## Math Crafts – Alphabet Symmetry

Attending to visual details is an important skill in math and science education: Make a set of letters and use a small mirror to look for horizontal and vertical symmetry.

Next, use mirrors to experiment with other properties of reflection. Look for interesting images in books, newspapers and magazines and see if you can make things happen by using your mirror.

If you have two mirrors, put them together to make different angles of reflection and see rotated images! (Mirrors and reflective properties are interesting for students of all ages, even adults!)

**MATERIALS:**

- 3×5 index cards.
- Packet of alphabet letters (I got mine at the dollar store.)
- Glue stick
- 1-2 small mirrors (plastic mirrors for kids)
- Small items like earrings, beads, macaroni; or magazine pictures. (These are for studying angles of reflection.)

**DIRECTIONS FOR ACTIVITIES WITH ONE MIRROR:**

**1. Glue letters to index cards. Use one mirror to look for lines of symmetry in the letter.**

For example: B has one line of symmetry (horizontal).

H has two lines of symmetry (horizontal and vertical).

A perfectly round circle has an infinite number of lines of symmetry!

**2. Think of reflection challenges. For example:**

Start with the letter R. Can you make a B out of an R?

Start with an R. Can you make a K out of an R?

Can you make a W out of an M?

Can you make an M out of an N?

**3. Look for the book M is for Mirror: Find the Hidden Pictures, by Duncan Birmingham.**

**4. Look for magazine pictures that have symmetry.**

For example, find the line of symmetry in a butterfly, a light bulb, a person’s face (though faces are not perfectly symmetrical!). Play with your mirror(s) and make other reflection discoveries.

**DIRECTIONS FOR ACTIVITIES WITH TWO MIRRORS:**

If you have two mirrors, you can study angles of reflection.

**1. Little kids can make big angles and little angles.**

Put small objects between the two mirrors and look inside. What do you see? (Lots of images!) Make the angle get bigger and smaller to see a different number of reflections!

**2. Older students can think about why this happens, by considering the exact ****angle of reflection**.

A complete rotation is 360◦.

Put two mirrors together to make a right angle (90◦).

Select a small item to put between the mirrors. If you make an exact right angle, you will see four images: the original item and three reflections, because 4×90=360.

If you make a 60◦ angle you will see 6 images: the original and 5 copies, because 6×60=360.

Use a protractor and some small objects (like earrings, paperclips, or stickers). Deliberately experiment with other angles.

Try 45◦ (for 8 images); 120◦ (for 3 images); 40◦ (for 9 images).

Here’s an example using 72◦ (for 5 images):

**QUILT DESIGNS:**

Another fun activity is to use mirrors to see reflected images in quilt designs. Many quilt designs are made by sliding, rotating, or reflecting a basic design. These two books are featured in the Let’s Read Math Quilts packet:

** Eight Hands Round**, by Ann Whitford Paul, and

** Sam Johnson and the Blue Ribbon Quilt**, by Lisa Campbell Ernst.