# symmetry

## SYMMETRY

Symmetry.

The more it changes, the more it stays the same.

Now that’s a wonder!

### EPISODE 1: Symmetry as a transformation

A symmetry is a transformation …

that leaves an object looking unchanged.

### EPISODE 2: Rotation symmetries of the square

How many rotation symmetries does a square have?

### EPISODE 3: Symmetry as a permutation

When we label the vertices of the square with 1, 2, 3, and 4 dots, we can find permutations that are equivalent to symmetries.

A permutation is an arrangement of a set or subset of objects.

Here are the 4 rotation symmetries of the square as permutations.

### EPISODE 4: Reflection symmetries of the square

Rotation symmetries stay as a group.

Reflection symmetries like to meet new “friends” when they transform one another.

### EPISODE 5: Bumper symmetries

What happens when you imagine the 4 rotation symmetries of the square as bumper cars, where they transform one another as they bump?

Grades 2/3 students used sticky notes to simulate this.

… coming soon

… coming soon

… coming soon