First of all, what’s a mirror book. It’s two mirrors taped together. It takes a minute to make and will entertain kids for hours.

Here’s how to make a mirror book:

- Get two rectangular frameless mirrors of equal size
- Put one on top of the other with the reflective sides facing toward each other
- Use ducttape to tape the mirrors together on one side.
- Stand them up and open the “pages” of your new mirror book

So now that you have it, what are you supposed to do with it?

*Image source: Natural Math on Flickr*

Show it to your child (with younger ones you might need to explain that those are real mirrors and should be treated with care). Take a toy or a pretty object and place it between the mirrors. Let your child observe what happens. Then move the mirrors and observe what happens to the reflections. That’s enough of the demonstration. Let the child play with the mirror book now.

*Image source: Natural Math on Flickr*

What will your child do? It depends on your child’s age, interests and personality. The first thing Rocket Boy did (he was about 3 year old at the time) was to dump a handful of LEGO blocks inside the book. Another thing he did was to put his head inside the book and move the mirrors to get “lots of me”.

What happens next is also different for each child. Rocket Boy and his friends have used mirror books to

- put rocks, acorns, sticks, feathers and all sorts of other “treasures”
- stage mega battles between LEGO minifigs
- create elaborate story scenes that involved all sorts of multiplying magic
- create mandalas
- make puzzles
- draw and paint and sculpt
- create mosaics and tessellations

Sometimes Rocket Boy would play for 20-30 minutes at a time. But most often he’d just run up to a book for a minute or so to check something, or place something new in it, perhaps change the angle of the mirrors, admire the result and switch to other things on his busy schedule.

*Image source: Natural Math on Flickr*

We also did some more formal explorations with it.

- We placed letters and numbers (from the magnetic set) into the book to check for hidden symmetries
- Inspired by the “Greedy Triangle” book, we turned a straight line into various geometric shapes eventually getting to, as Rocket Boy put it, “an angular circle”
- We magically turned numbers into each other, turned slices of pizza into entire pies
- Rocket Boy arranged mirror books (we have more than one) so that he created infinity or turned objects in the book into tree fractals
- Looked for multiplication tables hidden between the mirrors

One of our mirror books is always in the little “nature corner”. And I notice little changes in it after almost every walk.

As Rocket Boy played-learned with the mirror book, I introduced these math ideas

- angle
- symmetry – line symmetry and radial symmetry
- reflection
- multiplication
- pattern and tessellation
- polygons
- infinity and infinitesimals
- fractals

More ideas for math explorations with mirror books can be found in Moebius Noodles: Adventurous Math for the Playground Crowd. If you are looking for more pictures of what others are doing with mirror books, check out Natural Math mirror book photo album on Flickr.