Lesson video

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

Shorrock.

I am really looking forward to learning with you today.

We are gonna have a lot of fun as we move through this learning together.

Welcome to today's lesson.

This lesson is from our unit, measures, mass and capacity.

The lesson is called Solve problems involving mass.

We are going to look at lots of different scenarios related to mass and think about how we can use the bar model to support us to answer the questions.

We're also going to deepen our understanding on when we need to use our addition facts or our multiplication facts.

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

And I'm here to help you if it gets challenging.

So shall we find out, how do we solve problems related to mass? These are the keywords that we will be using in our lesson today.

Bar model, whole, part, and mass.

I'm sure you've heard those words before, but let's practise them.

My turn, bar model, your turn.

Well done.

My turn, whole, your turn.

Lovely.

My turn, part, your turn.

Well done.

And my turn, mass, your turn.

Brilliant, look out for those words as we move through the learning today.

When we use the words bar model, we mean a pictorial representation of a problem where bars are used to represent the known and unknown quantities, the parts and the wholes.

Bar models are usually used when we solve number problems as to related to additive facts or multiplicative fact.

When we talk about the whole, we mean all of something.

It's complete.

This is a picture of a whole pizza And a part is some but not all of something.

It is an amount or section which if you put it with the others, makes up the whole.

And you can see I've given you there a picture of a part of a pizza.

And mass.

Mass is a measure of how much matter something contains.

And the problems that we will be looking at today are all related to mass.

And mass is commonly measured by how much something weighs.

And can be measured in kilogrammes and grammes.

So today, we are learning about how we can solve problems involving mass and we are going to start by looking at problems that use our additive relationships.

These are the characters who will be helping us today.

Aisha, Sophie, Jacob, and Andeep.

When given a words problem to solve, it is important to be able to visualise it, to show that we can see the maths in the real world.

And then it is important that we can represent the problem mathematically so in a bar model, because this will help support us to solve it.

So let's look at this problem.

Jacob has a whole cake.

He also has a slice of cake.

(gasps) That's right.

That's what we need to do first.

Can you visualise that? What do you see in your head at the moment? I know what I see.

Jacob has a whole cake.

I can see a whole cake and a slice of cake.

Yes, I can see a slice of cake.

So that's us visualising the problem.

Ah, there you go.

Did you see something like that? What could the question be then, Jacob is wondering? What do you think the question might be? That's right.

The question this time is how much heavier is the whole cake than the slice of cake? So what information do we need to be able to answer this question? That's right.

We need to know the mass of the whole cake.

And the mass of the slice of cake.

Jacob places the whole cake on some scales.

Have a look at the scales.

What do you notice? Could you tell me what the mass of the whole cake is? That's right, Jacob.

The arrow is pointing to the 800 and what does that tell us? That's right.

It tells us the mass of the cake is 800 grammes.

Jacob then places the slice of cake on different scales.

What do you notice this time? Can you tell me what the mass of the slice of cake is? That's right, Jacob has noticed the arrow is pointing to between 100 grammes and 200 grammes.

And we need to work out the value of the unmarked interval so we can be accurate when we work out the slice of cake's mass.

There are five equal parts in between the marked intervals of 100 grammes.

100 is composed of five equal parts of 20.

So each unmarked interval is worth 20 grammes.

The arrow is pointing to the end of that second part.

So we can now work out the mass of that slice of cake.

We can count up in 20s from 100.

So 100, 120, 140.

The mass of the slice of cake is 140 grammes.

Let's remind ourselves of the problem.

Jacob has a whole cake.

Can you see that? He also has a slice of cake.

Can you see that? How much heavier is the whole cake than the slice of cake? So now that we know the mass of the cakes, what do we need to do first? Ah, thank you, Sophia.

Yes, we do now need to represent this.

And we can represent problems in many ways.

One of the most effective ways is to draw a bar model.

A bar model is made up of a whole and its parts.

And depending on the problem, the parts may be the same or they may be different.

And identifying the parts and wholes in our problem helps us to understand the structure of the problem and therefore helps us solving the problem.

Let's represent our problem in a bar model.

Jacob has a cake.

Okay, we don't really know yet if that's the whole or a part yet, we have to read the rest of the question.

He also has a slice of cake.

Okay, so in my head I'm thinking a cake is bigger than the slice of cake.

So maybe that will help us with our bar model, but we still need to read the rest of the question.

How much heavier is the cake than the slice of cake? Okay, how much heavier? That tells us we're looking for an unknown part.

So the cake must be the whole because we are told it is heavier and we are comparing a slice of cake to the whole cake.

So the slice of cake is a part.

How much heavier is the part that we need to find? It is our unknown part.

So if we represent our bar model, we can see the whole cake, the mass of the whole cake is our whole, the mass of a slice of cake is a part.

And how much heavier? That is the unknown part, the part that we need to find.

And we know that the mass of the whole cake is 800 grammes and the mass of the slice of cake is 140 grammes.

And now we have our bar model so we can use it to help us know what to calculate and how.

Let's check your understanding so far.

Can you represent this word problem in a bar model? Sophia has a whole pizza with a mass of 240 grammes.

Jacob has a slice of a different pizza with a mass of 80 grammes.

How much heavier is Sophia's whole pizza than Jacob's slice? Remember Izzy is saying, try visualising this first it will help.

Pause the video, have a go.

And when you are ready, press play.

How did you get on? Did you notice the words how much heavier? So we are looking for an unknown part.

The whole pizza, that must be the whole.

And the slice is the part of the whole.

We know that pizza had a mass of 240 grammes and the slice of pizza had a mass of 80 grammes.

So let's revisit our problem.

Jacob has a whole cake.

He also has a slice of cake.

How much heavier is the whole cake than the slice of cake? Let's now use the bar model to identify the calculation we need and then solve the problem.

So we know from the bar model, we can see we have the whole 800 grammes and one part, 140 grammes, and we need to find a part.

The parts are different, and we can tell that because the slice of cake is less than half of the whole cake.

Because the parts are different, we can use additive relationships to find a missing part.

To find a missing part, we need to subtract the part we know from the whole.

We know our whole is 800 grammes.

We need to subtract 140 grammes.

To do that, I'm going to partition the 140 into 100 and 40.

because I can do 800 - 100 = 700.

Then I can subtract the 40, which is 660 grammes.

So we now know the whole cake is 660 grammes heavier than the slice of cake.

Let's check your understanding.

Let's revisit your problem about the pizza.

Can you identify the calculation and solve it? So remember, Sophia has a whole pizza with a mass of 240 grammes.

Jacob has a slice of a different pizza with a mass of 80 grammes.

How much heavier is Sophia's whole pizza than Jacob's slice? Have a look at the bar model and I've given you a sentence to help.

To find a missing part we need to mm.

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

How did you get on? Did you remember that to find a missing part, we need to subtract the part we know from the whole.

240 grammes - 80 grammes.

I'm partitioned the 80 grammes, so that I could do 240 - 40, which I know would be 200.

And then I've got another 40 to subtract, which is 160.

So the missing part is 160 grammes.

The whole pizza is 160 grammes heavier than the slice of pizza.

Your turn to have a go.

For question one, look at the image of Andeep's partly eaten apple.

Sophia's whole apple has a mass 25 grammes more than Andeep's apple.

Can you work out what the mass of Sophia's whole apple is? I'd like you to draw a picture to help you visualise this.

Represented in a bar model and then use your bar model to identify the calculation and solve the problem.

And for question two, look at this problem.

Andeep has a tennis ball with a mass of 60 grammes.

Sophia has a football with a mass of 450 grammes.

How much heavier is the football? Can you draw a picture to help you visualise this? Represent it in a bar model, and then using your bar model, identify the calculation and solve the problem.

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

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

So you might have drawn a picture like this to help you visualise the problem about the apple.

There's Andeep's partly eaten apple and we know Sophia's apple is 25 grammes more than the partly eaten apple.

Your bar model might look like this.

Sophia's whole apple is what we're trying to find.

It's the whole.

Andeep's partly eaten apple is a part and the 25 grammes is a part.

Then we need to use the bar model to identify the calculation and solve the problem.

We needed to work out the mass of Andeep's partly eaten apple using the scales.

And I can see that the mass is halfway to 100, so it's 50 grammes.

To find the whole, we need to add the parts together.

50 grammes + 25 grammes = 75 grammes.

The mass of Sophia's whole apple is 75 grammes.

For question two, you might have drawn a picture like this to help you visualise the problem.

I've drawn a tennis ball and a football.

And I've drawn an arrow with a question mark above it because I need to find out how much heavier is the football.

Your bar model might look like this.

For the mass of the football is our whole and the mass of the tennis ball is a part, and we need to find that missing part were finding how much heavier? You there might have used your bar model to help you decide what to calculate.

We have the whole and a part.

To find a missing part, we need to subtract the part we know from the whole.

450 - 60.

Well, I'm going to do 450 - 50, and then subtract the other 10 and that gives me 390 grammes.

The football is 390 grammes heavier than the tennis ball.

How did you get on? Brilliant.

Fantastic effort so far, everybody.

I am really impressed with how you are deepening your understanding of solving problems involving mass and link to that additive relationship.

We are now going to move on and explore problems that involve the multiplicative relationship.

So let's look at a different problem.

Andeep has five identical cherries and they have a total mass of 30 grammes.

Hmm, can you visualise that? Can you see five identical cherries? That's right.

Something like that.

And Aisha is asking what the question might be? What do you think? The question is, what is the mass of one cherry? So what do we need to do? First, we visualise it.

What do we need to do next? Can you think? That's right, we need to represent this as a bar model.

First, we need to identify the parts and wholes.

A reminder of our problem.

Andeep has five identical cherries that have a total mass of 30 grammes.

While that word total, it tells us the mass of 30 grammes is the whole.

We've got five identical cherries.

So the five cherries must be five parts.

We know they're identical, so each of the five parts must be equal and that means their value must be the same.

What is the mass of one cherry? So you can see I've now got a question mark in my bar model replacing one cherry.

We need to find out what that mass of that one cherry is.

Once we have our bar model, we can use it to help us know what to calculate and how? We can look at the bar model and we can see that we've got the whole, and we've got five equal parts, and we need to find the value of one of those parts.

And because the parts are equal, we can use our known multiplicative relationships.

So to find the mass of one cherry, Aisha is saying the whole is 30 and there are five equal parts.

Five sixes are 30.

30 is composed of five equal parts of six.

The mass of one cherry is six grammes.

Let's check your understanding of the problem for you.

Andeep has 10 identical pebbles that have a total mass of 120 grammes.

What is the mass of one pebble? That's right.

Thank you, Izzy.

We really need to try visualising this first.

Have a think, what do 10 identical pebbles look like? And then I've got a bar model for you to use to help you solve this.

There's the bar model.

And some sentences for you to use to help you.

The whole is mm and there are mm equal parts.

10 mm are 120.

The mass of one pebble is mm grammes.

Pause the video, maybe find someone to have a discussion with about this.

When you are ready, press play.

How did you get on? Did you say the whole is 120 and there are 10 equal parts.

10 12s are 120.

The mass of one pebble is 12 grammes.

So you have been using your multiplicative relationships to help you solve this problem because the parts are equal.

Well done.

Let's revisit our question.

So the question is, Andeep has five identical cherries that have a total mass of 30 grammes and what is the mass of one cherry? So what do we know? Aisha is saying, well, we've worked out, haven't we? That the mass of one cherry is six grammes.

So let's add another part to the question.

Aisha has a radish and that has half the mass of the five cherries.

What's the mass of the radish? What do we need to do first? That's right, let's try visualising it.

Can you see those five cherries? Total mass of 30 grammes and a radish.

There we go.

That's what I'm visualising.

And then after we have visualised it, we need to add this information to a bar model.

We've still got the first part of the question.

So the whole is still 30 grammes and there are still five equal parts, but now we've got an additional bit of information.

We know that the radish has half the mass of the five cherries.

So half means the mass of the radish is one of two equal parts of the whole.

So I have added that to the bar model.

And we can now use our bar model to help us find the mass of the radish.

Aisha is telling us that, "The mass of the five cherries is 30 grammes and that is the whole.

The mass of the radish is one of two equal parts of the whole.

30 is composed of two equal parts of 15.

The mass of the radish is 15 grammes." Let's check your understanding.

Andeep has 10 identical pebbles that have a total mass of 120 grammes.

You've seen that part of the question before.

This is the new part.

Aisha has a stone which is half the mass of the 10 pebbles.

What is the mass of the stone? I've given you a bar model that you can use to help you and some sentences.

The whole is mm grammes.

120 is composed of two equal parts of mm.

So the mass of the stone is mm grammes.

Maybe talk to someone about this.

Share your thoughts on the questions.

Pause the video.

When you've done that, press play.

How did you get on? Did you say the whole is 120 grammes? 120 is composed of two equal parts of 60.

So the mass of the stone is 60 grammes.

Well done.

Let's revisit our question.

We know we have five identical cherries that have a total mass of 30 grammes and that we have a radish that has half the mass of the five cherries, and we wanted to know what the mass was of the radish.

So Aisha is just asking us to remember what do we know now? That's right.

We know the mass of one cherry is six grammes and we know the mass of a radish is 15 grammes.

Let's add another part to the question.

Yes, let's do that, shall we? Are you ready? How much heavier is the radish than one cherry? What do we need to do first? That's right, we need to visualise it.

Can you see a cherry and a radish? And the radish is heavier but we need to find out how much heavier? So I've got a little question mark in my visualisation.

So the question tells us that the radish is heavier.

How much heavier is the radish? You know, it tells us, but we need to find out how much heavier? So we need to compare the mass of the radish to the mass of just one cherry.

Well, I'm gonna do a different bar model here.

We can see we need to find the difference between the mass of the radish and that of the cherry.

We know the mass of the cherry is six grammes and the mass of the radish was 15 grammes.

So 15 grammes - 6 grammes = 9 grammes.

The radish is nine grammes heavier than one cherry.

Let's check your understanding.

We're going to use the previous bar model to represent the next part of the question and then solve the problem.

As a reminder, the question was, Andeep has 10 identical pebbles that have a total mass of 120 grammes.

Aisha has a stone which is half the mass of the 10 pebbles.

So the new part of the question for you to think about representing in a new bar model is, how much heavier is the stone than one pebble? Have a go, pause the video and when you are ready, press play.

How did you get on? This is the new bar model that I drew.

And I know that a stone is 60 grammes and the pebble is 12 grammes.

So I can work out how much heavier the stone is by subtracting 60 grammes - 12 grammes.

I'm going to partition the 12.

So 60 grammes subtract 10 grammes, gives me 50 grammes.

And take away the other two grammes is 48 grammes.

So the stone is 48 grammes heavier than the pebble.

How did you get on? Fantastic.

Your turn to practise now.

Can you solve this problem by drawing it to help you visualise the maths.

Representing it as bar models and identifying the calculations.

So the first part of your question is, Andeep has 10 identical pencils that have a total mass of 60 grammes.

What is the mass of one pencil? For the second part, Aisha has a ruler and that has half the mass of the 10 pencils.

So what's the mass of the ruler? And then can you tell me how much heavier the ruler is than one pencil? Pause the video to have a go at this and when you are ready for the answers, press play.

How did you get on? So if we look at the first part of the question, I visualised it like this.

There's my 10 pencils and they have a total mass of 60 grammes.

I drew a bar model.

60 grammes is the whole amount, there are 10 equal parts, but I needed to find the mass of one part.

I then worked out the mass of one pencil to be six grammes.

10 sixes are 60.

Then we needed to think about the ruler and I extended my bar model to look like this.

The ruler has half the mass of the 10 pencils.

I could then work out that the mass of the ruler is 30 grammes.

For the last part of the question, I drew a new bar model to help me.

The mass of one pencil was six grammes, the mass of the ruler 30 grammes.

And I knew that I had to subtract.

30 - 6 = 24.

So the ruler is 24 grammes heavier than the pencil.

How did you get on? Amazing.

Well done with your learning today, everybody.

I'm really impressed with how you have come on with your learning and deepened your understanding of solving problems involving mass.

We know that when we are given a word problem, we need to visualise it first so we can see the maths.

We then know that we need to represent word problems as a bar model and we have to identify the parts and whole.

And the bar model then helps us understand the structure of the maths and how to form a calculation to help solve the problem.

Fantastic learning today, everybody.

I look forward to seeing you again soon.