As defined in the required textbook, geometry is a “network of concepts, ways of reasoning and representation system” use to explore and analyze shape and space. Acquiring geometric thinking and understanding geometric concepts are essential for better understanding of algebra, proportional reasoning, measurement and integers.
What are geometry goals for children?
- spatial sense and geometric reasoning: children think and reason about shape and space.
- the specific geometric content objectives: shapes & properties, transformation, location, visualization
In class, we were given square tiles to explore. We were asked to make different shapes using 3, 4 and 5 pieces of squares. We then looked at the number of different shapes we can make. It was then that we learn that making the odd shape using the 5 squares is pentomino. It is just like the shapes we see in a traditional game of Tetris. We learnt that all the pentominoes have the same area but different perimeter.
We then explore the geoboard in a pictorial form. We were asked to draw out any shape leaving only one dot in the middle. This was an interesting activity. We then had to find the area of these shapes. We look at very interest shapes. It was easy to find the area of the odd shapes when we find other shapes within that odd shape. For example, different size triangles within that odd shape and square too. We also used addition and subtraction when looking for the area of the shape.
It is through this activity, that we discovered a pattern that allowed would help us find the area of the odd shape easily. As long as there is one dot in the middle, we only needed to count the number of dots in the perimeter and divide it by two. This is incidentally a simplified version Pick’s theorem. I thought that was really interesting. It also reinforces the importance of looking for patterns.