Reasoning With 2D Shapes

Australian curriculum number (ACMMG042; ACMMG045; ACMMG046)

This sequence starts with a task that focuses on developing students’ knowledge of the properties of shapes, particularly triangles, quadrilaterals, pentagons and hexagons. Students apply their knowledge of these properties to identify shapes that may not fit more common representations. Students then move on to work with transformations of two-dimensional shapes, using flips and turns. Students will learn to work systematically to find all the possible solutions to the task.

This sequence is for students who:

  • have had some experience with common two-dimensional shapes. 
  • recognise polygons, or two-dimensional shapes, as plane, closed shapes with three or more straight sides and corners (or angles).
  • are familiar with the fact that polygons can be classified according to properties, including the number of sides. Students should be able to use these properties to recognise and name two-dimensional shapes, including non-typical examples of shapes. 

Students would benefit from some experience manipulating two-dimensional shapes.


Lesson 1: Shape Makers

This task asks students to create two-dimensional shapes by joining pins on a circular geoboard. As they create shapes, they develop an understanding of the properties of triangles and quadrilaterals. They also identify what makes a shape regular or irregular.

Lesson 2: Joining Triangles

This task explores the different shapes that can be made by joining together a set number of identical equilateral triangles. Students first explore combinations of 2, 3 and 4 triangles. They are then asked to find all possible shapes that can be made from 5 triangles. They are asked to justify that they have found all possible combinations.

Lesson 3: Combining Squares

This task explores the different tetrominoes that can be made by joining together four squares. The students are asked to justify that they have found all five possible tetrominoes. The students then use two of each tetromino to create two different rectangles.


Last updated November 3 2017.