A short instructional video for Year 6 teachers/pupils exploring deeper problems about the relationship between area and perimeter. Presenters (Zoe and a second speaker) use two classroom activities: (1) test the claim “doubling area doubles perimeter” and disprove it via a counterexample using rectangles (3×2 → area 6, perimeter 10; doubled area 12 can have perimeter 16), and (2) a fencing problem where Joe has 200 m of perimeter to allocate to a rectangle and pupils investigate which dimensions maximize area, guided toward recognizing that a square maximizes area for a given perimeter.
Chapters
Hi, I'm Zoe and in this video.
We'Re going to be looking at examples of greater depth problems you can use to assess pupils understanding of area and perimeter.
Again, this is an area that pupils.
Find really quite confusing and the relationship between area and perimeter can be quite scary for them.
Having a chance to practice this, to.
Play around with it, lots of different examples should help them to firm that up.
So here's our first problem.
When the area of a shape is.
Doubled, the perimeter doubles too.
Is this true or false? Again, we've got a hypothesis, we've got a statement that we need to prove or disprove. The best way we can do this is by trying some examples. So I've just picked two rectangles. The first one had an area of.
6Cm squared, 3cm by 2cm, a good.
Opportunity to remind pupils perimeter the distance.
All the way around area, multiplying the.
Length by the width.
So here we can see the area is 6, but our perimeter is 10 centimeters.
So what we'd like to see here, now that we've got an area of.
12 centimeters squared, we're saying that our.
Perimeter should be 20 centimeters. Well, let's have a look.
Our area is 12 centimeters squared, so our length is 6 centimeters. Our width is 2 centimeters. We can see from this our perimeter would actually be 16 centimeters. So it's false.
Again, proof by counterexample, we've managed to say that we can't prove this, so therefore it must be false.
Again, mixing this up for pupils, could.
They find an example where it is true? Could they find other examples? What happens to the area if the perimeter is doubled, for example? So again, lots of opportunities for pupils to investigate this.
Moving on to our second problem, a.
Little bit more in depth, we're looking at year six here.
Joe has 200 meters of fencing.
What is the largest rectangular area he can enclose with this? First off, we're wanting pupils to realise.
200 meters is the perimeter of the entire rectangle. So therefore halving this, the length plus.
The width must make 100 meters. So we're wanting pupils to find numbers that fit.
Length plus width makes 100 and then.
To realize our length times our width gives our area and try to find the largest numbers that they can.
Again letting them explore various different rectangles so they can see the effect that.
The perimeter has on the area.
We're hoping that as they go through this they start to realize that the.
Closer to a square they get, the bigger the area because of course a square has a bigger area than a rectangle. And that is how we're getting pupils to think about that relationship between area and perimeter.
So there we have it.
Two activities you can use with pupils to assess where they are with area and perimeter.
