Art / Homeschooling / Maths / Unschooling

Playful Math with Mirror Books


Playful Math with Mirror Books

Did you know that young children are capable of understanding complex math concepts such as algebra and calculus?

I read a fabulous article recently that explained so well how instead of supporting the natural and playful way children learn about maths, we dumb it down into a step by step process which is in complete contrast to how their brains work. Instead of letting them playfully explore big math ideas we bore them with direct instruction in what we think are the easier aspects of mathematics first. They can only move on to more complex areas when they’ve mastered the basics, robbing them of finding the real life meaning and joy in maths.

Playful Math with Mirror Books

How many adults remember hating maths class at school, or think they are no good at it? Maybe if we worked WITH children’s brains instead of against them that number wouldn’t be so high. Despite never having direct instruction in maths apart from those times when they have asked me to explain something, I see my children exploring maths every single day. Being ‘schooled’ in maths myself sometimes I don’t even recognize it when I see it. Maths to me always meant numbers, and I’m only now discovering that it is so much more than that.

Playful Math with Mirror Books

Reading the article I mentioned earlier I was introduced to this book which explains the ways children can explore complex maths ideas through play. I ordered a copy for myself after reading some great reviews, thinking it would help me gain more understanding about what math actually is! I discovered lots of the ideas inside were things my kids already do, such as making paper snowflakes. Who knew that was maths? Symmetry, multiplication, patterns, rotation, reflection. I’m seeing maths everywhere now!

I wanted to show you something that the girls have been playing with from the book over the past few days that they’ve absolutely loved. It’s really simple and all you need is a couple of mirrors and some loose parts.

Making a mirror book

  1. Place your two mirrors together, face to face.
  2. Stick them together with some tape along one edge.
  3. Open the mirrors up like a book and stand them upright.

Leave the mirror book out with some loose parts and let your children play however they like, exploring symmetry, radial symmetry, angles, patterns, multiplication, tessellation, reflection, shapes, infinity, and more.

Playful Math with Mirror Books

I set out our mirror book with some of our Spielgaben pieces and some other blocks and loose parts and left it for the girls to find. At first they just built in front of the mirror, not really taking much notice. Until someone did this.

Playful Math with Mirror Books

The refection caught their eye at last and they realised that they could incorporate it into what they were making.

Playful Math with Mirror Books

They began placing pieces in front of the mirror with more intention…

Playful Math with Mirror Books

…and making beautiful patterns and ‘flowers’.

Playful Math with Mirror Books

Even Miss 2 had a go. She enjoyed gently throwing some pieces and watching all the reflected pieces fall in synchronicity.

Playful Math with Mirror Books

Miss 2’s finished product. Beautiful chaos.

Playful Math with Mirror Books

Playful Math with Mirror Books

Over a few days, they’ve been taking turns creating one after the other while the others watch, and made such beautiful patterns.

Playful Math with Mirror Books

I love this rainbow flower by Miss 7.

Playful Math with Mirror Books

An accidental discovery. When she was going to pack up the rainbow flower she moved the mirrors back and noticed she’d created something different. She then played around with the angles for a while creating different variations with the same parts. They now do this after every creation.

Playful Math with Mirror Books

The angle of the mirrors can be changed to make different numbers of reflections. This would be an easy way to explain multiplication visually.

Playful Math with Mirror Books

Playful Math with Mirror Books

I don’t know whether to call this maths or art, and I guess that’s the point. Most things are not easily divided into subjects. That would be oversimplifying and limiting. Maths, like art, is beautiful and can be found everywhere. Breaking it down into step by step parts makes it seem boring and tiresome. Math, like everything, should be a form of play.

Playful Math with Mirror Books

“Math is the beautiful, rich, joyful, playful, surprising, frustrating, humbling and creative art that speaks to something transcendental. It is worthy of much exploration and examination because it is intrinsically beautiful, nothing more to say.”  – James Tanton


The book ‘Moebius Noodles: Adventurous Math for the Playground Crowd’ can be found online at Book Depository here, or Amazon here.

The girls are creating with our Spielgaben set in the above pictures. An 11% discount is available from Spielgaben for all Happiness is here readers! All you need to do to claim your discount is send an email to mentioning Happiness is here and you will be provided with a discount coupon.


Playful Math with Mirror Books



February 29, 2016 at 8:37 pm

Such beautiful creations. I will definitely be checking out this book.

February 29, 2016 at 9:55 pm

I love this post. My kid’s are in school and having been home schooled for 1 year and then schooled the rest, the math brains have been manipulated by formal education.
I have a son, who is visual and makes connections in a different way, he hates math.
I am wondering how to make this work for a 13 year old.
I was the kid that was awful at math. Meaning, how do I help him make the connection that this is math and he can apply this to fractions, multiplication, etc.

    March 1, 2016 at 1:48 pm

    Hi Gailen. I would just do the same thing. Don’t worry about helping him make the connections. Pointing it out explicitly will probably put him off and make it seem like school. I would just let him play and make observations and ask open ended questions.

March 1, 2016 at 1:41 am

This looks great – the book is going on my wish list. I loved maths in school until we reached calculus, and then it all seemed to shut down. Only now, as I gradually see and sometimes slightly understand real world applications, am I realising it was because of how it was taught, not because I was being stupid.
A bit off-topic, but do you have a particular approach to keeping the loose parts under control, particularly with a toddler? In our house this type of thing tends to get used for all sorts of things (treasure, pretend food, money, etc.), which is good but it gets scattered all over! If I really sit with them for an activity it stays under control but they also lose interest much faster. I get the impression from your post that you leave the things out for an extended period so the children can explore it and revisit it. I’m a bit torn about how to achieve this! (My kids are 2 and 4 so maybe it comes with age and I’m over thinking?)

    March 1, 2016 at 1:50 pm

    Hi Jenny, I pretty much just put up with it LOL. My 2 year old scatters things everywhere too. I do find though that after a while they calm down. They just want to explore and see what they can do but if they’re out all the time the novelty of upending things wears off eventually 🙂

      March 3, 2016 at 10:09 am

      Thanks, Sara! Good to know I haven’t been missing something obvious 🙂 (I also appreciated your post a little while back showing your house isn’t perfect!). I guess I’m still ‘deschooling’ myself when it comes to housekeeping standards, and sometimes find it hard to remember/accept that since our lifestyle doesn’t involve farming out the kids for several hours a day, the house just isn’t going to be tidy. As always, love your blog and hugely appreciate you sharing the ideas and information and your wonderful parenting.

March 1, 2016 at 10:04 pm

These are just absolutely stunning. I need to get some more mirrors…. are these ones acrylic or glass?

March 2, 2016 at 1:28 am

I would love to use our Spielgaben like this. What great idea. What size mirror do you recommend? A quick look on Amazon shows 5.5″ which seems a bit small and 12″ which seems big…

March 2, 2016 at 8:52 pm

My goodness! These creations are stunning!! I had just convinced myself not to think about buying spielgaben for the moment… Now I’m not so sure 😉

March 9, 2016 at 10:15 pm

Great great idea!!!
Thanks for sharing!

April 4, 2016 at 11:26 pm

We’ve just done this… took my Star Wars obsessed 4 year old less than 3 minutes to realise he could create a clone army in the mirrors! Hours of fun! Thanks for the idea!

May 25, 2016 at 3:12 pm

I was inspired by this post to buy Moebius Noodles and then Playing with Math by the same publisher, and we LOVE them! Thank you so much for the suggestion!

karen Taylor
July 3, 2017 at 4:19 am

I am not good with math however this project is great for me use

July 22, 2017 at 10:38 am

I would LOVE to make these and do this in my second grade classroom, but am worried about the mirrors breaking, or having frames. Where did you get yours? Are non-breakable ones available?

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