Star Doodles and Factors

Today, we are going to investigate numbers with some doodles. Everyone look at the first side of the worksheet.

What do you think p stands for?

"Points," someone answers.

Not just points, but NUMBER of points. Let's do the first one together.

Choose any point. Then, going clockwise, jump 2 points from your first point. Connect this new point to the last point with a straight line. Go jump another 2 points and join this point to your last point. Keep going until you reach a point already joined up.

What do you get?

"A star."

There is a special name for this star. Does anyone know what this type of star is called?

"A pentagram," says someone.

Excellent. The secret society of Pythagoreans used this star as their secret symbol.

j stand for the NUMBER of points you jump. Write j = 2 under your pentagram. Now try the next group where p = 5 and j = 3.

What do you notice?

Now try the group where p = 6 and j = 2. Stop when you get to a point already connected.

At this point, many students were excited by the stars and completed 2 equilateral triangles to form the Star of David. That is, 2 lots of 3.

What happened?

"We got 2 lots of 3, which makes 6."

Go ahead now and experiment drawing different doodles with different values for p and j.

This is fun. Everyone thinks the stars are cool and many people decide which is their favourite.


Let's look at the group where p = 9. Can anyone predict what value of j we should use so that we connect every point before we get back to the point where we started?

"I think that will happen if we use a value for j that is a non-factor of the p number."

Non-factor; is that a real word? Sounds good to me.

A good conjecture; everyone try it.

I have some balls of wool. Let's gather into circles, pass the wool around and make some of our favourite stars.


This activity led to great discussions and fabulous fun. Terminology included factors (and non-factors), multiples, divisibility and prime numbers.
But the best thing about the lesson was everyone was able to access the work. At the other end of the spectrum, I thought I had understood everything about the lesson, until someone says...

"But what about when p = 10 and j = 4? 4 isn't a factor of 10."

P.S. Thanks to vihart for the inspiration.

Your Mind's Eye - Spatial Abstraction

Everyone stand up.

On the count of 3, point to the location I am about to name. Don't be influenced by anyone, they could be wrong.

The canteen   1, 2, 3 ...
Everyone got this right, as it was visible from the room!

The bus stop   1, 2, 3 ...
Most got this right. It wasn't visible but it wasn't far away.

The local shopping mall   1, 2, 3 ...
A few more arms are pointing the wrong way, but consensus wins over.

Los Angeles   1, 2, 3 ...
Now, being in Australia, this location was a source of great debate.

After looking at Mercator and Peters projections of the planet, everyone agreed on a direction.

Now someone says, "We could go the other way around the globe."
Easy, point in the opposite direction to the last answer.

But then someone says, "We could dig through the earth."
I think, in the end, we actually did point towards L.A.