Folding Sculptures: A Focus on Surface Area and Scale Drawings

Middle School Math

Proportional Relationships and Slope

A three-tiered cake with the height of the top tier measuring 6 inches, the height of the middle tier measuring 6 inches and the height of the bottom tier measuring 6 inches. A one- inch distance is labeled on the surface of the middle and bottom layers to show that each layer is 2 inches larger in diameter than the one on top of it. Lines are drawn at these measurements to show two triangles formed by the tiers. A crooked line is formed across the hypotenuses of two triangles. The bottom triangle has a horizontal run of 1 inch and a rise of 6 inches. The top triangle has a horizontal run of 2 inches and rise of 6 inches.
A constant difference refers to an equal amount that is being added or subtracted to two variables. In the cake Ms. Shafer is talking about, for every rise in height of 6 inches, the next tier of the cake is 1 inch over. This vertical rise of 6 inches and horizontal run of 1 inch is the constant difference.

 Here is how the line would look if the top cake layer was a four-inch diameter cake, leaving a run of 2 inches. Notice how this makes the line, or the cake, tilt.





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