The Mathematics of Kaleidoscopes

 With the New Zealand Mathematics Curriculum of the 1990's each Achievement Objective was prefaced by words such as; "Through problems and investigations students will achieve.."

This was a time when those involved in Mathematics Education Teaching and Learning also encouraged "Contexts for Studying Mathemathics" so that the maths skills and ideas had real life ideas to explore and learn the mathematics.

On Thursday I visited an Oral Surgeon, and before he filled y mouth with Instruments he asked me what I used to do. This of course opened a quick discussion about "How Children Learn Maths and My Philosophy"  When I mentioned Contextual Learning he said that he did Orienteering with his daughter! Wow what a great physical as well as mathematical activity. Geometry and Measurement in CONTEXT! I then offered to send him some repeatable maths activities for the family to do together, otherwise he was going to go online to find Maths Pages. I encouraged the games as they would be learning together, they are fun and they would be "talking mathematicss" 

This then got me thinking about other activities that students and families could become involved with. The first is KALEIDOSCOPES. I have never come across anyone who doesn't like at the wonderful patterns made by a Kaleidoscope.  But how many of us have explored the mathematics?  The attached PDF might be the start of a great exploration ending up with making your own kaleidoschope in the future.  Kelston Intermediate back in the 80's had a Metal Work Teacher who had a unit about the making of a Kaleidoscope but no real exploration of the mathematics that help make the patterns.

 

Enjoy your dip into the wonderful world of Kaleidoscopes (Acknowledgement to Creative Publications-Dale Seymour-for Kaleidoscope Math by Joe Kennedy and Diane Thomas)