Published 3 months ago by Ann Baker
Just had a great Place Value Day with the staﬀ at Salisbury Park Primary school. What an enthusiastic staﬀ — so much fun to work with.
A big focus of the day was magnitude.
If students haven't had suﬃcient experiences with fluid materials, they may not develop ideas of magnitude or eﬃcient strategies for counting objects by unitizing (making countable units).
Jigsaw puzzle pieces are cheap to acquire from op-shops which means that thousands become readily available without us needing to worry about them getting lost, etc.
After using them in many ways to count, subitize and make informed estimates, it was time explore how numbers grow in the base 10 system.
First, I asked the teachers to set out 1 puzzle piece, a line of 10 pieces and an array of 10 pieces.
They were then asked to describe the relationship between the 1 and the 10s.
Conversations then ensued about which looked like more, the line of 10 or the array with 10. From there teachers were asked to estimate, show with their hands, how long a line of 100 would be and how big an array of 100 would be. The goal was to see how numbers grow when increased by a magnitude of 10.
The photos below show:
Teachers constructing the line and the array.
What happens when the table isn't long enough (an arm is useful).
The invention of a system of 10s marked by the paddle-pop sticks.
The biggest surprise was that the line of 100 was 'so long'.
Teachers were then given a 'Fermi' problem : “How many jigsaw puzzle pieces would be needed to cover the classroom floor?”
They were reminded that the intent was to create a system of tens. First reactions were based on creating a square metre and then measuring and multiplying.
Jigsaw puzzle pieces are so cheap that key can be treated with less respect than some materials , so my question was “What if I gave you some blue tac and paper?”
Lights began to go on, sticking down 100 and using iterations of them led to excitement.
Seeing 1000 or even 10,000 set out en masse was exciting too.
Finally, the conversation turned to how to structure an activity such that the students do the thinking and see the utility of a system of 10s.
You know what? Jigsaw Puzzle pieces rock! Have fun — we certainly did!
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