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
The lesson
A rectangle's area is one side times the other side. If you split one side into two smaller parts, you can find the area of each part on its own, then add the two areas together. You get the same total either way.
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.
Watch it
Where it sits
Learn first
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Where this leads
8 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.