The "Star Card" is more than a card: it can be a package, which could contain a small gift such as a movie ticket or a folded ten-dollar bill! Students enjoy projects that provide them with "goodies", trinkets, or potential gifts for friends or family. And a mother would certainly be pleased to see her son or daughter apply their geometric knowledge in this way!
The Star card fits nicely into a study of polygons and related figures. The Star Card contains a regular pentagon at its center, as well as isosceles triangles, both acute and obtuse. Finding all the angle measurements and segment lengths could provide solid mathematical review, and this project could be "revisited" in the chapter on area of polygons.
1) Construct a regular pentagon:
2) Construct the midpoints of all 5 sides of the large pentagon and join consecutive midpoints with segments to form the medium pentagon (upside down) inside the first:
3) Select a pair of consecutive midpoints of the medium (upside down) pentagon and construct a line (not segment) through those two points. Connect intersections of the lines to form the points of the star. Construct segments then hide all the lines as shown, to create a 5-pointed star:
4) Then connect non-consecutive pairs of pentagon vertices to form the small star in the interior of the pentagon:
5) Finally, connect non-consecutive pairs of the newest pentagon's vertices to form the smallest star in the interior of the pentagon
Color the star card as shown below (you may use any color you like, of course!):
Write your message in the pentagon, on the uncolored side of the card, then fold the 5 points in towards the center to close the card. This is how the card will look on the outside, when folded:
When you open the card to the inside, your message will be seen as shown in the image below.
