Kia ora tatau
I'm
looking forward to tomorrow - and sad that there are only four sessions
possible this term. So this is our last. Never mind - we will round
up the term with (hopefully) lots of insights and fresh questions to
explore. Here's the plan:
(1) Boxes and three dimensions -
Last time we continued looking at boxes and cut one up (or looked at
one that I had cut in advance - that was fun, thought provoking - and it
used visualisation. I will bring them along again tomorrow, with a
slightly different twist (Jenny - you will see what happened - and not
be left behind).
(2) Rates of change and the beginnings of calculus.
Last time we investigated patterns where the rate of change was
constant (we added 3 coins each time to get to the next pattern) and we
saw on a graph that the pattern was a straight line with a gradient of
3). And we actually figured out the equation of the line (but only
just, time was running out). We learnt that figuring out the equation
was possible - but a bit tricky. So we won't bother with figuring out the formulae this week.
I will give them to you - and we will see what we can find out about
the shapes, and the gradients. And how this links to calculus. And how
its okay to make up fresh ways of explaining things (as long as your
associates know what you mean by what you say. (I wish/hope we might
have time to revisit "magical 3D numbers" that are less than 100 - but I
think we'd be better to finish with something more practical.)
(3) More visualisation.
The theme of these sessions has been around dimensions - lines have
one dimension, surfaces have two dimensions, solids have three
dimensions. So what has zero dimensions? Then we'll think about
something that is even more puzzling. I'll bring some scissors. And
we'll chat about whatever suits us.
Ngā mihi
Elaine
https://www.dropbox.com/h?preview=calculus+definition.png
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