Headline Story
Fun with Algebra, #5
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Introduction
Suggest that students organize their responses in some way, for example, in a table.
Headline Story
How many ways can Tom make a rectangle with a perimeter of 24 using square tiles? What is the least number of square tiles that Tom can use?
Possible student responses
- He could have made a 6 by 6 square using 36 tiles.
- The two dimensions of the rectangle have to have a sum of 12.
- The square will have the largest area and the longest and narrowest rectangle will have the smallest area.
- A rectangle that is 1 tile by 11 tiles uses the least number of tiles. It uses 11 tiles.
- There are 6 different rectangles whose dimensions are whole numbers (if we consider a rectangle and that rectangle turned sideways as the same).
- Possible dimensions, and their areas, can be listed in a table.
| Length | 1 | 2 | 3 | 4 | 5 | 6 |
| Width | 11 | 10 | 9 | 8 | 7 | 6 |
| Area | 11 | 20 | 27 | 32 | 35 | 36 |
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