Area

Today we were looking at measuring area. Ioan (9) and Finny (7) had previously looked at measuring area at the start of the first lockdown, when all our maths work was Rainbow themed, but it was all new to Cian (4).

Resources

Magnatiles
Counters
Crystals
Elephants
Grimm’s concentric circles

What is area?

Area is the amount of space taken up by a 2-D (flat) shape or surface.

I gave Finny, Ioan and Cian 4 magnatile squares each. I asked them to rearrange the magnatiles to make as many different shapes as they could.

However the squares were arranged, the shapes all had the same area. The area was 4 squares.

Finding the area of a square

I wanted the boys to compare and contrast which shapes were the most effective for measuring area. Finny had selected counters, Ioan had some of his crystals and Cian had some of his Schleich elephants.

At the end they discussed which objects had been the best to fill their square, then Cian treated us to a song.

Finding the area of my shape

I had cut out a cross shape and filled it with some of the Grimm’s concentric circles. The circles were all different sizes. Some had gaps between them and some were overlapping each other and/or the edges of the shape.

I asked the boys if they thought these circles were good counters for measuring the area of my shape.

Using large squares

Cian decided to use squares to measure the area. He worked out the area was 5 large squares. As he was placing his log slice number 5 below his magnatiles, he realised that we hadn’t counted the circles in the previous example, so went back and added the answer for me.

Using small squares

Finny chose to use smaller squares to measure the area. He explained that if you were using smaller squares, you would need more of them to cover the same area.

In the video above, Finny worked out that you would need four times as many larger squares as small squares, because you could fit four small squares in each of Cian’s large squares. This meant the answer was four times bigger and the area was 20 small squares.

Ioan decided to look at whether triangles would be any use for measuring the area of my shape.

Using equilateral triangles.

An equilateral triangle is a triangle in which all three sides have the same length. He could join them together to make sure there were no gaps, but the hexagon shape didn’t work well for measuring the area of my shape.

Using isosceles triangles.

An isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version would include the equilateral triangle as a special case

Yoshi tried laying the isosceles triangles in a fan shape and parallelogram, but neither worked for measuring the area of my shape.

Using right-angled triangles.

An right-angled triangle is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.

Ioan worked out that if Finny had an area of 20 smaller squares, he would have double that, because two of his right-angled triangles were the same size as a smaller square. His area was 40 right-angled triangles.