Pattern Blocks – How Many Can Sit? - Promethean Planet

Teacher TalkWhere’s the Mathematics?As children build new tables and count their sides, they begin to see howthe growth of the perimeter of a shape is related to the way the shape growsgeometrically. For example, as they join together triangles to make tables,children find that the perimeter increases by 1 unit each time a triangle isconnected to the existing shape. This may surprise children who may thinkthat the perimeter should increase by 3 units since a triangle has three sides.Other children may think the perimeter should increase by 2 units since oneof the sides of the new triangle will end up interior to the new shape. Asthey continue to “grow” the shape, children may come to see that each newtriangle takes away an existing seat at the table and adds 2 more, resultingin an increase of only 1 seat.new seat new seatlost seatnew seatJust as each added triangle makes room for one more person at the table,each added square makes room for two more people, each added pentagonmakes room for three more people, and each added hexagon makes roomfor four more people.lost seatnew seatnew seatnew seatlost seatnew seatnew seatnew seatnew seatnew seatlost seatnew seatnew seatnew seatChildren may use different methods for finding the number of people thatcan sit at the tables made from 100 single tables. Some children may basetheir predictions on patterns they see in the numbers in their chart. They60 THE SUPER SOURCE ® ◆ Pattern Blocks ◆ Grades 5-6 © ETA/Cuisenaire ®