A Symmetry Mini-Investigation

This investigation is inspired by the beautiful book Seeing Symmetry by Loreen Leedy. I really enjoyed the book and used it as a springboard into mini paper-folding symmetry investigations.

Often students can identify lines of symmetry when they are presented to them but have had limited experiences with deliberately planning folds and cuts to create symmetrical shapes Visualisation is central to spatial awareness and spatial sense. This activity builds on the paper folding activity presented on our Maths Problems for 2013 board of our Pinterest site.

The paper folding and cutting will provide experiences for students to:

•  visualise and predict the shapes and number of lines of symmetry that will result from a particular fold and cut
•  relate lines of symmetry to mirror images and reflections
• deliberately plan and explain how and where to fold the paper in order to make a specific shape or number of liens of symmetry including rotational symmetry (not as easy as it sounds

 There is a lesson plan on our site that you can download, but before you do that, have a look at these examples that the investigations can generate.

The idea is to start with the simple challenge of making one fold and cutting out a shape. At each stage, ask the children to predict what the cut-out shape will be and to name it if possible.

You'll see that I've used paper from an old fashion magazine. Well trends change, so there's no need to be looking back to the nineties for what to put on today!

I also quite liked the textures that the pages made.








The second stage is to make a second fold before you cut and this time, the shapes start to get quite complex.

I made this one up as a symmetry puzzle, with the folded paper stuck onto the sheet so that it could be opened up, one fold at a time.

And then there were three. This is my sting in the tail and it makes a great context for both naming strange shapes as well as looking for lines of symmetry.

At the end of the day, the resources are very simple and yet the outcomes are rigorous and educational valuable.
There is a sort of Arvind Gupta feel to the investigations - and if you haven't met Arvind yet, click his name to see a little bit of educational magic!