Issue each child a geoboard and a large rubber band. Challenge each child to create the geometric shapes discussed in the book by stretching the rubber band over the pegs on the geoboard, beginning with a triangle. Make use of tangrams to transform triangles into other geometric shapes. For example, placing two triangles together and alternating the direction of their right angles forms a square.
Instruct students to trace and cut out various geometric shapes to create pictures from them. Provide templates or have children use their imaginations to devise original shapes. Invite students to build a monster, an animal, a man or a symmetrical design. For example, when constructing a man, show students to use a square for the body and a circle for the head. Cut out rectangles for arms and legs or create joints with small triangles between a rectangle forearm and bicep.
Create a scavenger hunt worksheet that lists each polygon from "The Greedy Triangle" on a piece of paper and group students into threes or fours to find these shapes around the classroom or school grounds. The first team to complete the sheet wins. Challenge each student to make polygons with their body parts, like their hands and fingers, in a game of "Simon Says." The winner receives a small prize or a triangle sticker.
Have students sit in a circle. Give one student a ball of yarn and instruct her to hold onto one end while she tosses the ball to another student. That student then holds onto the string of yarn while tossing the ball to yet another student. The action repeats until a web forms inside the circle. Look carefully within the web to find geometric shapes from the book. Another activity is to have children lie on the ground as sides to various polygons. Challenge the class to create a polygon with the same number of sides as the number of children in the class.