Polygons with the Same Area, but Different Shape

Returning back to one of our student questions placed on our maths wonder wall:  "Is the area and the perimeter answer the same?"  we chose a number and then creatively drew as many shapes as we could that had the same area. 

Rather than doing this in one sitting, we spent about 5 to 10 minutes every few days revisiting this to create more shapes.  This strategy hopefully helped to reinforce the key understandings they were discovering themselves about mathematical space, area and perimeter whilst also keeping engagement high rather than a doing this as a solid 20 or 30 minutes.  The children experimented with drawing their polygons in the maths books and today published those they were the most proud of creating (samples below).

Children chose numbers such as 7, 12, 16 22 etc.....



All of these polygons drawn have an area of 7 square centimetres:

Lots of natural questions arose such as the names of different-sided polygons which the students found out on the net.

It sparked a lot of creative thinking as well as developing reasoning and problem-solving skills.......

Some sample reflections: What did this learning experience help me to understand?

- I learnt that polygons can have different shapes and perimeters,but the same surface area!

- When finding the name of a polygon, the size doesn't matter. What matters is the number of sides it has.

- I learnt that there is a pattern in the naming of polygons. Eg, if you want to know what a 16-sided shape is you just add 'hexa' + 'decagon.

- I learnt that there are interesting connections between polygons; this activity helped me deepen my understanding of angles too.

- It helped me to understand that no matter what the area of the shape or if the shape is irregular, it can still have the same amount of sides.

- It helped me understand that a square centimetre or a square metre can be a different shape other than a square.