Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you today in this lesson from our unit on comparing, ordering and partitioning two digit numbers.

Have you done lots of work with two digit numbers before? I wonder? Well, I hope you're ready to work hard and think hard today.

So let's make a start.

So in this lesson we're going to be solving problems that require addition and subtraction of tens and ones.

We've got some key words.

We've got addition, subtraction, parts and whole.

So I'll take my turn to say them and then you can take your turn.

My turn, addition.

Your turn.

My turn, subtraction.

Your turn.

My turn, parts.

Your turn.

My turn, whole.

Your turn.

Well done, I'm sure they're words that you know, but they're going to be really useful to us today, so watch out for them as we go through our lesson.

There are two parts to our lesson today.

In the first part, we're going to be representing problems. And you'll notice in the first part that we don't solve the problems. So we don't come up with any answers, we just represent the problems. And then in the second part of the lesson, we'll look at solving the problems. So if you're ready, let's make a start.

And we've got Izzy and Lucas helping us in our lesson today.

The children are getting pencils ready for their art project and you can see they've got colouring pencils in a pack and they've got some colouring pencils out of a pack.

How many pencils have the children collected altogether? Can you see that each colouring pencil pack has 10 pencils in? Izzy says, "I have collected 30 pencils." And Lucas says, "I have collected four pencils." Let's think about how we can work it out.

How many have they got all together? We know how many pencils each child has collected so we know a known part and another known part.

So we know the two parts.

But we do not know how many pencils they have altogether.

So we have an unknown whole.

So we've created a bar model there from what we know.

We've got two parts that we know, but we don't know what the whole is.

Izzy says, "We know my part." Izzy's pencils.

And Lucas says, "We know my part." Lucas's pencils.

"We don't know how many pencils there are all together.

So that whole is the number of pencils there are all together.

Lucas says, "We know that when we combine the parts to find the whole amount, this is addition." Izzy says, "I can write an equation to represent this." So we know that Izzy has 30 pencils and Lucas has four pencils.

So 30 plus four will equal our unknown whole.

And remember, I said we're not solving the problems in this part of the lesson, we're just representing them.

So we're going to leave that problem there.

We've represented it and we know the calculation we've got to do.

So the children have put their pencils together with some others.

Now they have 64 pencils altogether.

Izzy sharpens four pencils.

How many were not sharpened? So we know how many pencils there are in the whole group.

So this time our whole in our bar model is known.

"We know how many of the whole group was sharpened," so we know that that is a known part.

They were the sharp pencils.

"We need to find the other part." So we have an unknown part this time.

Izzy says, "I know in subtraction that we partition one part from the whole to find the other part." So the whole, subtract one part, gives us the value of the other part.

Lucas says, "We need to write a subtraction equation." Whole subtract part is equal to part.

So we know that there are 64 pencils together in our whole.

We know that four pencils have been sharpened, but we do not know how many pencils have not been sharpened.

So our equation will be 64 subtract four equals something.

And again, we're not solving it right now.

We're going to solve it in the second part of our lesson.

Over to you to check your understanding.

Which bar model represents this problem and write the equation to represent it.

So our problem is there are 40 pieces of yellow paper and six pieces of green paper on the table.

How many pieces of paper are there all together? Now the bar models have got lots of words in.

So take time to have a look.

Look out for the 40 pieces of yellow paper and the six pieces of green paper.

And our problem is to work out how many pieces of paper there are altogether.

So which bar model represents this and what equation could you write that we will solve later In order to find out how many pieces of paper there are altogether.

Pause the video, have a go and we'll come back for some feedback.

How did you get on? So we need to combine the green paper and the yellow paper to find the whole.

And when we combine the parts to reach the whole, it's addition.

So part plus part is equal to whole.

We knew about the two parts.

So A was correct.

The parts we knew were the 40 pieces of yellow paper and the six pieces of green paper.

The other two bar models both use one of the parts as the whole.

So that's not going to be the correct way to represent this problem.

And the equation we would need would be 40 plus six is equal to something, 40 pieces of yellow paper plus six pieces of green paper.

Let's have another go.

Which bar model represents this problem? And write the equation to represent it.

Izzy takes 46 pieces of paper and folds six of them in half.

How many pieces of paper were not folded in half? Again, have a look at the bar models carefully and pause the video.

How did you get on? This time when we partition one part from the whole to find the other part, it is subtraction.

We knew how many pieces of paper there were altogether and we knew that Izzy had folded some in half.

So it was the part that was not folded that we didn't know.

So we need to subtract the six pieces of folded paper from the 46 pieces of paper in the whole group.

Whole subtract part is equal to part.

So this time B was the correct bar model because it correctly showed that the whole was 46 pieces of paper.

Our unfolded paper and our folded paper were the two parts.

So our equation was 46, subtract six is equal to something.

46 is our whole, six was our number of folded pieces of paper.

So we need to subtract those from the whole to find out how many pieces were unfolded.

Izzy keeps the 20 pencils she has sharpened and Lucas gives her five more.

How many pencils does she have now? Izzy says, "We know how many pencils I had first." Izzy's 20 pencils.

She's done a bit more sharpening from when we last saw her.

"And we know how many pencils I gave to her," says Lucas.

He gave her five pencils.

So we know our two parts.

"We need to find out how many pencils I now have." Izzy's pencils now, that's the bit we don't know.

"We are increasing the amount.

We need to write an addition equation," says Lucas.

20 plus five is equal to something.

And again, we're not solving these now, we're just representing them, using what we know in the problem to help us to work out what the equation is.

Lucas collected a group of 86 pencils and gave Izzy six of them.

How many does he have left? So let's think about what we know.

Do we know about parts or wholes? Lucas says, "I know how many pencils I had to start with." The whole group of pencils was 86 pencils.

So we know about the whole.

Izzy says, "We know how many pencils you gave me." Six pencils were given to Izzy.

So we know about that part as well, don't we? "We need to find out how many I have left." So how many pencils are left? That's our unknown and it's a part.

Izzy says, "You have decreased the number of pencils so you must have subtracted." So we need to subtract the part we know from the whole to find the other part.

86 subtract six is equal to- and that will be our answer.

So can you match each problem to the bar model and then write an equation that would help you to solve it? So you've got two problems there.

Lucas has 58 pencils and puts 50 on the table.

How many pencils has he now? And then Lucas has 50 pencils and he picks up eight more from the table.

How many pencils does he have now? So which bar model represents which problem and how would you write an equation to solve each of those problems? Remember we don't want to solve it now, we just want the equation that you would use.

So pause the video, have a go and we'll look at the answers together.

How did you get on? Did you spot that the bottom bar model matched the top problem? Lucas has 58 pencils and he puts 50 on the table.

How many pencils has he now? We know how many pencils Lucas started with and we know that he put 50 on the table.

What we don't know is the missing part.

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

So 58 subtract 50 will give us our missing part.

So the other bar model must match the other problem.

Lucas has 50 pencils and he picks up eight more.

So this time we know the pencils he had to start with and the pencils he picked up.

So we know the two parts.

So we have to combine the two parts to make the whole.

So the equation would be 50 plus eight is equal to something.

Well done if you got that right.

Lucas draws this bar model.

He wonders if he can write a problem that could represent it.

So we've got a whole of 54 and two parts of four and 50.

Lucas says, "I think I can tell an addition story." Izzy says, "That means you must combine the parts to reach the whole." Lucas says, "Or increase one part by adding another part.

Part plus part is equal to whole." 50 plus four is equal to 54.

Izzy says, "I will create an addition problem where I combine the parts." She says, "I jumped 50 times and you jumped four times.

How many times did we jump all together?" 50 plus four.

Lucas says, "I will increase the amount in my addition story.

I had 50 stickers in my book and I stuck in four more stickers.

How many stickers are in my book now?" So he started with 50 and he added four more stickers.

Izzy thinks they can also create some subtraction problems for the same bar model.

Let's see if she's right.

Whole subtract part is equal to part.

54 is the whole and I will subtract four.

Izzy says, "I will create a subtraction problem where I partition one part from the whole." She says, "I had 54 conkers in my bag.

Four of them had shells." Those green spiky shells, they have.

How many of them did not have shells? So she has 54 conkers.

She knows that four of them have shells.

So the other part do not have shells.

So 54, subtract four is equal to the number that didn't have shells.

Lucas says, "I will create a story where I decrease the whole amount by subtracting one part.

I had 54 trains in the box and I took out four to play with.

How many were left in the box?" And he can represent that with the same subtraction.

54 trains and he takes four out of the box.

So the missing number, the missing part is how many trains are left in the box.

Perhaps you could make up some problems of your own to match the bar model? Time for you to do some practise.

You're going to draw a bar model to represent each problem.

Use a question mark to represent the unknown part or whole in your bar model.

Pause the video, and draw your bar models and then we'll look at them together.

How did you get on? Let's look at the first two first.

So in A there were 50 bricks in the toy box, then Lucas put in seven more.

How many bricks are in the toy box now? So when we increase one part by adding another part to reach the whole, its addition.

Part plus part is equal to whole.

So we know there were 50 bricks and Lucas added in seven more, so the missing part is our whole and we'd have to add the 50 and the seven together to work out what our missing whole was.

So let's look at B.

This time there were 29 bricks in the box altogether and 20 of them are large bricks.

How many are not large bricks? So we're not really taking any away, but we are sort of partitioning them into large bricks and small bricks.

So when we partition the amount by removing one part from the whole, it is subtraction.

Whole subtract part equals part.

So this time our whole was 29 and we knew that one part was 20, the large bricks.

So what we didn't know was how many of the bricks were not large, the other part.

So this time we knew the whole and one part and we were going to work out the other part and we know that we subtract one part to find the other part.

So 29 subtract 20 equals our missing part.

Let's look at C.

There were 36 bricks in the toy box, then Izzy used six of them to make her model.

How many bricks are in the box now? This time we are decreasing the whole amount by removing one part and that's subtraction.

Whole minus part is equal to part.

So there were 36 bricks, that was our whole, and we removed six of them.

Izzy used six of them in her model.

So our equation will be 36 subtract six, and that will give us the value of our missing part.

And for D, there are 70 bricks in the toy box and eight bricks on the floor.

How many bricks are there altogether? When we combine two parts to make the whole it is addition.

Part plus part is equal to whole.

So we knew the parts, the bricks in the toy box and the bricks on the floor.

So we have to combine them to find the missing whole.

70 plus eight will give us our missing whole.

Well done if you've got those right.

And let's move on to the second part of our lesson.

We're going to solve these problems. So Izzy had collected 30 pencils and Lucas has four pencils.

How many pencils have the children collected altogether? So we knew Izzy's part was 30 and we knew Lucas's part was four.

So we don't know how many pencils there are altogether, but we know that when we combine the parts to make the whole amount it's addition.

And we can write the equation, which was 30 plus four.

Part plus part is equal to whole.

There are three tens, which is 30 and four ones which is four.

There are 34 altogether.

So our missing whole was 34.

There are 34 pencils altogether.

Do you remember this one? The children put their pencils together with some others.

Now they have 64 pencils altogether.

Izzy sharpens four pencils.

How many were not sharpened? So Lucas says, "We know how many pencils there are in the whole group." There are 64 pencils altogether.

Izzy says, "We know how many were sharpened." Four pencils were sharpened.

We need to find the other part.

The other part is the pencils that were not sharpened.

Izzy says, "I know in subtraction we partition one part from the whole to find the other part." Whole subtract part is equal to part.

So Lucas says we need to write a subtraction equation.

64 subtract four is equal to 60.

60 pencils were not sharpened.

Time to check your understanding.

You're going to draw a bar model and write an equation to solve this problem.

You may remember it from the first part of our lesson.

There are 40 yellow pieces of paper and six pieces of green paper on the table.

How many pieces of paper are there all together? Pause the video, draw a bar model and solve the problem.

How did you get on? Could you use your bar model from earlier in the lesson? So there are 40 pieces of green paper and there are six pieces of yellow paper.

Those are our two parts.

We know there are four tens, which is 40 and six ones which is six.

So there are 46 pieces of paper all together.

We could combine the parts to find our whole of 46.

40 plus six is equal to 46.

And another one, again a bar model, and then the equation to solve this problem.

There were 46 pieces of paper.

Six were green.

How many were not green? This is a slightly different problem.

So have a think, draw the bar model and then see if you can solve the problem using an equation.

Pause the video and have a go.

How did you get on? So this time there were 46 pieces of paper.

That was our whole.

Six of the pieces are green and we had to work out how many of the pieces were not green.

So we knew the whole and one part.

When we know the whole and one part, we have to subtract the part from the whole.

So 46 has four tens, which is 40 and six ones which is six.

If 46 is the whole and six is a part, the other part must be 40.

So 40 pieces of paper were not green.

46 subtract six is equal to 40.

Izzy keeps the 20 pencils she has sharpened and Lucas gives her five more.

How many pencils does she now have? Do you remember this problem from the first part of the lesson as well? So Izzy says, "We know how many pencils I had first," which is 20.

And "we know how many pencils I gave you," says Lucas, which was five.

"We have to find out how many pencils I now have." So the new number of pencils that Izzy has.

"We are increasing the amounts," says Lucas, "We need to write an addition equation." We know the parts and we're going to combine them to find the whole.

So 20 plus five is equal to- Well, Izzy says, "There are two tens, which is 20 and five ones which is five.

There are 25 pencils all together." So Izzy now has 25 pencils.

So can you draw a bar model and then write an equation to solve this problem? There are 60 pieces of card and Izzy picks up three more.

How many pieces of card does she have now? Pause the video and have a go.

How did you get on? So there are 60 pieces of card and Izzy picks up three more.

So those were our parts and we need to combine them to find the whole.

We know that there are six tens, which is 60 and three ones which is three.

If 60 is a part and three is a part, then 63 is the whole.

There are 63 pieces of paper all together.

So that's our whole.

60 plus three is equal to 63.

Lucas had the whole group of 64 pencils and gave 60 of them to Izzy.

How many does he have left? Lucas says, "I know how many pencils I had to start with.

I had 64, so that's the whole." And Izzy says, "We know how many pencils you gave to me." So that was 60, one of the parts.

"We need to find out how many I have left." The other part.

Izzy says, "You have decreased the amount of pencils you had, you must have subtracted." "We need to write a subtraction equation," says Lucas.

64 subtract 60 is equal to our missing part.

We know our whole is 64 and we've subtracted the part we know.

64 has six tens, which is 60 and four ones which is four.

If 64 is the whole and 60 is a part, the other part must be four, so Lucas has four pencils left.

Who's right here? There's a bar model with 46 as the whole, 40 as a part and six as a part.

Izzy says, "I think this represents a subtraction problem." And Lucas says, "I think this represents an addition problem." Who's right? What do you think? Well, they could both be right, couldn't they? If we start with the whole and subtract one part, it is subtraction.

And if we start with one part and add the other part, it is addition.

So our parts and our wholes can represent parts to be combined in an addition or a part to be subtracted from a whole in the subtraction.

Let's write some addition equations.

So we could say 40 plus six is equal to 46.

Or six plus 40 is equal to 46.

Or we could say 46 is equal to 40 plus six.

And 46 is equal to six plus 40.

Let's write some subtraction equations.

46 subtract 40 is equal to six.

And 46 subtract six is equal to 40.

Or we could say six is equal to 46 subtract 40.

And 40 is equal to 46 subtract six.

You might want to just have a look at those and remind yourself where the whole is in each of those equations and where the parts are.

Are we combining the parts to make a whole or are we subtracting one part from the whole to find the other part? There are lots of ways we can think about the parts and whole in this bar model and make addition and subtraction equations from them.

Time to check your understanding.

Can you draw a bar model and an equation to help you to solve each problem? And what do you notice? So A says, Lucas has 58 pencils and he puts eight on the table.

How many pencils has he now? And B says, Lucas has 50 pencils and he picks up eight more from the table.

How many pencils does he have now? Pause the video and have a go.

And how did you get on? So for A Lucas has 58 pencils and he puts eight on the table.

How many pencils has he now? So 58 is our whole, eight is a part and 50 must be the other part because we know if 58 is the whole and eight is a part, 50 is the other part.

58 subtract eight is equal to 50.

And for B, Lucas has 50 pencils and he picks up eight more from the table.

How many pencils does he have now? This time we know about one of the parts which was 50 and the other part which was eight.

So the whole is 58.

If 50 is a part and eight is a part, then 58 is the whole.

Lucas has 58 pencils now.

Both of our models were the same once the problem was solved because in A we start with 58 and subtract eight, and in B we start with 50 and add eight.

So we can see that that same bar model can be used to represent both of those problems. This means both problems have 58 as a whole and 50 and eight as the parts.

Time for you to do some practise.

Now you've represented the problems in task A, use what you have learned to write the equations and solve the problems. So A was the problem about the bricks in the box.

So there were 50 bricks in the toy box and then Lucas put in seven more.

How many bricks are in the box? And B was about more bricks in the box, 29 bricks in the box altogether, 20 of them are large, and how many are not large? Then, can you write a different problem that the equation could represent? So we had 50 plus seven and 29 subtract 20.

Can you write a different problem that each of those equations could represent? Remember to include combining parts and increasing an amount for addition problems and partitioning and decreasing an amount for subtraction problems. And then you're going to do the same for C and D.

So pause the video now and have a go at solving those.

How did you get on? So for A, we knew that the calculation we had to solve was 50 plus seven.

The whole was missing, so we must add 50 and seven.

And 50 plus seven is equal to 57.

So for B, there were 29 bricks in the toy box altogether, 20 of them are large bricks.

How many of them are not large? So last time we worked out that 29 was the whole and 20 was the part.

And to solve the calculation, we had to subtract the known part from the whole.

So the part is missing I must subtract.

29 subtract 20 is equal to nine.

So nine of the bricks are not large, that's our missing part.

In C, there were 36 bricks in the toy box and Izzy used six of them in her model.

How many bricks were in the box now? So we knew that the whole was 36 and one part was six.

A part is missing, so I must subtract.

36 subtract six is equal to 30.

So our missing part was 30.

That's how many bricks there are in the box now.

And indeed there are 70 bricks in the toy box and eight bricks on the floor.

How many bricks are there all together? So we knew that 70 was a part and eight was a part.

So our whole is missing.

So the whole is missing.

I must add 70 plus eight is equal to 78.

So there are 78 bricks all together.

What about a different problem for each of these? So you could write a problem where you combine the groups here for A.

We knew the parts were 50 and seven.

So we could say there were 50 children in the playground and seven children in the hall.

How many children were there all together? For B we could write a partitioning problem.

We knew about the whole and one of the parts.

There were 29 biscuits in the biscuit tin.

20 of them were chocolate biscuits.

How many were not chocolate biscuits? So for C, you could write a problem where you decrease the whole amount.

Again, we knew about the whole and one part.

So we were thinking about subtraction.

There were 36 cars in the garage and then six drove away.

How many cars were left in the garage? And for D, again, we knew the parts, so this is addition.

But this time we could think about an increasing problem.

There were eight cars in the car park.

By lunchtime, 70 more cars had come in.

How many cars are in the car park now? And we'd have to combine those parts to find the whole.

I hope you have fun creating your own problems to match the bar models.

And we've come to the end of our lesson.

We've been solving problems by adding and subtracting tens and ones.

We've been using our place value a lot to help us.

Did you notice that we were always thinking about a number of tens and a number of ones? So what have we learnt about today? Well, when tens and ones are combined to make a two digit number, it can be represented as an addition equation.

And when a two digit number is partitioned into tens and ones, it can be represented as a subtraction equation.

And that we can use bar models to help us to understand and represent a problem.

Thank you for all your hard work and your mathematical thinking today.

I've enjoyed working with you and I hope we get to work together again soon.

Bye-Bye.