# Day 4 (15 August 2013)

Use 3 square tiles to make 1 figure.

On a condition that : Any 2 tiles that touch must touch completely

So I worked on this problem with my peers. And wow! We came up with at least 9 figures…

BUT!

Dr. Yeap explained that if the figures can overlap, then they are the same.

Hence, that left us with only 2 figures…

In this video we count Polyominoes of different forms, and investigate some nice tiling problems. Some of these puzzles are very challenging, but fun even for primary school students.

Through this lesson, I came to realize that it is actually not difficult for educators to give children the concrete experiences to learn a Math concept. Any Mathematical concepts can be done through the CPA approach and it is really up to the individual educator to make the effort to make learning easy, fun and interesting for the children.

GEOMETRY

When Dr.Yeap posted the class the question:

Can you find the area of the polygon you have drawn?

My first reaction was ‘What? Find the area? How???

Then I began to think of ways in which I could tackle the problem.

1. I began to fall back on the typical area calculation using the formula method ‘Length x Breadth’ (No, it doesn’t work)

2. Oh there! I saw a square… oh no, wait, let’s see… if i try to turn the orientation of my triangle, oh yes… i can get another square. That makes two squares…and a triangle left. That’s 2 and a half square units.

Dr. Yeap then posted another question:

Is there any other method to find the area of the polygon you have drawn?

I studied the answers (areas of the 4 different polygons examples) on the whiteboard. I look at my paper, practically staring at the dots. Then I had an idea. Could it be the dots? I started counting. I have 5 dots. If I divide my 5 dots by 2, I would get an area of 2 and a half units. But is this the method to do it? (I went on to check if this ‘theory’ apply to the other examples.) To my surprise, IT DOES! I was in total awe.

It was an eye opener on how easily we could derive to the answer (the area of the different polygon) just by counting the number of dots. (Note: This theory only apply on the condition that there is one dot inside the polygon drawn.) It’s again about visualization isn’t it?

Then I was puzzled.

So, how can we find the area if I have more than one dot inside the polygon drawn?

Aha! That is when Dr.Yeap introduced Pick’s theorem to the class.

Pick’s theorem provides a relatively simple alternative. In order to use it, two definitions must be stated:

Boundary Point (B): number of dots outside

Interior Point (I): number of dots inside

A = 1 + B/2 – 1