# [IAEP] 40 maths shapes challenges

Maria Droujkova droujkova at gmail.com
Sat Sep 5 07:45:42 EDT 2009

```On Sat, Sep 5, 2009 at 2:23 AM, K. K. Subramaniam <subbukk at gmail.com> wrote:

> On Friday 04 Sep 2009 10:12:36 pm Maria Droujkova wrote:
> > Circle is one of the hardest in Scratch. Unless I am missing a command.
> Maria,
>
> Could you be more specific please? hardest to understand through Scratch or
> hardest to create after having understood?
>
> Subbu
>

The smooth circle is hard (trig?), the approximation of a circle by polygons
is easy. Actually, it's one of the first thing, beyond going straight 10
steps, many kids I worked with try in Scratch:

- When Space is pressed
- Move 10 steps
- Turn right 15 degrees

This polygon looks "close enough" to kids that they call it "circle."

This discussion was very helpful. A Math Club I lead for 5-6 years old is
crazy about Scratch. The last unit we did, all August, was on maps and
mazes, suggested by kids based on their roleplays (pirates mostly). That
lead into some interesting shape work. I was eying these puzzles, but wanted
some story tie-in. This conversation reminded me of Flatland. Luckily, last
year a very nice short movie came out, quite accessible to 4-6 year olds:

In that story, Triangle parents have Square kids, Square parents have
Pentagon kids and so on. The more angles there are, the higher the society
status, until polygons have so many angles that they look like Circles, at
which point they become (evil) priests. So, I am thinking of inviting kids
to work with this in Scratch. Hopefully, we will arrive at a general way of
programming regular polygon angles, as a time-saving device (from doing
every shape by hand). But this is not the main mathematical reason I want
this.

The last time polygon approximation came up for this kids, we were making
gift boxes (general prisms) out of paper. First, kids drew pictures, say, a
dinosaur or a light saber, then made the boundary into straight segments,
then drew rectangular flaps next to each segment, cut out and lifted flaps
to form the box.

My hope is that Scratch polygons will be another entry into this calculus
example space devoted to approximation. Ideas and advice appreciated.

Cheers,
Maria Droujkova