# Reasoning With 3D Objects

Australian curriculum number (ACMMG066; ACMMG063)

Students explore symmetry and the composition of three-dimensional objects. They will interpret and represent three-dimensional objects in two dimensions, and apply their knowledge of transformations to show congruency or difference between objects. Applying transformations of these objects develops students’ mental rotation skills.

This sequence is for students who:

• have prior experience identifying and creating symmetry in objects.
• have an understanding of transformations, particularly flips (reflections) and turns (rotations), and how these can be used to show congruency.
• ideally have prior experience with 2D representations of 3D objects.

### Lesson 1: Building Symmetry

This task presents students with a non-symmetrical three-dimensional model made of five interlocking cubes. They are asked to make the model symmetrical by changing the position of one block or by adding an extra block to the model. Students are asked to find all possible solutions to the challenge. As the students explore the different possibilities, the language of symmetry and transformations is explored.

### Lesson 2: Four Cubes

This resource consists of two sections. The first section asks students to build objects using four cubes and following simple rules. After some exploration, they are encouraged to work systematically to find different solutions. Using transformations, the students reason and justify that all the constructions they have made are different and that they have found all possible solutions. Students then draw the two-dimensional representations of these three-dimensional objects.