What is this lesson about

Students will use squares (these could be square tiles or Triqo pieces) to discover pentominoes

(shapes created by joining 5 squares along an edge). The students then use Triqo squares to

determine which squares fold to make open top boxes. Note this lesson may involve several ses-

sions. The first would involve finding all the pentominoes and the second would involve working

out which ones may be folded to create a box without a lid.

Australian Curriculum Link

The grid above indicates that the lesson is designed to stimulate geometric problem solving

and reasoning. Specifically this lesson would fit the following content from the Australian Cur-

riculum. ACMMG111: Connect three-dimensional objects with their nets and other two-dimen-

sional representations.

Elaborations• identifying the shape and relative position of each face of a solid to determine the net of the

solid, including that of prisms and pyramids

• representing two-dimensional shapes such as photographs, sketches and images created by

digital technologies

Bring 2D to life with triqo

Assessment

National tests such as the NAPLAN often contain pictures of 2D nets (the flat shape that may be folded to make a 3D object) and students are asked to visualize which net folds to make a cube. Some questions even ask the student to visualize which face will be opposite another when the net is folded to make a cube.

Hannah folds this net to make a cube.

Which face is opposite face C (orange)?

A

B C D

F

E

F UI VL WN XP YT Z

1

triqo leskaart 01-w.indd 1 23-08-12 10:02

Introduction

1. Set the challenge to discover all the pentominoes. A pentomino consists of five squares connected together so each square has at least one side in common with other square.

2. There are 12 pentominoes to make using the 5 squares.

3. Use the square tiles to discover and make the 12 pentominoes.

4. Record each pentomino on 10 mm grid paper (this may be used for assessment purposes).

5. Are there any duplications, reflections or rotations included?

6a. Check– How many pentominoes are 5 squares in a row? b. How many pentominoes are 4 in a row? c. How many pentominoes are 3 in a row? d. How many pentominoes are 2 in a row?

7. Identify which pentominoes you think can be folded to form a box without a lid.

8. Check your prediction by creating the pentominoes that you think fold to make open top boxes using Trigqo squares.

9. Record which ones fold to make an open top box.

10. Of the twelve pentominoes, eight will fold to create an open top box.

playing with pentominoes

triqo leskaart 01-w.indd 2 23-08-12 10:03