Lesson video

Hello, my name's Mrs. Cornwell and I'm going to be helping you with your learning today.

We're going to be using some of the things you already know to help you with some new learning, and I'm really looking forward to working with you today.

So let's get started.

Come to today's lesson, which is called Using bar models to subtract and it comes from the unit Additive Structures: Addition and Subtraction.

Okay, so in today's lesson we're going to use bar models to represent and solve subtraction problems and also equations.

And we're going to see how they can help us to understand the problems more confidently and to see what the different parts represent.

So let's get started.

So our keywords today are, we've got subtract, my turn, subtract, your turn.

And minuend, my turn, minuend, your turn.

And subtrahend, my turn, subtrahend, your turn.

And difference, my turn, difference, your turn.

Excellent.

Well done.

Okay, so in the first part of today's lesson we're going to represent subtraction on a bar model.

Jun has some conkers on a tray.

He sorts them between two smaller trays like this.

So there's his whole group of conkers and he sorts them onto two trays.

Which number would represent the whole amount? That's right, there were seven conkers altogether, so there were seven in the whole group, wasn't there? Which numbers would represent the parts? That's right, so we've got four conkers with shells there and three conkers without shells.

Those were the two parts of the whole.

Let's tell a subtraction story.

There are seven conkers altogether.

Four of them have shells and three of them do not have shells.

Write an equation to represent this.

So we know 7 is the whole amount, the minuend, isn't it? And then if we subtract four, 7 - 4, the remaining part is 3 and we can see there the two parts, can't we? 7 - 4 is equal to 3.

Jun says, "These trays, the trays remind me of something.

It makes me think of a bar model.

I can represent subtraction on a bar model." We can use a bar model to partition, or subtract, one part from the whole.

We know subtraction is when we find one part of a whole amount, don't we? So let's have a look at these balloons and see if we can put these onto the bar model.

There are seven balloons, two have spots.

How many do not have spots? So Jun decides to use a bar model to help him represent the problem and it will help him understand the problem, won't it? There are seven balloons in the whole group.

This is called the minuend.

Where should he put that do you think? Where should he put the minuend? The whole group.

That's right.

Two balloons have spots, so this is the subtrahend, the amount to be subtracted.

That's right, so that's one part, the part to be subtracted.

7 is the whole, 2 is a part, and 5 is a part.

When we know the whole and we know one part, we can find the other part.

This part is called the difference.

And there we are, that was the other part, wasn't it? 7 - 2 is equal to 5.

What numbers could Jun write in the bar model to represent the balloons? So let's think of our stem sentence.

Mm is the whole, mm is a part, and mm is a part.

So we know 7 is the whole group of balloons, isn't it? And then we can see 2 is a part and 5 is a part.

So 7 is the whole amount, the minuend, and there's your 2, the subtrahend that was subtracted, and there's your 5, your remaining 5 that were the difference.

What does each number represent? So the 7 represents the total number of balloons altogether, doesn't it? The 5 represents the five balloons without spots, and the 2 represents the two balloons with spots, doesn't it? Well done.

Okay, so let's complete the bar model to solve this problem.

So there are eight drinks, okay? Two are hot drinks, so how many are not hot drinks? So what do we have to do to solve that problem? So we've got 8 as the whole group, the minuend, and then we have to subtract or partition 2 from the whole group, don't we, okay? And then we can see how many are remaining.

We can see 8 - 2 is equal to 6.

That's right.

Well done.

So what were the wholes and the parts in that subtraction story? Let's look at our bar model.

That's right, 8 is the whole, 2 is a part.

That was the part that was subtracted, wasn't it? And 6 is a part.

When we know the whole and we know one part, we can find the other part.

This part is called the difference, isn't it? So let's think about what the numbers represent then.

The 8 represents eight drinks in the whole group, that's right.

The 2 represents the two hot drinks, and the 6 represents the six drinks that are not hot.

Well done.

So now it's time to check your understanding.

Izzy has this group of objects.

Tell a subtraction story, then record the numbers in the correct place on the bar model.

Okay, so pause the video now while you try that.

Okay, and let's see how you got on.

Okay, so we know that there were seven apples altogether in the total group, the whole group, weren't there? So that's the whole amount.

Five of them have been eaten and two of them have not.

So you could partition the 5, subtract the 5, and then you could see that there were 2 remaining there, couldn't you? Okay, so you may have done that and you would've written 7 - 5 is equal to 2.

You may have also said, there was a different subtraction you could have said for that picture.

So you may have said there are seven apples altogether in the total group, but then you may have said two of them have not been eaten and five of them have been eaten.

So you might have decided to subtract the 2.

So that would've been 7 - 2 is equal to, that's right, 5.

Either of those would've been correct, so well done with that.

There are five animals altogether in the total group.

Three of them are cats.

How many are not cats? So which bar model represents that problem do you think? Have a careful look.

Remember to think about the parts and the whole.

So mm is the whole, mm is a part, and mm is a part.

That's right.

5 is the whole, 3 is a part.

3 represents the three cats, and 2 is a part which represents the two dogs.

So it would've been that bar model that was correct, wouldn't it? So now it's time to check your understanding.

Which bar model represents the picture shown? And you've got a stem sentence there to help you.

Mm is the whole, mm is a part, and mm is a part.

So pause the video now while you think about that.

Okay, let's see how we got on.

So what was the whole amount? That's right, 5 is the whole, 2 is a part and 3 is a part.

So the bar model that represents that picture would've been that one, well done.

Okay, so another check now.

Complete the stem sentences to say what each part of the bar model represents.

Okay, so the 5 represents, and the 2 represents, and the 3 represents.

Pause the video now while you complete those sentences.

Okay, and let's have a look together.

The 5 represents, that's right, the whole group of five cups.

The 2 represents the two cups without juice.

And the 3 represents the three cups with juice.

Excellent.

Let's write a subtraction equation to represent this bar model.

Hmm, something different about this bar model.

Can you spot what it is? Jun's noticed it.

He says, "The question mark shows the part I am trying to find." So there's a question mark for the missing part there that we need to find out.

7 is the whole, 2 is a part, and mm is the part.

That's the part we're trying to find.

Izzy says, "2 is a part.

I must subtract 2 from the whole group." And that's to find the missing part, isn't it? So 7 - 2 is equal to, that's right, 5.

So the missing part must be 5.

Well done.

7 is the whole, 2 is a part, and 5 is a part.

So time to check your understanding again now.

So write an equation to represent this bar model.

Okay, so you can see the numbers there.

So pause the video now while you try that.

Okay, and let's see how you got on with that.

So our equation 9 - 4 is equal to 5 because 9 is the whole amount.

And then you can subtract 4, which is one of the parts to find the remaining part.

You could have also said 9 - 5 = 4 because it just depends which number you chose to subtract.

You could subtract either part from the whole and it would leave the other part, wouldn't it? So well done with that.

Okay, so let's look at this together then.

Izzy draws a bar model to represent this equation.

8 - 3 is equal to 5.

There is no picture.

How will I know where to put the numbers? Hmm, what questions will I ask myself? Which number is the minuend? This represents the total number altogether.

That's right, it's 8, isn't it? 8 is the whole group.

And where should Izzy write the subtrahend? This is the part that has to be subtracted.

That's right, she can write it there, can't she? That's the smaller part in the bar model, isn't it? So that makes sense that that one will be the 3.

Now she can see that 8 - 3 is equal to 5.

Let's check your understanding now.

So use the equation to complete this bar model, okay? So it says 10 - 4 is equal to 6.

Pause the video now while you try that.

Okay, and then let's see how you got on.

So 10 is the whole amount, the minuend, 4 is the subtrahend, the amount to be subtracted, and so 6 must be the part remaining, the difference.

Well done if you spotted that.

So the task in the first part of today's lesson is here: match each picture to the correct bar model.

So you're thinking about what the whole amount is, what the subtrahend is to be subtracted, and what the part remaining, the difference is.

Okay, so pause the video now while you have a try at that.

So now here's the second part of today's task.

Use the pictures to complete the empty bar models and that's for part A, B, and C, okay? And then use the complete bar models to subtract a part of the picture.

So that's part D, E, and F.

So you've got the completed bar model there and you have to subtract one of the parts on the picture, don't you, to leave the remaining part.

So pause the video while you try that.

Okay, and let's see how you got on.

Okay, so let's see how we got on with the first part of your task.

So match each picture to the correct equation.

So we can see the whole group has got six apples in that first picture.

And we can see that three have been partitioned, they have been subtracted, and there are three remaining.

So it will be that bar model, won't it? That's right.

And then let's have a look at the other answers.

Well done if you got those.

Let's have a look at the second part of our task then, how did we get on? So we can have a look at this first example.

A, we can see that there are five dogs.

Okay, so that is the whole amount.

And then we can see that we had one dog that was subtracted, one was partitioned, and so there were four remaining.

Okay, and then here are the answers for the other pictures.

So well done if you got those.

Okay, so let's have a look at the second part here.

So we've got D, E, and F.

So if you look at D with the four cars, you can see there's four as the whole.

And then we had to subtract two as one part, didn't we? And there were two remaining.

And then we've got 8 as the whole and then you can either subtract 1 or 7, can't you? In this case we subtracted 1 and there was 7 remaining.

And then we had 10, and again, you could either subtract the 7 or the 3, okay? But in this case we subtracted 3 and there was 7 remaining.

So well done.

Excellent work.

So in the second part of today's lesson, we're going to use bar models to subtract.

So there were nine bananas altogether.

Here's the problem.

Five bananas had been peeled.

How many had not been peeled? And Jun says, "I can't see a picture.

I don't know how to represent this." "I will use counters to represent the problem," he says.

So there's his counters and they're representing the nine bananas.

And then he says, "I will use a bar model to help me." So there's his bar model.

Where should Jun put the whole group of counters? That's right, he puts it where the whole group goes, because that's the minuend.

"How will I show the five to be subtracted?" he says.

That's right, he partitions it from the whole amount, doesn't he? Okay, he subtracts it.

"Now I can see that 9 - 5 is equal to 4," he says.

So he knows that 4 must be the remaining part.

9 - 5 is equal to 4.

Okay, so now we've got another problem.

Use your counters to represent this on a bar model.

There were six pencils.

Three were sharpened.

How many were not sharpened? And then we're going to write the equation as well to help us with that, aren't we? So let's think about the equation.

Okay, so how many counters will you need? That's right, we'll need six because that represents six pencils.

What number needs to be subtracted? That's right, three were sharpened, so we're going to partition or subtract those three, aren't we? So 6 - 3.

So how many counters will we need to put on the bar model then? That's right, six.

What number needed to be subtracted? That's right, it was 6 - 3.

So that's one part has been partitioned.

And then we can see that there will be three remaining.

That will be the other part, won't it? And we can write the number 6 - 3 is equal to 3.

So now it's time to check your understanding.

Match the counters to the bar model that represents them.

Okay, so pause the video now while you try that.

Okay, so let's have a look.

So we've got a first group of counters there.

Think about what the whole group is.

We can see there's five counters and one part is three and the other part is two, so it will be that bar model, won't it? Okay, and then the next one we've got five counters and we can see that we've got four red and one white.

So it will be that bar model.

And finally, four counters is the whole, with three is a part and one is a part.

So well done if you spotted that.

Izzy and Jun each wrote an equation to represent this bar model.

Who is right? Okay, so we've got 7 - 1 is equal to 6 and 7 - 6 is equal to 1.

That's right.

They're both right, aren't they? Because it doesn't matter which part you subtract, it will leave the other part, won't it? The bar model shows 7 - 1 is equal to 6, and there's seven and you subtract one and there are six remaining.

But it also shows 7 - 6 is equal to 1.

You subtract six and there's one remaining.

So well done if you spotted that.

And there we can see the numbers written in there, can't we? So time to check your understanding again.

Write two different subtraction equations to represent this picture and then represent each on a bar model.

So pause the video now while you try that.

Okay, so let's see how we got on.

So you could have said five because that's the whole group, the minuend, minus four is equal to one, and that would've been 5 - 4, that's the 4 that's going to be partitioned, is equal to 1.

Okay, you could have also said, 5 - 1 is equal to 4.

There's the whole group of five.

And then subtract the one or partition the one and it's equal to four.

So well done if you got those.

Jun is writing subtraction equations.

He wants to see how many he can write with a minuend of 5.

Let's work systematically to find all the possibilities and use a bar model to solve each equation.

So we're going to work in order, aren't we? Which equation should Jun write first? There's his bar model and he's going to write 5 - 0 is equal to and there's five, five in the whole group.

And you can see that's just all stayed in one part, hasn't it? 5 - 0 is equal to 5.

And then we've got 5 - 1 next.

So 5 - 1 will be equal to 4.

That's right, 4 is the remaining part, the difference, isn't it? Then we can have 5 - 2 is equal to 3, that's right.

And then we could say 5 - 3 is equal to 2.

And then 5 - 4 is equal to 1.

5 - 5 is equal to 0, isn't it? Well done.

Excellent.

Okay, so now here's your task for the second part of today's lesson.

So how many subtraction equations can you write with a minuend of 6? Write each one down, then solve it using counters on your bar model.

So remember how we find all the possibilities.

So try and find all of the possibilities by working systematically.

Pause the video now while you try that.

So let's see how you got on.

You may have done this.

6 - 0 is equal to 6.

Okay, and then 6 - 1 is equal to 5.

6 - 2 is equal to 4.

6 - 3 is equal to, that's right, 3.

6 - 4 is equal to 2.

6 - 5 is equal to 1.

And 6 - 6 is equal to 0.

How can you find all the possibilities? What can you do? That's right, you can work systematically so you know you've found all the possible combinations.

So well done if you did that.

Okay, so let's think about what we learned in today's lesson.

We found out using a bar model can help us to represent and understand subtraction problems and equations.

And we also found out that the bar model shows you how you can subtract one part of a whole group to find the rest of the group.

So I've really enjoyed working with you and finding out all of the different ways we can represent subtraction on a bar model.

So well done with that.

That was excellent work.