Lesson video

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Hi everyone.

Miss Jones here, and welcome to today's lesson.

Today we will be combining two topics that you hopefully have a good idea about already.

Perimeter and expressions.

To combine them and make perimeter expressions.

But before we can begin, please make sure you have a pen and paper as well as clearing any distractions and trying to make sure you have a nice quiet space to work in.

Pause the video now to make sure you have all of that ready for today.

Let's start.

How many different triangles can you draw by connecting dots on this three dot by three dot grid? So you may want to draw out three dots by three dots and experiment with how many different triangles you can draw.

If you want an example keep watching but if you're happy, pause the video now.

Now here's another example of a different triangle.

We can see here that we've actually just moved this vertex along one here, and that's created a different triangle.

So pause the video to have a go.

These are all of the different triangles here, we could have had eight different triangles.

Some of you may have done something like this, where we've got this triangle and you also found this one, and this one, and this one but, they are actually the same triangle we consider them to be identical, or congruent.

Congruent's a word that you will see come up quite a few times later on.

But for now, congruent is an identical shape, but it's been reflected, rotated, or translated.

Perimeter is the total length of all sides of a shape.

When the side lengths are written algebraically the perimeter can be written as an expression.

We can see an example here.

So we've been given this length here as p, it goes between two dots horizontally or vertically, and we can see this length q, which is the diagonal length.

The expression for this perimeter is one, two, three, four, five, six p add one q which we just write as q.

So six p add q for this perimeter.

Have a go at this, what are the perimeter expressions for these two shapes here? Pause the video to have a go.

Hopefully you managed to get that we have one, two, three, four p and one q.

So our expression is four P add q for the first one, and for the second one, we have one, two, three, four p again but this time, we have one, two, three q.

Really well done if you got those.

You can find perimeters quickly by grouping parts together.

We can find the perimeters in a factorised or unfactorized form.

So again, we're using the same length p and q.

We have this shape here, which if we count each one individually, we've got one, two, three, four p add two q, which we can see here.

But actually, we could split this into two groups.

You could group them together to make our counting quicker.

So now we have two groups, of two p and q.

So we can write it as two lots of two p add q, and that is our factorised form.

Now have a go at writing these in factorised and unfactorized form.

Pause the video to have a go.

So I actually start with the factorised form cause personally I think it's a bit quicker.

Because I can see four and.

On the first one, I can see four identical groups.

One, two, three, four.

And that's four groups of one q and one p.

Four groups of q add p.

And the unfactorized version is four p, so sorry, four q add four p.

Doesn't matter which way round is cause they're commutative.

Here on the second shape, again I actually have four groups, I can see straight away and in those four groups, so four dots of one, two, three p add q, which means altogether my unfactorized version 12 p add four q.

Brilliant job if you managed to get both of those, and hopefully you can recognise that sometimes it can be quicker just to group things together.

And we saw that.

and we're going to see that sorry, in our counting strategies that we'll come to later on.

Pause the video to complete your independent task.

The first question is asking you to simply simplify the following expressions.

So you've got p add p, add p, add p four p's.

N add three m, add two n, add two m, hopefully we can remember to collect the like terms. Imagining if you had those blocks perhaps, where have three n's add five m.

For the second question, we've been asked to complete the missing information.

So we've got a shape here, and we want to find the perimeter.

Now we see that we want it to equal two things.

So that means you want the perimeter in factorised and unfactorized form.

So you might see straightaway that we could split this into two groups.

But if not, maybe you counted them first altogether.

So we've got one, two, three, four, five, six, seven, eight p And we've got one, two, three four q.

And you may have split this into two groups possibly like I suggested, or you could even split it into four groups of two p add q.

So for example, let's split it like this and there yes.

Et cetera, et cetera.

And for the other questions, here are your answers.

The last bit you could have written.

you could have drawn in different ways but this is just an example, and you just need to check that you've got six p's and six q's.

Really well done if you got all of those or some of those correct.

The Explore task.

Match the expression to the shape with the corresponding perimeter.

So at the bottom here we have three expressions and a missing one.

And we've got three shapes and a missing shape.

You need to match the expression with the perimeter and fill in the missing expression that goes with one of these three shapes.

And fill in the missing shape that goes with one of these three expressions.

Pause the video now, to have a go at that.

And this is what you should have got.

As with the last time, this shape is an example there are different shapes you could have got, as long as you've got 12 p's and one q.

Really well done if you managed to have a go at that, and you managed to get some, or all of those correct, and that again brings us to the end of today's lesson.

Well done for all of your hard work and please make sure that you complete your quiz to check your understanding at the end.

And I will see you next time.