Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in our maths lesson today.

We're going to be thinking all about place value, numbers up to 100, and how we can apply that, and other strategies to adding and subtracting.

So I hope you're ready to work hard, and have some fun in our maths lesson today.

So in this lesson in our unit of securing place value to 100 and applying to addition and subtraction, we're going to be solving problems by applying different strategies for adding and subtracting multiples of 10.

We've got quite a lot of keywords today.

Lots of them I expect you'll be quite familiar with, but we're going to make sure that we use them really accurately to help with our work today.

So we've got add, subtract, strategy, part, and whole.

Let's just practise saying those.

So I'll have my turn and then it'll be your turn.

So my turn, add, your turn.

My turn, subtract, your turn.

My turn, strategy, your turn.

My turn, part, your turn.

My turn, whole, your turn, excellent! Let's look and see what those words mean.

So when you add, you bring two or more numbers or things together to make a new total.

And we know that the symbol for addition is that + sign.

When you subtract, you take one number away from another.

And this is the symbol we use for subtraction.

A strategy is a way to solve a problem.

Different strategies might be used for different problems. Partitioning and bridging through 100 is an example of a strategy.

A part is a piece or a section of the whole.

And the whole is all of a group or number.

When you have the whole, you have all of something.

So quite a few keywords So watch out for those as we go through our lesson.

There's two parts to our lesson today.

In the first part, we're going to be looking at some problems and identifying when we have to add or subtract, how do we work that out? How do we know what the calculation we need is to solve our problem? And in the second part, we're going to choose the best strategies to solve those problems. So the first part of our lesson is all about exploring some problems, but not actually getting the answers, we'll do that in the second part, so let's get going.

And we've got Andeep, Jacob, and Izzy helping us in our lesson today.

So here's our first problem.

A cake costs £1.

60 or 160 p.

Izzy has 80 p and Jacob has 70 p, do they have enough money to buy the cake? So when you have a problem to solve, you need to work out what sort of problem it is and how you will solve it.

Izzy's got an idea.

Izzy says, "I can represent the problem on a bar model." Let's have a look at Izzy's bar model.

Okay, so Izzy's drawn a bar model.

So she's got the hole at the top and then two parts underneath.

Izzy says, "70 p and 80 p are the parts.

The hole needs to be 160 p or more." So we dunno what the whole is yet, but we know that it's got to be 160 p or they won't be able to afford their cake.

And Izzy says, "To calculate the whole, you need to add the parts." So to solve this problem, you have to add the parts and compare the whole to 160 p.

And the calculation we'll need is 80 + 70 = hmm.

We're not gonna solve it right now, we're going to save that for the second part of our lesson.

What we're interested in in this first part is how we make sense of the problem that's presented to us, how we can maybe use a bar model to help us understand it, and how we can work out what calculation it is that we need to solve.

So let's think about this in a different way.

What is the whole in the problem? Izzy says, "The whole is how much money she and Jacob have all together," we don't know that.

What are the parts in the problem? Izzy says, "The parts are how much money she and Jacob have each." And what's the 160 p in the problem because that looks like it might be the whole, mightn't it? And Izzy says, "No, the 160 p is the cost of the cake.

We need to compare this with the whole." So let's have a look at another problem.

This time, Izzy has £1.

50 or 150 p and she pays a 80 p for a drink.

Has she got enough money left to buy an 80 p drink for Jacob as well? Izzy says, "I can represent the problem on a bar model." Let's have a look at her bar model.

Oh, that looks quite different from the last bar model, doesn't it? This time we've got the 150 p in our whole, and 80 p is a part, and an unknown as a part.

Izzy says, "The whole is 150 p.

80 p is a part, and we don't know the other part." To solve this problem, you have to subtract the part you know from the whole to work out the other part.

So we need to do 150, subtract 80 to find out what our missing part is.

Let's have a think about the problem and those parts and wholes again.

So what is the whole in the problem? Izzy says, "The whole is the 150 p." It's her own 150 p, isn't it? What are the parts in the problem? Izzy says, "One part is the 80 p she spends, and the other part is how much money she has left.

And we need to know if that's enough money to buy Jacob a drink as well." So here's another problem.

Andeep's sunflower is 70 centimetres tall.

If it grows another 50 centimetres, will he break the 130 centimetre class record for the tallest sunflower? Hmm, I wonder, how are we going to solve this problem then? Andeep says, "I can represent the problem on a bar model." There's Andeep's bar model, he's got 70 centimetres and 50 centimetres on the bottom and an unknown along the top.

So let's have a think about this.

Andeep says, "70 centimetres and 50 centimetres are the parts." 70 centimetres is how tall it is already, and 50 centimetres is the next part it's going to grow, it's going to grow another 50 centimetres, and he says, "The whole needs to be more than 130 centimetres." So he's got to work out the whole and compare it to that 130 centimetres.

So to solve this problem, you have to add the parts and compare the whole to 130 centimetres.

So 70 + 50 is = to, hmm.

Okay, time for you to have a think.

Which bar model represents this problem? So the problem is Jacob had 150 centimetres of string, he gave 70 centimetres to Izzy for her conker, How much string does Jacob have left? And you've got three bar models there.

So pause the video and decide which of those three bar models represents the problem with Jacob's string, and how much he has left.

Did you go for C? So let's have a think about that.

150 centimetres is the whole.

So Jacob had 150 centimetres of string.

70 centimetres is one of the parts, that's the part he gave to Izzy for her conker.

To calculate the missing part, which is how much string he's got left, you have to subtract the part you know from the whole.

So we have to do 150 subtract 70, so well done if you picked C.

Think about the other ones.

150 centimetres has to be the whole, that's the string that Jacob starts with.

In the other two bar models, it's a part.

Okay, so we've got another problem to think about here.

Izzy is pouring a drink for herself and Andeep, there is 140 millilitres of juice in the jug.

If she gives herself and Andeep 50 millilitres each, how much will be left in the jug? So what's the whole in the problem? Well, "The whole," Izzy says, "Is the 140 millilitres of juice that's in the jug." How many parts are there in this problem? Izzy says, There are 3 parts in the whole.

There's Izzy's 50 millilitres, there's Andeep's 50 millilitres, and the juice left in the jug." So this time, we've got three parts, but she says, "I can still represent this with a bar model." So let's have a look.

So there is Izzy's bar model.

Izzy says, "The whole is the 140 millilitres of juice in the jug.

The 3 parts are Izzy's 50 millilitres, Andeep's 50 millilitres, and the juice left in the jug." Now we know that to calculate a missing part, you need to subtract the parts you know from the whole, and its parts we know from the whole in this case, isn't it? So we're gonna have to do some calculating.

So we've got to do 140 subtract 50, and subtract another 50 from our whole to find out how much is left in the jug.

Okay, so another check for you.

We're back to Jacob and his string again.

So which bar model represents this problem? Jacob had 150 centimetres of string.

He gave 70 centimetres to Izzy for her conker and 50 centimetres to Andeep.

How much string does Jacob have left? So pause the video, have a look at the bar models, and decide which one represents this problem.

Did you go for B? So why is B the correct one? Well again, we are thinking what is the whole, aren't we? So 150 centimetres of string is the whole.

This is the string that Jacob had, and he gave some Izzy, and he gave some to Andeep, and he's got some left over.

His 150 centimetres of string has been split into three parts, the part for Izzy, the part for Andeep, and the part that he has left, and B represents that, 150 centimetres is the whole, and 70 centimetres, 50 centimetres, and the string that is left are the parts.

To calculate the missing part, you have to subtract the parts you know from the whole.

So we'd have to calculate 150 subtract 70, subtract another 50.

Time for you to do some practise.

So for each problem, you're going to complete the stem sentences, the bar model, and write down the calculation needed to solve the problem.

So you've got a problem here with Izzy and Jacob and a strawberry lace.

You've got a problem with Andeep and Jacob who want to buy a cake.

You've also got Izzy and Jacob with a strawberry lace as well.

And and Andeep and Jacob are saving up to buy a game.

And for this final question, you're going to draw a bar model to represent this and complete the stem sentences again, but what do you notice about this problem? So pause the video and have a go at representing those problems. How did you get on? So for one, Izzy and Jacob have a strawberry lace that is 130 centimetres long.

Izzy gives Jacob 70 centimetres, how much does she have left? So for our stem sentence, what was the whole? Well, 130 centimetres is the whole, and the parts are, 70 centimetres, that she gives to Jacob and what is left.

So our bar model has the whole, with 130, one part is 70, and the other part we don't know.

What we do know is that to find a missing part, we subtract the part we know from the whole.

So the calculation we need is 130 subtract 70.

Question 2, Andeep has 90 p, Jacob has 60 p, a cake costs £1.

40 or 140 p.

Have they got enough money to buy the cake? So what is the whole this time? Well, the whole is how much they have in total, but we don't know that.

So the hole is our missing bit.

The parts are 90 p and 60 p.

So if we've got a missing whole, we need to add the parts.

So the calculation we need is 90 plus 60 and we've then got to compare that to 140 p to see if they've got enough money to buy their cake.

So did you spot this time that there were three parts in our whole? So the whole was 150 centimetres, that strawberry lace that they started with, the parts are 60 centimetres, and 50 centimetres, and how much is left.

So the calculation we need to do is 150 subtract 60 subtract 50.

So this time, 190 p is the whole, and the parts are 70 p, 80 p, and how much more they need to save.

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

So the calculation would be 190, subtract 70, subtract 80.

So in this case, 190 centimetres is the whole.

And the parts are Izzy's part and Jacob's part.

And there's something in there about Izzy having 10 centimetres more than Jacob, isn't there? And we'll have a think about that one later, but just have a think about this problem it doesn't actually say that they have to use all the string so there could be some left over and if there's some left over, there's a third part to our bar model, but also there could be an awful lot of different answers.

We'll come back to this again in the second part of our lesson.

Okay, and speaking of the second part, here we go.

So we've had a look at representing problems and identifying when we need to add and subtract to work out the answer to the problems. Now we're gonna think about choosing the best strategies to solve the problems. So let's have a go.

So now you know how to solve a problem and we've identified those calculations that we need to do, you need to choose the best strategy to calculate.

So let's solve the problems from the first part of the lesson, thinking about the strategies that we're going to use.

So do you remember the cake, the cake costing £1.

60 or 160 p? Izzy has a 80 p and Jacob has 70 p.

Do they have enough money to buy the cake? So we drew the bar model last time with Izzy's help.

So we know that the parts are 80 p and 70 p, and our whole has got to be £1.

60, otherwise, we're not gonna have enough money for the cake.

So we need to add 80 + 70.

And as Andeep says, "You need to add the parts and compare the whole to 160 p." What's the best strategy to use to calculate our answer? Izzy says, "You could bridge through 100." You could do that.

Andeep says, "You could use a known fact." Oh, so there's two strategies there that we could use.

Let's have a think about them both.

Andeep says, "I know that 8 + 7 is = to 15." So 8 tens plus 8 tens is equal to 15 tens, and 15 tens is equal to 150." So Andy says, "That 80 plus 70 is 150." and he's done that by using a known fact.

Izzy says, "I know that 70 is equal to 20 + 50.

So she's partitioned one of the addends, she's partitioned the 70 into 20 and 50 so that she can do 80 plus 20, which is equal to 100, and then 100 plus the 50, which is the other part that we partitioned the 70 into.

And 100 plus 50 is 150.

So, of course, they've both got to the same answer.

So 80 plus 70 is equal to 150 p.

Izzy says, "150 p is less than 160 p." And Andeep says, "Izzy and Jacob do not have enough money to buy the cake." That's a shame, isn't it? So in this problem, Izzy was pouring a drink for herself and Andeep, there is 140 millilitres of juice in the jug.

If she gives herself and Andeep 50 millilitres each, how much will be left in the jug? So we drew the bar model for this last time, so let's have a think about how we're going to solve this problem.

Izzy says, "To calculate the missing part, you need to subtract the parts you know from the whole." So the calculation we had was 140 subtract 50, and subtract another 50.

Andeep says, "I can combine the parts.

I know 50 plus 50 is equal to 100." So we can change our bar model.

100 millilitres is what Izzy and Andeep drank in total.

So now we've only got two parts.

We've got the part we know about, which is what Izzy and Andeep drank in total, and we've got the juice that's left.

So now our calculation is 140 subtract 100.

And Andeep says, "Now I can use place value to calculate.

140 subtract 100 is equal to 40.

If I take away the 100, I know I've got 40 left." So Andeep's used place value.

So he knows that there will be 40 millilitres left in the jug.

So let's have a think about Jacob's string again.

So again, this was one where we had more than two parts in our whole.

So Jacob had 150 centimetres of string.

He gave 70 centimetres to Izzy for her conker, and 50 centimetres to Andeep.

How much string does Jacob have left? 150 centimetres is the whole, 70 centimetres, 50 centimetres, and the string that is left are the parts.

So we need to calculate 150, subtract 70, and subtract 50.

And Izzy reminds us, "To calculate the missing part, you need to subtract the parts you know from the whole." Andy says, "Well, I know that 150 subtract 50 is equal to 100".

So he spotted that there's a 50 as one of our parts.

So he says that if we take away the 50, we will have 100 left.

And he says then, "I know that 100 subtract 70 is a bit like 10 tens subtract 7 tens, which equals 3 tens." So Izzy says, "150 subtract 50, subtract 70 is equal to 30.

So Jacob has 30 centimetres of string left." So we've used some place value there and we've used a known fact to help us.

So one for you to have a think about.

Do you remember the problem about Andeep's sunflower? It was 70 centimetres tall and Andeep wanted to know if it grows another 50 centimetres, will he break the 130 centimetre class record for the tallest sunflower? What's the best strategy to use to calculate and solve the problem? Pause the video and think about the best strategy to use to calculate 70 plus 50.

How did you get on? So you could have used a known fact.

So 7 plus 5 is equal to 12.

So 7 tens plus 5 tens is equal to 12 tens, and 12 tens is equal to 120.

So 70 plus 50 is equal to 120.

So Andeep's sunflower would be 120 centimetres tall.

Andeep says, "My sunflower will not break the glass record, 120 centimetres is less than 130 centimetres." But Andeep said, "There's another strategy you could use.

You could partition the 50 into 30 and 20 to bridge 100.

So 70 plus 30 plus 20 is equal to 100 plus 20, which is equal to 120." Sadly, it's still only 120 centimetres, which is still less than 130 centimetres.

So really good strategies, Andeep, but I'm sorry, your sunflower is not gonna break the class record this time.

I wonder what strategy you used.

Okay, so we're going to solve those problems from the practise from the first part of our lesson.

So we knew what the calculation was, and we drew our bar model.

So you might want to go back and have a look at those.

What I'd like you to do, though, is to show your working out and then use the little bullet-pointed list to tick the strategy or strategies that you used in order to solve the problems. So you've got the five problems that we had in the first part of the lesson to solve.

So the strawberry lace, Andeep even Jacob buying their cake.

Izzy and Jacob with another strawberry lace, Andeep and Jacob with their game, and then Izzy and Jacob with their conkers.

So thinking about the strategy that you use and recording the way you work out your answers, pause the video, have a go, and then we'll look at them together.

So how did you get on? I wonder what strategies you used.

So these are the ones that I used.

So Izzy and Jacob and their strawberry lace, the whole was 130 centimetres.

Izzy gave 70 centimetres to Jacob.

What does she have left? So we need to subtract the part we know from the whole.

So the calculation is 130 - 70.

I thought bridging through 100 was an efficient strategy to use here, it fitted with the numbers and it fitted with the way I was thinking about them.

So I partitioned 70 my subtrahend into 30 and 40.

So I could subtract the 30 from the 130.

So 130 subtract 30 is equal to 100, and 100 subtract 40 is equal to 60.

So I know that Izzy has 60 centimetres of strawberry lace left.

For the second one, we were combining the parts.

So Andeep had 90 p, Jacob had 60 p.

Did they have enough money for a cake that costs 140 p? So this time we had to combine the parts to make our whole, so the calculation is 90 plus 60.

So you could bridge through 100, but you could also use a known fact of 9 plus 6 is equal to 15.

So that's the one I decided to go for.

So 9 tens plus 6 tens is equal to 15 tens.

And I know that 15 tens is equal to 150.

So 90 plus 60 must equal 150.

The cake costs 140 p, and 150 is more than 140 p so they do have enough money to buy their cake.

So Question 3 was about Izzy and Jacob and the strawberry lace.

So Izzy gives herself 60 centimetres and gives 50 centimetres to Jacob, and she wants to know how much she's got left.

Her whole lace was 150 centimetres long.

So this is one where we've got those three parts, haven't we? So the calculation we need is 150 subtract 60 subtract another 50.

So I think using place value is a good strategy to begin with because 150 subtract 50 is equal to 100.

So I can take away the 50 centimetres that she gave to Jacob quite easily.

150 subtract 50 is equal to 100.

Now I can use a known fact 'cause I've got to do 100 subtract 60, I've got 100 centimetres of lace and I've got to subtract the 60 centimetres that Izzy gave to herself.

I can use a known fact for this 'cause I know that 10 subtract 6 is equal to 4.

So 10 tens subtract 6 tens is equal to 4 tens.

100 subtract 60 is equal to 40.

So I know that Izzy has 40 centimetres of strawberry lace leftover.

And I use two strategies this time.

I use place value to take away the 50, and then I used a known fact to subtract 60 from 100.

So Question 4, a game costs 190 p or £1.

90.

Andeep has saved 70 p and Jacob has saved 80 p, how much more money do they need to save? So there are three parts again.

So how are we going to solve this one? The calculation we need is 190 subtract 70 and subtract another 80.

Hmm, well, I'm going to use a known fact to subtract 70, but this time, I'm not actually going through a 100, am I? I know that 9 subtract 7 is 2.

So 190 subtract 70 must be equal to 120.

I haven't had to bridge through my 100 because I had 9 tens in 190 and I was subtracting 7 tens in 70, so I've now got 120 and I need to subtract 80.

I'm going to use bridging to do this, 120 subtract 80, I'm going to partition my 80 into 20 and 60, so I can easily take away the 20 from the 120, and then take away 60 from 100.

So 120 subtract 20 is equal to 100, and 100 subtract 60 is equal to 40.

So Andeep and Jacob need to save 40 p more so that they can buy their game.

And this time, we used a known fact and then we used some partitioning, and to bridge through 100.

And our final problem was about Izzy and Jacob and the string for their conkers.

So there was 190 centimetres of string, and Izzy has 10 centimetres more than Jacob.

So how much string could they have each? Well, using place value, I know that 190 is equal to 100 plus 90, and I know that 100 is 10 more than 90.

So Izzy could have 100 hundred centimetres and Jacob could have 90 centimetres.

, well, that worked out quite nicely.

So I used my place value.

But Izzy could also have 90 centimetres of string and Jacob could have 80 centimetres, and there would be some string left over.

So if we didn't use all the string, our bar model would look a bit different, wouldn't it? We'd have Jacob's part and Izzy's part and a third part, which would be the leftover string.

I wonder if you spotted that as well.

Well, we've come to the end of our lesson.

Thank you very much for all your hard work.

We've been representing problems on bar models and realising that that can help you decide on the calculation you need to solve it.

You can see if you need to add or subtract.

Identifying the parts and whole in a problem, also helps you to see if you need to add or subtract because we know that to find the whole we combine and add the parts, and to find a missing parts, we subtract the parts we know from the whole.

And we've also looked to see that different problems need different strategies.

Sometimes one strategy is better than another depending on the numbers in the problem.

I hope you'll have lots of fun solving more problems in the future, and I hope I'll get to work with you again, bye.