
- Draw an area model showing 5×(7+3) = 5×7 + 5×3
1 · Read
A rectangle's area is one side times the other side. But a big rectangle, like a school garden that is 6 meters by 13 meters, can be hard to multiply in your head. Split one side into two smaller parts, find the area of each part, then add them together to get the same total.
To work out 6×13, split 13 into 10 and 3. Then 6×13 = 6×10 + 6×3 = 60 + 18 = 78.
You can split either side of the rectangle, not just one way. Splitting only breaks the counting into easier steps. It does not change how much space is inside.
Split one side of a rectangle into parts, multiply each part separately, then add the results to get the same total area.
Rewritten readings were written for this dataset.
2 · Watch
Take it off screen
Where it sits
Where this leads
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.