Lesson video

Hi everyone, Ms. Jones here.

And today we are going to be learning all about perimeter inequalities.

But before we can start, please make sure you have a pen and some paper as well as removing any distractions and trying your best to find a quiet space to work.

I'm really excited to begin but make sure you've got all of that ready before we can start, and pause the video to get all of that sorted.

So the first thing I would like you to do, is to write an expression for the perimeter of each of these shapes here.

Then I would like you to consider which perimeter is greater and by how much.

Similarly, I would like you to draw two shapes with the following perimeters: 2q + 2p and 3q + 2p, and think about which perimeter is greater and by how much.

Remember you've got your values of p and q here, pause the video to have a go at that.

Look, these are the answers that we should have gotten.

4p + 3q is an expression for this perimeter, and 4p + 4q is an expression for this one.

And we can see that this shape is greater by 1q or by q.

Here are some examples of the shapes we could have drawn for these two perimeters, and we can see that this perimeter is greater by 1q.

And we're going to look at how to represent that, in a minute.

We can use an inequality to compare the lengths and perimeters of different lines and shapes.

For example, we can write different expressions for the lengths of each coloured path below.

So, for example, let's have a look at the green one.

I can see I've got one, two, three qs, and I've got one, two, three, four, five, six, seven, eight p.

So green can be represented by the expression 3q + 8p.

For the pink one I've got one, two, three, four, five, six, seven, eight p and one q, so I've got q + 8p.

Once you've found all of the lengths of the different coloured lines, I would like you to compare the lengths of each.

So for example, if I look at 3q + 8p and q + 8p, I could say that the green one is greater than the pink one.

And we can write that, using that inequality sign that we've seen before.

Extra points if you write by how much it is greater than or less than each expression.

So for example, I could have written green is greater than pink, and it's greater by 2qs.

You might notice that some of them won't be inequality, so think about what those are going to look like.

Pause the video to have a go at comparing some of these lengths and filling in the orange and the blue.

So for the orange, you should have got q + 8p, and for the blue, you should have got 2q + 8p.

So we can see straight away, hopefully, that these two lengths for the pink and the orange are equal.

So actually we're going to write an equation for that, pink equals orange.

And then here are some more examples of the comparisons you could have made.

Amazing job if you managed to do that, and obviously extra points if you managed to say how much greater or less than each expression was.

Pause the video now to complete your independent task.

For the first question you were putting in the correct symbol, whether it's > or <.

The second question, you were finding an expression for the perimeter, and then using those expressions, you needed to complete the inequality.

So here are the answers that you should have gotten.

Well, I don't know if you managed to get all or some of those correct, especially when we're looking at the inequalities here.

Use the triangles drawn or draw your own triangles to help complete the inequalities with the < or > symbol.

So for example, we can see that we've got a triangle here and we've got 3p, one, two, 3p and we've got r.

And we can use that triangle to determine which expression and which part of that triangle is greater than the other.

I would be thinking here, "What is the most direct route from one point to the next?" that will help you work out which one is going to be smaller.

So pause the video to have a go at this.

And these are the answers that you should have gotten.

As I said, using how direct a route is will help you conclude which one is larger.

So 3p is a much longer route to get from this point to this point than r was.

Similarly with this p + q takes longer than r would take longer if you were to imagine walking along those lines.

Really well done if you managed to draw some triangles to use to help you write the inequality here so you can see we've got 2ps and we've got 2qs and both are trying to get from one point to the other point.

And we can see that actually 2q has a longer way to get there, similarly p + r is a longer way to get to a point than 2qs would be.

Really well done if you managed to get those, especially if you managed to draw those triangles 'cause some people find that a little bit tricky, so that was really good.

Remember to complete your quiz and test what you've done, try and make sure that you understand what we've done in the lesson and really good job today.

We'll see you next time.