Lesson video

Hello.

How are you today? My name is Dr.

Shorrock, and I'm really excited to be learning with you today.

We are going to have great fun as we move through the learning together.

Today's lesson is from our unit Compare and Describe Measurement Using Knowledge of Multiplication and Division.

This lesson is called Solve Comparison and Change Problems Using Multiplication.

In the lesson today, we will be looking at problems where we can compare two lengths or describe a change in one length.

Sometimes new learning can be challenging, but I'm here to guide you, and I know if we work really hard together, then we will be successful.

So, shall we find out how can we solve comparison and change problems using multiplication? These are the keywords that we will be using in our learning today.

We've got comparison and change.

Let's practise those words together.

My turn, comparison.

Your turn.

Nice.

My turn, change.

Your turn.

Brilliant.

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

So when we talk about a comparison, we are determining how different two objects are.

In this lesson, we're going to be thinking about how many times longer, taller, or deeper an object is than another.

But we can also make a comparison between one object before and after it has changed.

Examples of a change include the change in height of a flower when it's growing, or a change in depth of a puddle due to rainfall.

So today's lesson, we are going to start by looking at how we can represent comparison and change problems. These are the children who will help us in our learning today.

We've got Lucas, Sam, and Izzy.

Let's have a look at this problem.

Lucas has a piece of elastic.

The elastic is 10 centimetres long.

Can you visualise that? What do you see in your head at this moment? That's what I see as my elastic, and it is 10 centimetres long.

He stretches it until it is two times the original length.

Can you visualise that? Have you got your original elastic, and we're stretching it two times the original length.

There we go, that's what I was doing.

So what might our question be here? We don't have a question yet.

I wonder if you think what it could be.

That's right, what is the length of the elastic now? We can represent this in a table to help us solve this change problem.

So we know the elastic is 10 centimetres long, and it is being stretched until it is two times the original length, and we can show that change in our table.

And we want to find out what the length of the elastic is now.

We can also represent change problems as a bar model.

So we know the elastic is 10 centimetres long, and it is stretched until it is two times the original length, and we need to find the length of the elastic now.

And we know now that this will be the unknown whole because it is greater in length.

So that's our unknown whole.

And we know the elastic must be a part, the original 10 centimetre elastic must be a part because it is the original length.

So we've got 10 centimetres which is a part, and it's the length of the elastic at the start.

And we know the hole is the length of the elastic at the end, and it's equivalent to two of the original lengths, because it has been stretched two times the original length.

Let's check your understanding.

We have a 15 centimetre piece of elastic and it's stretched to twice the original length.

What is the length of the elastic now? Could you have a go at representing this change problem in a table and as a bar model? Pause the video, maybe compare your answers with somebody else, and when you are ready to go through the answers, press play.

How did you get on? This is what my table looks like.

I've drawn the original elastic at 15 centimetres.

I am showing that it has been stretched twice the original length by showing I'm multiplying by two, and I have got my stretched elastic with a question mark representing what we are trying to find now.

I also represented this in a bar model.

My original elastic is 15 centimetres, and I'm trying to find the length now that it has been stretched to twice the original length.

Let's look at a comparison problem now where we compare two things.

Sam has been for a walk and has found a stick and a leaf.

The stick is three times the length of the leaf.

Can you visualise that? This is what I see.

There's my stick and there's my leaf, and I've made my leaf smaller because the stick is three times the length of the leaf.

What might the question be then? That's right, we want to find out what is the length of the stick.

So to help with this comparison problem, it's useful to represent it as a bar model.

So we know that Sam has been for a walk and found a stick and a leaf, and the stick is three times the length of the leaf.

So the length of the leaf must be a part, because it is shorter and it's the original length.

And we know that the length of the stick must be our unknown whole.

It's longer and it must be equivalent to the length of three leaves, because we have the information that the stick is three times the length of the leaf.

So our stick is the unknown whole.

Let's check your understanding.

Could you represent this comparison problem as a bar model? A wardrobe is three times the height of a desk.

Pause the video whilst you draw your bar model, and when you're ready to see how I drew it, press play.

How did you get on? So this is how I drew my bar model.

I drew a bar for my desk and I drew a longer bar for the wardrobe, a bar that was three times the length of the bar of the desk, because the wardrobe is three times the height of the desk.

And I popped a question mark in the bar for the wardrobe, because that is what we are trying to find out.

Your turn to practise now.

For question one, could you represent these change problems in a table and as a bar model? For part A, a sunflower is 13 centimetres tall.

Over the next few months, it grows to 10 times its original height.

What is its height now? For part B, the water in a rain barrel was 40 centimetres deep.

After heavy rainfall, the depth was four times the original depth.

What is the depth of water now? And for part C, six years ago, Sam planted a two metre tree in her garden.

The tree is now seven times that height.

How tall is the tree now? For question two, could you represent this comparison problem as a bar model? Sam, Lucas and Izzy all have a length of string.

Lucas's string is two times the length of Sam's string, and Izzy's string is three times the length of Lucas's string.

Have a go at both questions, pause the video, and when you are ready for the answers, press play.

Let's see how you got on.

This is the table that I drew to represent the sunflower.

You can see it's 13 centimetres originally, and it grows to 10 times its original height, and I have represented that using an arrow and multiplying by 10.

And then I've got a question mark with my sunflower that has grown.

We can also represent this in a bar model.

My first part is 13 centimetres, and there are 10 equal parts, because the sunflower grows to 10 times its original height.

For question B, we had a problem about water in a rain barrel, and it was 40 centimetres deep to begin with, and then the depth increased four times the original depth.

So I've represented that with an arrow and multiplying by four.

And then I have my question mark to represent what is the depth of the water now.

We can also represent this in a bar model.

My first part is 40 centimetres, and we need four equal parts.

For part C, six years ago, Sam planted a two metre tree in her garden, and that's where I've started in my table with two metres.

The tree is now seven times that height, and that has been represented with an arrow and multiplying by seven.

And we have a question mark to represent how tall the tree is now.

We can also represent that as a bar model.

The tree was two metres tall and that was seven, it's now seven times that height, so we need seven equal parts.

For question two, you had a comparison problem to represent as a bar model.

So we had Sam's string, and then we were told Luke's string was two times the length of Sam's string, and that Izzy's string was three times the length of Lucas's string.

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

Fantastic learning so far.

You have really deepened your understanding and made good progress with how we can represent comparison and change problems. We are now going to move on to look at how we solve those problems. So let's revisit our change problem.

This problem is the problem about the elastic that was 10 centimetres long and then it was stretched until it was two times the original length.

And we want to find out the length of the elastic now.

We can use our representations to form an equation to help solve the problem.

So we've got our change table and our bar model, and from the table we can see we need to multiply 10 centimetres by two, and from the bar model, we can see that we have two equal parts, and because the parts are equal, we multiply, so we also need to multiply 10 centimetres by two.

So 10 centimetres multiplied by two is 20 centimetres.

The elastic is now 20 centimetres long.

And let's look at this equation in more detail.

The 10 centimetres, well, that represents the original length of the elastic.

What about the timesing by two? What does that represent? That's right, it represents the two times the amount the elastic was stretched.

And what about the 20? That's right, the 20 centimetres represents the length of the elastic after it was stretched.

So the 20 centimetre length of stretched elastic is twice the length of the original 10 centimetre length of elastic.

Let's check your understanding.

Let's revisit this problem.

We had a 15 centimetre piece of elastic stretched to twice its original length.

I've shown you the representations for the table and the bar model.

Could you use those representations to write an equation and solve it? Pause the video whilst you do that, and when you are ready to go through the answers, press play.

How did you get on? Did you form an equation? 15 centimetres, it had to be multiplied by two, because we were stretching the elastic to twice the original length.

15 multiplied by two is 30.

15 twos are 30.

So the elastic is now 30 centimetres long.

Well done.

Let's revisit our comparison problem.

If we remember, Sam has been for a walk and found a stick and a leaf, and the stick is three times the length of the leaf, and we want to work out what the length of the stick is.

We can use our representations to form an equation and solve the problem.

This is the bar model that we had.

We've got the leaf is 20 centimetres.

We can see the parts are equal, so we need to multiply, and we need to multiply by three because a stick is three times the length of the leaf.

So I can form my equation, 20 centimetres multiplied by three is equal to 60 centimetres.

We know two threes are six, so 20 threes must be 60.

So the stick is 60 centimetres long.

Let's look at this equation in more detail.

What does the 20 centimetres represent? That's right, the 20 centimetres represents the length of the leaf.

What about the three? That's right, the three represents the three times the length of the leaf.

And the 60, well, that represents the length of the stick.

So the 60 centimetre stick is three times the length of the 20 centimetre leaf.

Let's check your understanding.

Let's revisit this problem.

A wardrobe is three times the height of a desk.

Can you use the representation that we came up with before to write an equation and solve it? Pause the video whilst you do this.

You might want to compare answers with somebody else.

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

How did you get on? This is the equation that I formed.

I've got 40 centimetres, which is the height of the desk, and we know the wardrobe is three times that height, so we need to multiply by three.

Four threes are 12, so 40 threes must be 120.

So the wardrobe is 120 centimetres tall.

Well done if you then converted it to say that this is equivalent to one metre 20 centimetres.

Let's look at just an equation now without a context.

So without a story, we've got seven times three is 21.

Seven threes are 21.

What can we say from the equation? What could you say? Ah, thank you Sam.

Yes, we can say that seven multiplied by three is equal to 21.

Anything else? Ah, thank you Lucas.

Yes, we could.

We could say that 21 is three times the size of seven.

Let's check your understanding on that.

Which of these statements correctly describes this equation? You've got six times seven is 42.

Six sevens are 42.

Is it, A, six times by seven is equal to 42? Is it, B, 42 multiplied by six is equal to seven? Or is it, C, 42 is seven times the size of six? Pause the video, maybe have a chat to someone about this, and when you are ready for the answers, press play.

How did you get on? Did you say definitely the top one, part A, six times by seven is equal to 42? Times by is the same as multiplying by, isn't it? And then C as well, 42 is seven times the size of six.

Well done.

It's time for you to practise now.

I'd like you to use your representations from task A to form an equation and then solve these change problems. As a reminder, problem A was about a sunflower, which is 13 centimetres tall.

And over the next few months, it grows to 10 times its original height.

What is its height now? For part B, the water in a rain barrel was 40 centimetres deep.

After heavy rainfall, the depth was four times the original depth.

What is the depth of the water now? And for part C, six years ago, Sam planted a two metre tree in her garden.

The tree is now seven times that height.

How tall is the tree now? For question two, I'd like to use your representations from task A and to complete the sentence to solve this comparison problem.

As a reminder, Sam, Lucas and Izzy all have a length of string.

Lucas's string is two times the length of Sam's string, and Izzy's string is three times the length of Lucas's string.

I'd like you to complete the sentence, "Izzy's string is mm times the length of Sam's string." And for question three, we've got some equations here without context, so without a story.

Could you just complete these statements, so fill in the blanks.

Part A, you've got nine times eight is 72, so 72 is mm times the size of eight.

For part B, 280 is five times the size of 56, so you've got 56 mm equals 280.

And for part C, six eights are mm, and so then you've got mm is eight times the size of six.

Pause the video while you work through all three questions, and when you are ready to go through the answers, press play.

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

So you had to form an equation using your representations that you did in task A.

So I have my equation is 13 centimetres because that's the height of the sunflower, and it grew 10 times its original height, so I'm multiplying by 10.

13 10s are 130.

So the sunflower is 130 centimetres tall, which is equivalent to one metre 30 centimetres.

For part B, my equation is 40 centimetres and I'm multiplying by four, because the depth was four times the original depth.

I'm going to do four fours and then multiply by 10.

16 multiplied by 10 is 160.

So the depth of the water is now 160 centimetres.

This is equivalent to one metre 60 centimetres.

And for part C, I formed my equation.

The tree was two metres to begin with, and it grew seven times that height, so I'm multiplying by seven.

Two sevens are 14.

The tree is now 14 metres tall.

For question two, you are asked to use your representations from task A to complete the sentence below.

So Izzy's string is six times the length of Sam's string.

This is because Lucas's string was twice Sam's string, and Izzy's string is three times Lucas's string.

Three twos are six.

And for question three, you had some statements to complete.

For part A, 72 is nine times the size of eight.

For part B, 56 multiplied by five is equal to 280.

And for part C, six eights are 48, so 48 is eight times the size of six.

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

Fantastic learning today.

You've really made progress on solving comparison and change problems using multiplication.

We know that a change in length can be described using our knowledge of multiplication, and we can say that mm is mm times the size of the mm.

And we know comparison and change problems can be represented visually in tables and/or as bar models to help solve the problem.

It's been a pleasure learning with you today, and I look forward to seeing you again soon.