![]() In this lesson, students will create fun five-pointed 3D stars. Students will work in groups. Each group needs scissors and lots of Scotch tape. Starting from scratch, they will need a protractor and a ruler. ![]() ![]() 2. Score along the dotted lines as shown in Figure 1. Each hexagon makes a "pocket" (one point of the star) when you tape together the two longest sides. 3. Do this four more times, creating a total of five pockets. 4. Next, tape one side of the mouth of a pocket to one side of the mouth of another pocket. Do this four times and you will have five pockets that fold flat. Open them like a fan, and be sure that each pocket fills with air. Now you have a five-pointed 3D star! 5. The two sets of images below show the construction of two similar 3D stars. The smaller red star has its linear dimension ½ of the bigger yellow star. What do you think the relative volumes of the two stars will be? ![]() ![]() ![]() ![]() ![]() ![]() 6. Whatever the shape of an object is, if you stretch (or shorten) it in one direction by a factor f, the new volume equals f3 times the old volume. If one shape S is similar to another shape T, then you can obtain S from T by stretching it or shortening it by the same factor f in three perpendicular dimensions. So the volume of S is 7. In the case of the five-pointed 3D stars above, a similar star whose linear dimensions are one-half of the original, has a volume (1/2)3 = 1/8 of the original. The red star will hold 1/8 as much as the yellow one! Lesson Index |