Cut it Out

Activity One

Predicting the shape before opening it up is a key part of this activity. It focuses students on the likely attributes of the shape and is useful preparation for discussing symmetry.
Circles that are folded in half and cut up will always generate shapes with at least one line of reflection symmetry along the fold line. That is why mirror symmetry and fold symmetry are sometimes used synonymously. Note that a half-folded circle cut up may have two lines of symmetry if the cuts are made symmetrically. For example:

Activity Two

In a similar way, a circle that is folded into quarters and then cut will generate a shape that has at least two lines of reflection symmetry (along the fold lines) and half-turn symmetry. The example shown in this activity will look like this when it is opened up:

The pattern continues with circles that are folded into eighths and cut up. These shapes always have at least four lines of reflection symmetry and at least quarter-turn symmetry.

Answers to Activities

Activity One
Answers will vary.
Activity Two
1. Teacher to check
2. a. They will all have at least 2 lines of symmetry.
b. The pattern will have at least 4 lines of symmetry.