Lesson video

Hello, I'm Mr. Langton.

In this lesson, we're going to look at forming and solving equations from descriptions.

You need to make sure you have something to write with and something to write on, and try and find a quiet spot where you won't have any distractions.

When you're ready, we'll begin.

Okay, we'll start off with our try this activity.

An isosceles triangle has a perimeter of 30 centimetres.

The two longer sides are twice as long as the shorter side.

How long are the sides? Pause the video and have a go.

When you're ready unpause it and we'll go through it together.

You can pause it in three, two, one.

Okay if you had a go, let's see what we can find out.

Now we don't know the length of any of the sides yet.

So I'm going to start off by calling one of them X.

Now it says the two longest sides are twice as long as the shorter side.

So that means that this one is two X twice as long and this one is also twice as long.

Now altogether that the perimeter of that triangle is going to be X plus two X plus two X.

And we're told that the perimeter is 30 centimetres.

So that equals 30 centimetres.

So simplifying that will give us five X is equal to 30 and so one X must equals six.

So the shorter side must be six centimetres long.

And the longest sides, they're twice as long as the shorter one, so each of those must be 12 centimetres long.

Right, now these next problems look much trickier than what we've already done.

You can be pleased to know that once you've had a little bit of a go at it you're going to fly through it.

We'll starts off with the one on the left.

I think of a number now.

Now as we said, if we don't know what it is we're going to call it by a letter, it's an unknown.

So let's call it X.

I'm going to multiply that number by three.

So I multiply X by three, I've got three X and then I'm going to add seven and the result is 25.

I can find out what that number is now can't I.

I subtract seven from each side.

Then three X equals 18.

Then if I divide by three, I get X equals six.

Easy.

Right.

The one on the right is a little bit trickier, but we'll work through it slowly.

We'll be fine.

I think of a number, that's X.

If I double it and then add five, I get the same results as subtracting it from 20.

Now that line there is a little bit tricky.

So I'm subtracting a number from 20.

So that's not X take away 20.

If I'm subtracting it from 20, that means 20 take away X.

Now I'm going to solve this.

I'm going to start off.

Let's subtract five from each side first.

That's going to give me two X on the left.

And if I take away five, I'm going to have 15 take away X.

Now let's add X to each side.

And I'm going to get three X equals 15.

So X equals five.

Now the important thing is just read it really, really carefully and take your time.

Read it slowly, step by step, and write down everything as you go along.

So I thought of the number, so that's X.

So I wrote down X, straight away.

I doubled it, so I multiplied X by two and I got two X, and just work through step by step.

Okay, so now you can pause the video to have a go at the worksheet.

If you struggling unpause it and I'll put a few hints and tips on the next slide.

Then once you've had a go at that, you can pause it again and you can finish it yourself.

Let's see how you get on.

Okay so I'm going to start off just by working out the equations for each one.

I'm not going to find the value of the number.

I'm not going to get to the answer.

I'm just going to start off by forming an equation.

So for the first one, I think of a number which is X, and multiply it by five, and then I add seven.

And my answer is 22.

What was I thinking of? I'm just going to leave that there for a little bit.

If you want to go without me, you can have a go.

Antoni is A years old.

Binh is three years older than Antoni.

Let's write that there.

So whatever Antoni is, Binh is three years older.

Now, Cala is twice as old as Antoni.

That's going to be twice as old.

The total of their ages is 51.

So if I add together their ages, I get 51.

I could simplify that.

Four A plus three equals 51.

I'm going to leave that there so you can have a go yourself.

Move on to the third one.

Xavier thinks of a number, which we're going to call X.

Five times that number, that's five X, taken away from 21 leaves seven.

That was sneaky wasn't it.

Five times that number taken away from 21.

You need to write it like that.

Finally, this is one of my favourite ever questions.

A bottle and a cork costs one pound 50, the bottle costs one pound more than the cork.

How much does the bottle cost? So the bottle and the cork costs one pound 50, and the bottle is one pound more than the cork.

So whatever the cork costs, I need to add on one pound to that to get the cost of the bottle.

So if I look here, if I said that the bottle is the cork plus a pound I can replace that there, so I've got my cork plus a pound plus another cork makes one pound 50.

And I'll leave you to solve that.

So if you want to have a go at those four now, pause it and carry on.

And then I'm going to go over the answers in a moment.

So now I've changed colours, let's solve these problems. Five X plus seven equals 22.

So my first step will be to subtract seven from each side.

That's going to give me five X equals 15.

So X equals three.

So I was thinking of the number three.

Let's check that shall we.

Think of a number, three.

Multiply it by five, 15.

And add seven, 22.

The answer is 22.

That's correct.

Right, so four A plus three equals 51.

If I sub.

Let's write that here.

Four A plus three equals 51.

If I subtract three from each side, I'm going to get four A equals 48, and if I divided by four, A is 12, divided that by four as well.

So that means that Antoni is 12 years old.

Binh is three years older, so Binh must be 15.

And Cala is twice as old as Antoni, so 12 times two is 24.

And let's check that.

We said Antoni is 12, Binh is 15, and Cala is 24, and if we add those together.

39, 49, 51, yep it makes 51.

So we've got it right.

Right, Xavier's number.

21 take away five X equals seven.

I'm going to add five X to each side.

That's going to give me 21 equals seven plus five X.

I'm going to subtract seven.

That's going to give me 14 equals five X.

And if I divide by five, I'm going to get 2.

8.

So that is really sneaky isn't.

Xavier was thinking of 2.

8, it wasn't even a whole number.

And finally the bottle and the cork.

We said the C plus one plus C equals one pound 50.

So that means that two C plus one is one pound 50, so two C.

Two corks would cost 50 pee, so one cork costs 25 pence.

We're going to do the explore task in two parts.

The first part's on the screen now, and we'll work through this one together.

Antoni has got one pen pot.

Cala has got two pen pots, and she says that her small pot is the same size as Antoni's, but the bigger one holds 12 more.

We'll start off by labelling Antoni's pot A and Cala says it her smaller one is the same, so that's A.

It says that her larger one, holds 12 more pens.

So whatever Antoni's is plus 12 is the larger one.

Now Antoni makes a second statement.

Is that together both of your pots hold five times as many pens as mine.

So Cala's together will be A plus A plus 12.

So together Cala can hold two A plus 12 pens.

Now Antoni says if we take his pen, his pen pot and multiply it by five it's five times as big, then they'll be equal.

And now we've got an equation we can solve.

If five A equals two A plus 12, then three A will be 12, and so A equals four.

So Antoni's pen pot holds four pens.

Now for the last bit.

I'm going to leave you to play with this one.

But two different size of pen pots.

This time the large pot holds so many more pens than the small pot.

And Antoni's statement here, together your pots hold so many times as many pens as mine.

And I want you to come up with as many ways as you can.

At least three different ways to fill in those blanks and see if you can find how much would be in a small pot.

So you have some fun with that and I'll see you later.

If you'd like to share any of the answers that you come up with, ask your parents or carer to share them on Twitter tagging Oak National with the hashtag learn with oak.

Good bye.