This worksheet is designed to replace a lecture on the topic of what happens to the area and volume of geometric shapes and solids when the linear dimensions are doubled, tripled, and so forth. Students apply the formulas for area and volume to geometric shapes and discover that the ratio of areas equals the square of the ratio of sides, and the ratio of volumes equals the cube of the ratio of sides.
I start out class with a 15-minute "mini-lesson," giving my students some basic examples of what today's lesson will be about: I just make up a square and work out its area, and then double all the sides, and recalculate the new area, which is always four times greater. I then do the same thing with a triangle. Once the mini-lesson is over, I have them get to work within their groups on this worksheet.
I use this activity within cooperative groups, and I circulate to make sure they are getting the purpose of the questions.
The file includes spiral review problems.
This worksheet is intended to be written on directly.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.
Immediately before this worksheet, I use the worksheet named 'Volumes and Surface Areas of Solids Spring 2014' (http://www.teacherspayteachers.com/Product/Volumes-and-Surface-Areas-of-Solids-Spring-2014-1267955
), and immediately after this worksheet, I use the assessment named 'Geometry Quiz Probability and Areas Spring 2014' (http://www.teacherspayteachers.com/Product/Geometry-Quiz-Probability-and-Areas-Spring-2014-2-versions-2-pages-each-1267964