As Pi Day rolls round again, I've pinched one of my colleague's "Pi Kits" and have now done this lesson with Year 7, 8 and 9 this week. It's my favourite way of teaching circumference and area of a circle, both the first time pupils encounter it and as a reminder before teaching any new circle topics. I'm surprised that some pupils have often come across pi prior to this lesson, or can even quote the formulae for circumference and area, but have almost no understanding of what it is and why it's so fundamentally important in circles.
I changed things a bit this year; usually I just investigate circumference and diameter, then do a bit of bluffing about how pi miraculously "pops up" in the area formula too. However, I extended my investigation this year to include area for some groups, and it worked really well.