Lesson video

Hi I'm Miss Kidd-Rossiter and I'm going to be taking today's lesson on exploring rectangles.

We're going to build on the work that we've already done on areas, perimeters, and cutting and combining rectangles.

And it's going to be a really, really great lesson.

I hope you're going to enjoy it.

Before we get started, can you make sure please that you're in a nice, quiet place if you're able to be.

You've got no distractions, you're sitting comfortably, and you've got something to write on and something to write with.

If you need to pause the video here to get any of that sorted then please do.

If not, lets get going! So today's try this activity then.

You've got a rectangle on your screen that has a width of 6m and a length of 8m.

And you are asked to describe how the area changes if first of all, we increase the width by one metre.

Second of all, we increase the length by one metre.

And thirdly, if we increase both by one metre.

Once you've investigated the area, could you think about how the perimeter changes? And then if you really want a challenge, replace one metre with a different measure, different length, and then repeat the process.

What do you notice? Can you form any conjectures? If you're struggling a little bit, it might really help you to draw each one of the statements.

I know that would help me.

So pause the video now and have a go at this task.

Excellent, let's go through it then together.

So for the first one, we're increasing the width by one metre.

So if I draw that you would do it with a nice ruler to make sure you've got your straight edges so I apologise for mine.

My length is still 8m but my width has increased to 7m.

So what's the area of this rectangle now then? Can you tell me? Excellent, it's 56m squared.

And what was the area of my original rectangle? Can you tell me? Excellent, 48m squared.

So here, our area has increased by 8m squared hasn't it? What would our perimeter of this shape be? What would our perimeter of this shape be? Tell me now.

Excellent, it would be 28m, wouldn't it? Because 8 add 6 is 14.

Add another 8, add another 6 is 28m.

So this one here our perimeter would be what? Can you tell me now? Excellent it would be 30m.

So our perimeter has increased by 2m this time.

Our second statement then.

This time the length increases by 1m.

So again, it's going to help me to draw it but you don't have to if you can do it with out.

So this time, my length is 9m.

And my width is still 6m.

What would the area of this shape be then? Tell me now.

Excellent, 54m squared.

And what's the perimeter of this shape? Tell me now.

Excellent, 30m.

Ooh, that's interesting.

What's happened there? So my area has increased by 6m squared this time.

And my perimeter has again increased by 2m.

Finally then, what if we increase both by one metre? So our length would go to 9m.

And our width would go to 7m because we're increasing by one metre.

What would our area be here then? Tell me now.

Excellent, 63m squared.

And what would our perimeter be here? Tell me now.

Excellent, 32m.

So that's interesting, isn't it? This one, the one I increased the width by one metre.

My perimeter increased by 2m.

When I increased my length by one metre, my perimeter increased by 2m.

And when I've increased both by one metre, my perimeter is increased by 4m.

That's interesting, isn't it? What about my area then? So my area here was increased by 8m.

8m squared, I'm sorry I should be very careful with my units.

And when I increased my length by one metre my area was increased by 6m squared.

But here, my area has increased by 15m squared.

I'm going to leave that with you to think about it.

Can you form any conjectures on that? Really good work.

So the connect part of today's lesson then.

How would you find the area of this rectangle? And then can you draw some other rectangles that have the same area? Pause the video now and have a go at this task.

Excellent, could you explain to me how you found the area using a full sentence? If you haven't done that already, pause the video now and write that down.

Excellent work, well done.

So you could've said something like "I have four rows of three squares so I do four times three and that means that my area is 12 cm squared".

So that was a nice full sentence that included my calculation, 4cm times 3cm equals 12 cm squared.

So I'm looking for some different rectangles that have the same area.

How many have you managed to draw? If you haven't managed to draw at least another three, pause the video here and have a go at that.

And if you have, then can you make sure please that you're thinking about using side lengths and not integers.

Excellent, so you could've drawn one that was 6cm by 2cm.

That's another option.

You could've drawn one that was 24 cm.

What would my length need to be if my width is 24 cm? Tell me now.

Excellent, half a centimetre.

Well done.

You're now going to apply today's learning to the independent task.

So pause the video here, navigate to the independent task.

And when you're ready to go through some answers, resume the video.

Good luck! Excellent work on that independent task.

Well done.

Let's go through some answers.

So draw four different rectangle with an area of six units squared.

Here are some that you could've drawn.

This one on the left is obviously a three units by two units rectangle.

This one is a six units by one unit rectangle.

This one is a 1.

5 units by four units rectangle.

And this one is a 12 units by 0.

5 units rectangle.

These are not exhaustive.

There are other options that you could've drawn but here are some examples of answers.

Question two then.

Find the area of the following rectangles.

The first one is 20m squared.

4m multiplied by 5m gives us 20m squared.

The second one is 10m squared.

4m multiplied by 2.

5m gives us 10m squared.

And finally, 12m squared.

4m multiplied by 3m gives us 12m squared.

Moving on the explore task now then.

Are these statements always true, sometimes true or never true? And can you draw some examples for each? Pause the video now and have a go at this.

So the first statement then, for any rectangle there is another with the same area but a greater perimeter.

This is always true.

Because if you think of an example like a four by four square.

Let's say 4cm by 4cm the perimeter here would be 16 cm.

And the area here would be 16 cm squared.

If we draw a rectangle that has the same area, that is longer and thinner.

So let's say an 8cm by 2cm rectangle, this will have a perimeter of 20 cm.

So the perimeter is greater and for the area it will remain at 16 cm squared.

So there's always another that you can draw with the same area but a greater perimeter.

If you make the rectangle longer and thinner.

If we consider the same square for the second statement.

Oh, apologies for that, that's not a very good square.

Let's try again.

If we consider the same square, 4cm by 4cm.

Then we've still got our perimeter is 16 cm and our area is 16 cm squared.

This time, we want the same perimeter but a smaller area.

So again, if we make a longer and thinner rectangle.

This time, the perimeter has got to stay as 16.

So let's make it a 6 by 2cm rectangle.

The perimeter remains a 16 cm but the area is smaller and goes to 12 cm squared.

So this one, again is always true.

'Cause if you make a longer and thinner rectangle with the same perimeter, it will have a smaller area.

That's it for today's lesson.

So thank you so much for all your hard work.

I hope you've enjoyed this lesson.

Don't forget to go and take the end of lesson quiz so you can show me what you've learned.

And hopefully I'll see you again soon.

Bye!.