General+Bending+Al+Lesson+Instructions

General Instructions for Facilitating the Bending Aluminum Activity
Give students a piece of paper that measures 8”x10”. Explain that the paper represents a piece of aluminum, out of which a rain gutter for a house will be formed. They need to fold up the 8” width on both sides so that the cross-section is a rectangle (with no top, similar to a gutter). So, for example, if they fold it up 1” on each side the cross-sectional area of the gutter will measure 1x6, so the area will be 6 in2. If they fold it up 1.5” the gutter would measure 1.5x5, so the cross-sectional area would be 7.5in2. As they continue the investigation they will notice a pattern—that if they continue the half inch interval the area will go up until it peaks at 8in2 and then it will fall back down at the same rate it increased. This data may be collected in a chart (height of gutter, cross-sectional area), the points could be graphed, and/or the problem can be extended to its algebraic representation: Cross-sectional Area = x(8-2x), where x is the height of the gutter. Students then could graph the parabola and see that the graph goes through their points. This would be a good introduction to graphs of quadratics and finding maximums and minimums. (Lesson taken from Daniel Brahier's Teaching Secondary Mathematics Third Edition p 212)


 * x || x(8-2x) ||
 * .5 || 3.5 ||
 * 1 || 6 ||
 * 1.5 || 7.5 ||
 * 2 || 8 ||
 * 2.5 || 7.5 ||
 * 3 || 6 ||
 * 3.5 || 3.5 ||