Lesson video

Hello, welcome to today's learning.

My name is Dr.

Shorrock and I'm really looking forward to learning with you today.

We are going to have a lot of fun as we move through the learning together.

Today's lesson is from the unit, "Compare and Describe Measurements Using Knowledge of Multiplication and Division." This lesson is called Compare and Describe Length Using Knowledge of Multiplication.

As we move through the learning today, we're going to look at how we can compare and describe length, and how we can use this comparison to determine the length of an unknown.

Sometimes learning can be a little bit tricky, but I know if we work really hard together, we will be successful.

And I am here to help you along the way.

So shall we find out how can we compare and describe length using our knowledge of multiplication? 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 twice.

Let's practise those words.

So my turn, times the length.

Your turn.

Nice.

My turn, times the height.

Your turn.

Brilliant.

My turn, times the depth.

Your turn.

Brilliant, and my turn, twice, your turn.

Fantastic.

So do look out for those words as we move through the learning today.

So let's look at these key words, times the length, height, or depth, well it's just a phrase.

It's used to compare and describe length or height.

And you'll see we use it lots throughout the course of this lesson.

I'll give an example here, one tree might be three times the height of another tree, is three times as tall.

And twice is a word we use that means two times as many.

So I might say I asked you twice, and it means I'm asking you two times.

In math we can say twice four is eight because two times four is eight.

So our learning today starts with comparing and describing lengths multiplicatively.

And then we're going to move on and look at some special cases.

In our learning today, we've got Lucas and Sam to help us.

Lucas and Sam have got a length of ribbon each.

What do you notice? Is there something about them? Hmm, I know one's purple and one's green, but is there anything else that you notice? Ah, Lucas has noticed that the purple ribbon, his purple ribbon is shorter than Sam's green ribbon.

Ah, and that's right then, if the purple ribbon is shorter, then Sam is right to say that the green ribbon is longer than the purple ribbon.

And Sam is wondering how many times the length of the purple ribbon, the green ribbon is.

Hmm, I wonder.

What do you think? Ah, yes, thank you Lucas, we can find out by measuring the length of the purple ribbon, and then we can compare it to the length of the green ribbon and that's what we're learning about today, doing a comparison between length of objects.

Lucas measures the length of his purple ribbon using a ruler.

Can you see, he's very carefully lined his ribbon up with the ruler and the zero on the ruler, it makes it much easier to measure if you line your object up with the zero.

Lucas has measured and he's saying his ribbon is five centimetres long.

And we can use that length of that ribbon to measure the length of the green ribbon.

I wonder if you know how.

So first of all, we can estimate how many lengths of purple ribbon are equal to the length of the green ribbon.

What do you think? Yeah, I think there would be more than two, Lucas, I agree with you, but maybe not as many as four, so there would be fewer than four.

So Lucas is going to estimate that there are three lengths of purple ribbon, which are equal to the length of the green ribbon.

Would you agree with Lucas? I think I do, I can see that there would definitely be more than two, and there would definitely be fewer than four, so it must be three.

So we have one length of purple ribbon is five centimetres, a second length would be another five centimetres, and a third length would be another five centimetres.

And Sam is telling us that the combined length of the three purple ribbons, so if we put them together, is equal to the length of the green ribbon.

Can you see that from the diagram? We can say that the green ribbon is three times the length of the purple ribbon.

And this is language that we're going to be using quite a lot in this unit, so let's practise saying that.

So we say that the green ribbon is three times the length of the purple ribbon.

So my turn, the green ribbon, is three times the length of the purple ribbon.

Your turn.

Fantastic.

And can you see why? That green ribbon is the same as three lengths of the purple ribbon? Let's check your understanding so far.

Have a look at the representations.

Which image is described by this stem sentence? The green ribbon is four times the length of one purple ribbon.

Pause the video, maybe talk to somebody about this and see if you can agree.

When you've done that and you are ready, press play.

How did you get on? Did you work out that it was image B? Because the green ribbon here is the same as four times the length of one purple ribbon.

Four of those purple ribbons would be the same length as the green ribbon.

Let's revisit our ribbons.

And as Lucas is saying, we could form an equation from this image to represent this.

We've got five centimetres multiplied by three, is equal to 15 centimetres.

Five three times is equal to 15 centimetres.

The five centimetres represents the length of one purple ribbon.

I wonder if you know what the three represents.

That's right, the three represents the number of purple ribbons that are equal to the length of the green ribbon.

What about the 15 centimetres? What does that represent? That's right, the 15 represents the length of the three purple ribbons.

Hmm, does it represent something else? That's right, it also represents the length of the green ribbon.

So the green ribbon is 15 centimetres long.

We've got five centimetres, three times, is 15 centimetres.

Let's check your understanding.

Could you use the stem sentence to form an equation? Then calculate the length of the green ribbon.

So this is the stem sentence.

The green ribbon is four times the length of one purple ribbon.

You can see one purple ribbon is five centimetres.

I need you to form an equation and then calculate the length of the green ribbon.

Pause the video, have a go, and when you are ready to see the answer, press play.

How did you get on? Did you form an equation to say five centimetres, 'Cause that's the length of the purple ribbon? And we needed four of them to be equivalent in length to the green ribbon, so it's five centimetres multiplied by four, and that is 20 centimetres.

The length of the green ribbon is 20 centimetres.

How did you get on? Brilliant, well done.

So it's your turn to practise now.

I want you to have a go at using some paper strips that are 12 centimetres, three centimetres, and four centimetres in length.

Could you use the paper strip that is 12 centimetres as the longer strip? And then use the given stem sentences to describe this longer strip in relation to each of the smaller strips.

So for part A, could you use the paper strips of three centimetres, and for part B, the paper strips that are four centimetres, and I've given you the stem sentence to use to compare them.

The length of the longer strip is _ times the length of the _ centimetre strip.

For question two, could you draw a line that is two centimetres long? Then draw a line that is three times the length of this two centimetre line, and then draw a line that is five times the length of the two centimetre line, and then draw a line that is 10 times the length of the two centimetre line.

For each example, could you form an equation to calculate the new length? Have a go at these two questions.

Pause the video and when you are ready, check your answers, press play.

Shall we see how you got on? For question one, you need to use some paper strips and compare them.

So for part A, when you used paper strips of three centimetres, you might have completed the sentence to say, the length of the longer strip is four times the length of the three centimetre strip.

Because four of those three centimetre strips with the same length as the 12 centimetre strip.

When you use paper strips of four centimetres, your sentence would be, the length of the long strip is three times the length of the four centimetre strip, because three of those four centimetre strips were the same as the whole 12 centimetres.

Well done.

For question two, you were asked to draw some lines of different lengths, and then form the equations to work out the length of those new lines.

You were asked to draw a line that was three times the length of the two centimetre line.

So two centimetres, three times is six centimetres.

For part B, you had to draw a line that was five times the length.

So two centimetres multiplied by five is 10 centimetres.

And for part C, you were asked to draw a line that was 10 times the size of the two centimetre line.

Two centimetres times 10 is 20 centimetres.

How did you get on with those two questions? Well done.

Fantastic learning so far, you have really deepened your understanding of how we can compare and describe length multiplicatively.

Now we're going to have move on and have a look at some special cases.

So Lucas and Sam find some other ribbons.

What can you see about those ribbons already? What do you notice? Ah, does that help you? That's right, Lucas is noticing that the length of the pink ribbon is two times the length of the blue ribbon.

Ah, thank you Sam, that's right.

We say that the length of the pink ribbon is twice the length of the blue ribbon, that's that key word, twice, it means two times.

So we can also say that the length of the pink ribbon is double the length of the blue ribbon.

So double, twice, and two times mean the same thing.

Let's check your understanding of that key word.

Look at these ribbons, which statements are correct? The length of the blue ribbon is double the length of the red ribbon.

The length of the red ribbon is double the length of the blue ribbon.

The length of the red ribbon is twice the length of the blue ribbon.

The length of the blue ribbon is two times the length of the red ribbon.

Pause the video, maybe have a chat to somebody, see if you agree.

And when you are ready to go through the answers, press play.

How did you get on? Did you work out that the length of the red ribbon is double the length of the blue ribbon, and the length of the red ribbon is twice the length of the blue ribbon? Double and twice both mean two times as much.

Let's revisit our ribbons.

I've given us a length to the blue ribbon now, it is six centimetres.

And we can use the length of the blue ribbon to calculate the length of the pink ribbon.

We can form an equation to help us, thank you Lucas.

We've got six centimetres, twice, which is 12 centimetres.

The six represents the length of one blue ribbon.

What does the two represent? That's right, the two represents the number of blue ribbons that are equal to the length of the pink ribbon.

And what does the 12 centimetres represent? That's right, the 12 centimetres represents the length of the two blue ribbons.

Does it represent something else? That's right, it also represents the length of the pink ribbon.

So we have determined the length of the pink ribbon using our comparison to the blue ribbon.

The pink ribbon is two times as long as the blue ribbon.

So the pink ribbon is also 12 centimetres long.

Let's check your understanding.

Look at these ribbons and the corresponding equation.

Which part of the equation must represent the length of the blue ribbon? Is it the three centimetres, the two, or the six centimetres? Pause the video, and when you think you are ready, press play.

How did you get on? Did you identify that it must be the three centimetres? The first factor there represents the length of the shorter ribbon.

Three centimetres must represent the length of the blue ribbon.

Lucas and Sam find some more ribbons.

What do you notice this time? That's right, Lucas has noticed that the orange ribbon is the same length as the green ribbon.

We say that the length of one green ribbon is equal to the length of the orange ribbon.

They are the same, aren't they? They are the same length.

We can also say that the orange ribbon is one times the length of the green green ribbon.

And we can form an equation to represent this.

We've got 10 centimetres, which is the length of the green ribbon, and we're multiplying it by one.

Because the orange ribbon is one times the length of the green ribbon, they are the same length.

So the orange ribbon is also 10 centimetres long.

And this is because when one is a factor, the product is equal to the other factor.

So 10 multiplied by one must be 10.

They are the same length.

So if two objects are the same length, one object is one times the length of the other.

Let's check your understanding with that.

Which equation correctly describes the length of the green ribbon? Is it A, one centimetre times 25 is equal to 25 centimetres? Is it B, 25 centimetres multiplied by two is equal to 50 centimetres? Or is it part C, 25 centimetres multiplied by one is 25 centimetres? Pause the video.

When you are ready for the answer, press play.

How did you get on? Did you realise that it must be 25 centimetres multiplied by one? The length of the first ribbon is 25 centimetres, and the green ribbon is the same length, it is one times the length of the other ribbon.

Your turn to practise now.

For part one, I'd like to use a strip of paper that is four centimetres long.

Can you draw a strip that is twice the length? And draw a strip that is double the length? What do you notice about those strips that you've drawn? And then for part C, I'd like you to draw a strip that is one times the length of the four centimetre long piece of paper.

What do you notice? For question two, I'd like you to look at these ribbons and equations.

Could you tick the equation, or equations that could match this representation? And then for part B, could you write another four possible equations that could match this representation? For question three, I have a problem to solve.

Sam has built a tower of bricks that is 19 centimetres tall.

Lucas also builds a tower of bricks.

The height of Lucas's tower is one times the height of Sam's Tower.

How tall is Lucas's Tower? Have a go at all three questions.

Pause the video, and when you are ready to hear the answers, press play.

Shall we see how you got on? You are asked to draw a strip that was twice the length of the four centimetre strip.

Four, twice, is eight centimetres.

You are also asked to draw a strip that says double the length.

What did you notice? That's right, you might have noticed that the strip that was twice the length and the strip that was double the length were equal in length.

This is because double and twice both mean two times.

You were also asked to to draw a strip that was one times the length, what did you notice? You might have noticed that the length of the strip, that was one times the length was equal to the original strip.

This is because one times the length means that the lengths are equal, they are the same.

For question two, you were asked to tick the equations that could match this representation.

The green ribbon could be 15 centimetres, and multiply that by two would be 30 centimetres.

Underneath, two centimetres times 15.

Well, we haven't got a piece of ribbon that has got 15 lots of a two centimetre one, so that wouldn't work.

30 centimetres is equal to two times 15 centimetres.

That would work because that is the same as the first one.

We've got two lots of a 15 centimetre ribbon.

And the third one would work as well.

We could have a ribbon that was 12 centimetres, the green ribbon could be 12 centimetres, double it, and you would get 24 centimetres.

You might have written equations like these, where the multiplier was always two.

So the green ribbon could have been 14 centimetres times two.

It could have been five centimetres times two.

I could have written my equation the other way round.

So 28 centimetres equals 14 centimetres times two.

Or the green ribbon could have been 50 centimetres, and multiply that by two.

For question three, you were asked to solve a problem.

And you might have formed an equation to represent this problem.

You've got 19 centimetres, was the height of Sam's Tower.

And Lucas's Tower is one times the height, so we're multiplying by one, and that is 19 centimetres.

So the height of Lucas' Tower is also 19 centimetres.

Fantastic learning today everybody.

We have been deepening our understanding of comparing and describing length using knowledge of multiplication.

We know that lengths can be compared using multiplication.

We've been using that stem sentence that something is something, times the length of that something.

And that can be used to compare and describe lengths.

And we know that we can represent comparisons of length as a multiplication equation.

So really well done today, fantastic learning with you, and I look forward to seeing you again soon.