The purpose of this activity is to engage students in an investigation into the results of transformations on given shapes.
This activity assumes the students have experience in the following areas:
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
Tuila cuts these regular polygons out of cardboard.
She chooses one shape and draws around it. She then reflects (flips) it along one side, and draws around it again. She does this several times to make a pattern. Using the same shape, she makes a second pattern by rotating the shape (turning on a corner) and drawing around it. She then makes a third pattern with this shape by translating (sliding) the shape and drawing around it.
For the chosen shape, she finds that all of the patterns look the same, no matter whether she reflects, rotates or translates the shape to make the pattern.
Tuila says this happens with all three shapes.
The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
Allow students time to work through their strategy and find a solution to the problem.
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
The student follows the instructions to Tuila with different shapes to form patterns. They conclude that the patterns for a square are the same but the patterns vary for other shapes.
Click on the image to enlarge it. Click again to close.
The student imagines the effects of rotations on different shapes.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/transforming-patterns at 8:50pm on the 26th February 2024