Lesson video

Hello, how are you today? My name is Dr.

Shorrock, and I am really looking forward to learning with you today.

We are going to have a lot of fun as we deepen our understanding.

Welcome to today's learning.

This lesson is from our unit, "Compare and describe measurements using knowledge of multiplication and division." This lesson is called, "Compare and describe length using knowledge of division." As we move through the learning today, we are going to look at how we can compare length and how we can use this comparison to determine the value of an unknown length.

Sometimes new learning can be a little bit tricky, but I know if we work really hard together, and I'm here to guide you, then I know that we can be successful.

So then, shall we find out how do we compare and describe length using our knowledge of division? These are the keywords that we will be using in our learning today.

We've got times the length, height, or depth, and we've got unit fraction.

Let's practise those words.

My turn.

Times the length.

Your turn.

Nice.

My turn.

Times the height.

Your turn.

Fantastic.

My turn.

Times the depth.

Your turn.

Brilliant.

And last one.

My turn.

Unit fraction.

Your turn.

Nice.

Well done.

Look out for those words as we move through the learning today.

When we talk about times the length, height, or depth, it's a phrase we use, and we use it to compare and describe length or heights of different objects.

For example, one tree might be three times the height of another tree, which means it's three times as tall.

And a unit fraction, these are fractions where the numerator is 1, and there are some examples of unit fractions shown.

1/2, 1/4, 1/10.

These are the children who are going to be helping us in our learning today.

We have Lucas and Sam.

Today's learning is going to start by looking at doubling and halving.

Lucas and Sam find some ribbons.

What do you notice? Hmm.

I notice one is blue and one is pink.

But is there anything else that you notice? Ah, thank you Lucas.

Lucas has noticed the blue ribbon is shorter than the pink ribbon, and I guess that means the pink ribbon is longer than the blue ribbon.

Anything else? Oh, thank you.

Sam is telling us the pink ribbon is two times the length of the blue ribbon.

We can say the pink ribbon is double the length of the blue ribbon, or we can say that the pink ribbon is twice the length of the blue ribbon.

All those words, double, twice, and two times mean the same thing.

Lucas is saying that we can represent this as an equation.

We've got 6 centimetres multiplied by 2 is equal to 12 centimetres.

What does the 6 represent? That's right, the 6 could be that length of the blue ribbon.

So why are we multiplying it by 2? Ah, that's right.

That's because the length of the pink ribbon is twice or two times the length of the blue ribbon.

And 12 centimetres.

Then that must be the length of the pink ribbon.

So we have just described the length of the pink ribbon in relation to the length of the blue ribbon.

The pink ribbon is twice as long as the blue ribbon.

But now let's have a look at describing the length of the shorter ribbon in comparison to the pink ribbon.

So this time the pink ribbon is our whole, and we can see that we have divided the whole into two equal parts, and each part is 1/2 of the whole.

And do you notice anything about 1/2 of the pink ribbon in relation to the length of the blue ribbon? That's right.

The blue ribbon is 1/2 times the length of the pink ribbon.

Let's check your understanding so far.

Could you have a look at these images and let me know which image represents this statement? Ribbon A is 1/2 times the length of ribbon B.

So pause the video, maybe find someone to chat to about this.

And when you are ready, press play.

How did you get on? Did you notice that it must be C? If we look at representation A, well, our statement is ribbon A is 1/2 times the length.

So that means ribbon A must be shorter, and representation A, ribbon A is longer, so it can't be representation A.

If we look at representation B, well, ribbon A is smaller there, but it's not 1/2 of B, is it? No.

Look at representation C.

Here, ribbon A is 1/2 times the length of ribbon B.

And if we look at representation D, well again, ribbon A is longer there, so it can't be that one.

Well done.

So let's revisit our ribbons.

Now we can use the length of the pink ribbon this time to calculate the length of the blue ribbon.

So our whole pink ribbon is 12 centimetres and we can form an equation to help us.

So this time we've got the whole 12 centimetres, and we know that the blue ribbon is 1/2 times the length of the pink ribbon.

So we've got 12 centimetres and we're going to multiply by 1/2 and that will tell us the length of the blue ribbon.

We've got 12 centimetres is representing our length of our pink ribbon, and the 1/2 that's representing the part of the pink ribbon that is equal in length to the blue ribbon.

And the question mark that's representing the length of the blue ribbon, that's the unknown that we need to find out.

Now we need to solve the equation, but how do we solve an equation when we have to multiply by a unit fraction? Ah, Sam is telling us, remember when we multiply by a unit fraction, it is the same dividing by the denominator.

Ah.

So instead of multiplying by 1/2, we can divide by 2.

It is the same calculation.

So when we multiply by 1/2, it is the same as dividing by 2 or halving.

1/2 of 12 centimetres is 6 centimetres.

So 1/2 times the length of 12 centimetres is 6 centimetres.

Let's check your understanding.

Which options describe the length of the orange ribbon? So you can see I've got a purple ribbon that is 62 centimetres, and I've got the orange ribbon.

Have a look at options, A, B, C, and D.

Pause the video, maybe talk to someone about this.

And when you are ready, press play.

How did you get on? Did you say it was option A? Because 62 centimetres, we're multiplying it by 1/2.

So we are saying that the orange ribbon is 1/2 times the length of the 62 centimetres.

So option A works.

What about option B? Hmm.

Well, we don't want to double the 62 centimetres because the orange ribbon is shorter, so it can't be option B.

Option C, 1/2 of 62 centimetres is 31 centimetres.

That works.

And option D? Yes, that's correct as well, because remember we've just learned that when we multiply by a unit fraction, in this case 1/2, it is the same as dividing by the denominator of that unit fraction, so 2.

So 62 centimetres divided by 2 also is a correct option.

Well done.

It's your turn to practise now.

Could you complete the equations to describe the length of the shorter ribbon in comparison to the longer ribbon? So you've got two equations, have a think about what you would, how you would complete them, and then you've got a statement to complete.

The yellow ribbon is mm times the length of the brown ribbon.

For question two, look at this representation of two towers.

Could you tick the equations that could describe the relationship between the heights of the towers? So you've got six equations to choose from.

And then for part B, could you write three more equations that could describe the relationship? And for question three, you have a problem to solve.

Sam's journey to school is 1 kilometre, 200 metres.

Lucas's journey is 1/2 times the length of Sam's journey.

So how far is Lucas's journey to school? You might like to try to draw a representation to help you.

Have a go at all three questions, pause the video, and when you are ready to go through the answers, press play.

Shall we see how you got on? For question one, you were asked to complete some equations to describe the length of the shorter ribbon in comparison to the longer ribbon.

So we've got 154 centimetres multiplied by 1/2.

Remember multiplying by unit fraction is the same as dividing by its denominator.

So the other equation would be 154 divided by 2, and if I halve 154, we get 77 centimetres.

So the shorter ribbon is 1/2 times the length of the longer ribbon.

For question two, you were asked to tick the equations that could describe the relationship between the heights of the towers.

So the first equation could, because the 12 metres could be the height of the yellow taller tower, and we'll multiply it by 1/2 because the smaller tower is 1/2 times the height.

It could also then be the second equation because the factors are just switched round.

It could then be 4 metres is equal to 8 metres divided by 2.

8 metres could be the height of the taller tower, and then we are halving to get 4 metres.

And then it could be the last equation because we've got 16 metres.

Could be the height of the taller tower, and the shorter tower is 1/2 times the height.

You might have written three more equations like these.

So just check your equations were either multiplying by 1/2 or dividing by 2.

And for question three, you had a problem to solve.

I chose to represent this in a bar model.

You can see I've got Sam's journey is the whole 1 kilometre, 200 metres, and Lucas's journey I've represented by 1/2 of that whole, because we know his journey was 1/2 times the length of Sam's journey.

Then I can use that to form an equation.

I've got 1 kilometre, 200 metres multiplied by 1/2, and I thought this would be easier to do if I converted the kilometre and metre measurement into just metres.

So that is 1,200 metres multiplied by 1/2.

And we know that when we multiply by a unit fraction, we divide by the denominator.

So I've got 1,200 metres divided by 2 and that is the same as 600 metres.

12 divided by 2 is 6, so 1200 divided by 2 would be 600.

So 1/2 of 1,200 metres is 600 metres.

Lucas travelled 600 metres to school.

How did you get on with those questions? Brilliant, fantastic everybody, you are doing such great learning so far on comparing and describing lengths using your knowledge of division.

We've looked at doubling and halving, and we are now going to move on to looking and comparing and describing other lengths multiplicatively.

Lucas and Sam find some other lengths of ribbon.

What do you notice? I notice one is purple and one is green.

But is there anything else you might notice? Could you compare their length? The purple ribbon is five centimetres, the green ribbon is 15 centimetres.

What could we say? That's right Lucas.

We could say the purple ribbon is shorter than your green ribbon.

Can we be any more mathematical? Ah yes, thank you Sam.

The green ribbon is 3 times the length of the purple ribbon.

Can we see why Sam is saying that? Because one length of purple ribbon is five centimetres, two lengths would be 10 centimetres.

So three lengths would be the equivalent to the length of the green ribbon at 15 centimetres.

And we can represent this in an equation.

We've got 5 centimetres 3 times.

So that is saying that our green ribbon is 3 times the length of the purple ribbon, and that is 15 centimetres.

So we have just described the length of the longer ribbon using the shorter ribbon.

Let's do that the other way round.

Let's now describe the length of the shorter ribbon using the longer ribbon.

So the green ribbon is now our whole and we're going to divide it into three equal parts.

And so each part is 1/3 of the whole.

So we can see that the length of the purple ribbon is equal to 1/3 times the length of the green ribbon.

Let's check your understanding.

Which image represents this statement? The green ribbon is 1/4 times the length of the yellow ribbon.

Pause the video, maybe find someone to chat to, and compare your answers.

And when you are ready to go through this and check, press play.

How did you get on? Did you say it was representation B? This is the representation where the green ribbon is 1/4 times the length, so it had to be smaller than the yellow ribbon.

So option A wouldn't work, but also it needed to have four equal parts equivalent to one part of the green.

Well done.

Let us now relate this to the actual length of the ribbons and form an equation to represent this.

So we now using our green ribbon as the whole.

This is 15 centimetres.

It's the original length that is being used for comparison.

We know that the purple ribbon is 1/3 times the length of the green ribbon.

This 1/3 describes the length of the purple ribbon in relation to the green ribbon.

So the length of the purple ribbon is equal to 15 centimetres multiplied by 1/3.

And Lucas is prompting us.

How do we multiply by a unit fraction to calculate the length of a purple ribbon? Can you remember how do we multiply by a unit fraction? So when we multiply by a unit fraction, in this case 1/3, it is the same as dividing by that denominator, in this case 3.

So let's have a look.

We've got 15 centimetres divided by 3 and that is 5 centimetres.

15 centimetres and multiply by 1/3 is also 5 centimetres.

So we say the purple ribbon is 1/3 times the length of the green ribbon.

And the purple ribbon is then 5 centimetres long.

Five centimetres is 1/3 times the length of 15 centimetres.

Five centimetres is 1/3 of that length of 15 centimetres, isn't it? Because the 15 centimetres, if we can split that into 3 equal parts, each part is the same as 1/3.

Let's check your understanding.

Which statements are represented by this image? Is it statement A, the length of the blue ribbon is 10 times the length of the orange ribbon? Is it B, the length of the blue ribbon is 1/10 times the length of the orange ribbon? Or is it C, length of the orange ribbon multiplied by 1/10 is equal to the length of the blue ribbon? Pause the video while you have a think and when you're ready to hear the answer, press play.

How did you get on? Did you realise that it can't be A because it says the length of the blue ribbon is 10 times the length? Well, it's not, the blue ribbon shorter isn't it? B, the length of the blue ribbon is 1/10 times the length of the orange ribbon.

And that's correct because we can split the whole orange ribbon into 10 equal parts, and the length of the blue ribbon is equal to one of those parts, and the length of the orange ribbon, if we multiply that by 1/10, which is the same as dividing by 10, and we have divided the length of the orange ribbon into 10 equal parts, it would be equal to the length of the blue ribbon.

So that is also correct.

Well done if you've got both of those.

Another check here for you.

Which equations describe the length of the yellow ribbon? So pause the video, have a look at all four equations, and see which ones you think describe the length of the yellow ribbon.

When you're ready to go through the answers, press play.

How did you get on? We've got 45 centimetres multiplied by 1/5 is equal to 9 centimetres.

And because we are multiplying by 1/5, it is the same as dividing by the denominator, in which case 5.

So the whole was 45 centimetres and the shorter yellow ribbon was equivalent to 1/5 of the length of those 45 centimetres.

Your turn to practise now.

For question one, I'd like you to use a paper strip of 16 centimetres and a paper strip of 2 centimetres.

Using your strips of paper, they will help you to complete this stem sentence.

The length of the shorter paper is mm times the length of the longer paper strip.

For part B, there are two equations for you to complete.

Describe this relationship.

For question two, The length of ribbon B is 1/10 times the length of ribbon A.

Can you tell me how long is ribbon B? And then for part B, how many centimetres longer is ribbon A than ribbon B? And for question three, could you complete the equations to describe and then calculate the length of the shorter ribbon? The length of the longer ribbon in each case is 60 centimetres.

Pause the video while you have a go at all three questions and when you are ready for the answers, press play.

How did you get on? Let's have a look.

So for question one, were you able to work out that the length of the shorter paper strip is 1/8 times the length of the longer paper strip? And that meant we were multiplying by 1/8.

So 16 centimetres multiplied by 1/8 and that is equal to 2 centimetres.

And remember when we multiply by a unit fraction, it is the same dividing by that denominator.

So our second equation is 16 centimetres divided by 8, and that is also equal to 2 centimetres.

For question two, we were asked to calculate how long ribbon B is knowing that ribbon B is 1/10 times the length of ribbon A.

So I formed some equations.

The whole is 480 centimetres and I need to multiply by 1/10.

And I know that is the same as dividing by 10.

So ribbon B is 48 centimetres long, 48 is 1/10 times the size of 480.

For part B, we were asked to find how many centimetres longer ribbon A is than ribbon B.

This is looking at an additive relationship.

So I've got the whole ribbon A is 480 centimetres and I need to subtract the 48 centimetres to find that difference.

480, well, I took off 40 first, then I took off 8, so I got 432.

So ribbon A is 432 centimetres longer than ribbon B.

For question three, you are asked to complete the equations to describe and calculate the length of the shorter ribbon.

In the first representation, there are five equal parts.

So I'm multiplying by 1/5, which is the same as dividing by 5.

So the length of the shorter ribbon here was 12 centimetres.

For the second representation, there were four equal parts, so I needed to multiply by 1/4 to find the length of the shorter ribbon.

This is the same as dividing by 4.

Either way, we got the answer of 15 centimetres for the length of the shorter ribbon.

And for the last representation, there were three equal parts.

So I was multiplying by 1/3, which is the same as dividing by 3.

60 centimetres divided by 3 is 20 centimetres.

So the length of the short ribbon in that last example is 20 centimetres.

How did you get on with all of those? Well done, fantastic learning today everybody, you've really deepened your understanding of how we can compare and describe length using our knowledge of division.

We know then that lengths can be compared using division.

And we know to use the stem sentence that mm is mm times the length of the mm.

And that can be used to compare and describe length.

And we know that comparisons of length can be represented as a multiplication equation with a fractional multiplier.

And we know that if we have a fraction, a unit fraction that we are multiplying by, then it is the same as dividing by that denominator.

Brilliant learning today everybody, well done, and I look forward to seeing you again soon.