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Dog number 1 had a head which was 1x1x2, four legs which were 1x1x2 and a body which was 1x1x4. |
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Dog number 2 had a head which was 2x2x4, four legs which were 2x2x4 and a body which was 2x2x8. |
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Dog number 3 had a head which was 3x3x6, four legs which were 3x3x6, and a body which was 3x3x12. |
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Dog number 4 had a head which was 4x4x8, four legs which were 4x4x8 and a body which was 4x4x16. |
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Dog number 5 had a head which was 5x5x25, four legs which were 5x5x10 and a body which was 5x5x20. |
The students were then given a series of questions about the ratio of each of these measurements.
Students found that if the lengths were in a ratio of a to b, then the areas were in a ratio of a squared to b squared, and the volumes were in a ratio of a cubed to b cubed.
| This meant that the heights of dog 2 to dog 3 were 2 to 3. | |||
| The area of the top of the heads of dog 2 to dog 3 were 4 to 9. | |||
| The volume of the body of dog 2 to dog 3 was 8 to 27. | |||
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What was really surprising was that the height of dog 1 to dog 5 was 1 to 5, but the area of the front of the face of dog 1 to dog 5 was 1 to 25, and the volume of the dog 1 to dog 5 was 1 to 125. That's a really big dog!!!
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Student Activity Sheet with Answers
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