Snowflakes and symmetry

I wanted to find a way to explore the idea of symmetry again with the small boy, following on from our brief play with lines of symmetry and capital letters.  Given the large number of Winter-themed decorations appearing everywhere, he's started to ask about snow despite there being no sign of real snow here yet. Snowflakes have six-fold reflective symmetry so I thought it might be fun to combine some further play with mirrors and symmetry with learning a bit about snowflakes.

I think snowflakes are fascinating - there's an infinite number of shapes that they can form, but they are all six-sided, with six-fold mirror and rotational symmetry. Their hexagonal shape is because water molecules with their two hydrogen atoms and single oxygen fit together in the most efficient way in a hexagonal ice structure. The small boy and I have talked about the shape of snowflakes and how they form when water freezes in clouds. Last weekend and he pointed out an incorrect 8-pointed snowflake light decoration in a shopping centre, so he's clearly been listening!

The small boy helped me to build a simple snowflake design with some of our Magformers magnetic shapes on his magnetic blackboard. We started with six equilateral triangles to form a hexagonal centre and extended it from there. He then drew a snowstorm around it in chalk (which I was quite pleased about as he's not big on drawing, although I was grateful for his explanation of what the drawing was!).  The snowflake and snowstorm lasted approximately half an hour before the smaller boy decided to rearrange them and wipe off some of the snowstorm with his sleeve in the process...

Magformers shape snowflake on magnetic blackboard

Separately, I set up a symmetry puzzle on the floor with our Magformers. The challenge was to build a whole snowflake when I had put together just over half (this time with colours to match as well rather than all white, and with a hexagon in the middle). He found this remarkably easy, so I set up another one with only one sixth of the snowflake plus the central hexagon, and I put out more shapes than he needed to finish it. He had to think this one through a bit more, decided to change my original pattern to make it more snow-coloured and added several incorrect shapes as he made it before taking them away and correcting the pattern unprompted. As with our play with Duplo brick patterns, I was surprised by how strong his sense of the correct pattern was.

Magnetic shape snowflake symmetry challenge

The other snowflake-themed activity we did was to make paper snowflakes. My hazy memory of doing these at school was making an 8-pointed snowflake, but I wanted ours to have 6 lines of mirror symmetry like the real thing (as I would no doubt have been told they were wrong otherwise!). They are straightforward to make, but this is how we did it:
1. Make a square from A3 or A4 paper by folding an isosceles triangle from one corner (I.e. fold so the two edges are level as per photo below).
2. Cut the square, leaving a rectangular piece of paper (which you can use in the same way to make a smaller snowflake).
3. Fold the triangle in half.
4. Fold a third of this triangle over on one side.
5. Fold another third on top of the first 
6. Turn it over, then cut all layers of the paper at an angle below the level of the shortest side.
7. Cut shapes in all layers of the paper. We started out doing this with blunt child-safe scissors but it was tough going and the small boy gave up. Instead he directed me cutting with sharp scissors!
8. Carefully unfold the paper to see your finished snowflake design.

Steps to make a paper snowflake (numbers correspond to descriptions above)

We made several paper snowflakes of different sizes. The one the small boy did some cutting on was made from A3 paper as I wanted it large enough to have scope for overenthusiastic chopping.  However, I had forgotten just how blunt the child-safe scissors are, and we switched to using sharp scissors with him directing the cuts he wanted me to make after he got frustrated at how little progress he was making. I also made another big snowflake which looked more like the snowflake shapes he's seen on decorations. He liked the paper snowflakes anyway despite not being able to do as much cutting as I had envisaged, and I made some smaller snowflakes from the offcuts to look at with his shatterproof mirror.

Another paper snowflake

He enjoyed experimenting with the lines of mirror symmetry, placing the mirror across the snowflake so the reflection completed the parts his mirror obscured, and finding different places to put the mirror to achieve the same effect. I briefly mentioned rotational symmetry i.e. the idea that you can turn the snowflake (by a sixth of a turn, 60 degrees) and it looks the same, but he decided he wanted to make it snow instead of listening. So we had fun throwing the snowflakes up in the air and watching them spin and swirl as they fell to the floor, accompanied by Jingle Bells on repeat at the small boy's request. It felt like a nice festive end to our snowflake play, and his baby brother enjoyed joining in with catching the snowflakes!