Thursday, 15 August 2013

Lesson 4 : Geometry

Today, I had learnt something new about the topic of Geometry. I can use geoboard to find the area of a figure, using the dots. This is something new to me, as I was only taught during my school days, that geoboards are only used for symmetry. Little did I know that actually the concept is about the same except that finding the area of the figure is much more abstract than symmetry in which I just need to find make a figure into equal parts or create another part to make a whole.

By introducing geometry to the children, get them to explore with the coloured square tiles by using a specific number of square tiles to form a figure, making sure that the sides touch one another and it must not be a repeated pattern.
This ensure that the children understand that with squares, we can produce other figures , grasping the concept of 1 square unit. 

By getting children to learn how to find the area of a figure, firstly, I need to show the children an example of 1 square unit. 
Then, I can get the children to explore with the concrete material, in which in this case is using a rubber band to create a figure that has a dot in it. When doing this activity, I wondered to myself "Why must we create a figure with a dot in it?" There must be something more to this. So I created a figure that has a dot in it.

By using 1 square unit, the children will be able to identify the area of the figure that they had created by counting the number of squares and visualize that one square is the same as 2 triangles. Thus, children must have the content knowledge of counting numbers, in which in this case is counting the numbers of square units, and understanding of shapes - 2 triangles = 1 square, 2 squares = 1 rectangle, and ability to visualize the different shapes that comprises of the figure.
As people think differently just like children do, there are different figures that were created that have a dot in it. With this, we found out that through drawing figures with one dot in it, area of the figures are different and thus perimeter are different too.

In class, we found out that in figures with one dot in it ...
5 dots  (perimeter) = 2 1/2 squares (area)
12 dots = 6 squares
9 dots = 4 1/2 squares

There is a number pattern in our findings in which ...
2 1/2 x _ = 5
2 1/2 = 2.5
5 / 2.5 = 2
Thus the number of dots is twice as much as the area in squares.
Out of curiosity, I actually tried to see if this formula applies the same to the rest of the number of dots in the figure.

I tried for 0 dot in the figure using a square with 4 dots ...

4 dots = 1 square

1 x 2 = 2
2 + 2 = 4
6 dots in a triangle = 2 squares
2 x 2 = 4 
4 + 2 = 6

I tried using 3 dots in the figure ...

15 dots = 8 squares

8 x 2 = 16
16 - 1 = 15

4 dots  in the figure
16 dots = 9 squares
9 x 2 = 18
18 - 2 = 16
5 dots in the figure,
18 dots = 10 1/2 squares
10 1/2 x 2 = 21

21 - 3 = 18
Through my findings, the formula does applies to the rest of the number of dots in the figures except that when there is 0 dot in the figure, I have to add 2 to the sum to match the total number of dots.
However, as I increased 1 dot in the figure, the number gets bigger but subtracting it instead.
3 dots = -1
4 dots = -2
5 dots = -3

I find this activity rather interesting, as it challenges my ability to think in depth as I wondered why must we put 1 dot in the figure, and does this apply the same to the number of dots as I increase or decrease the number of dots in the figure. 
With this, I managed to solve this problem with abstract thinking and children were able to do this, provided they are given the opportunity to explore with the concrete materials and picture it through visualization.

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