Lesson video

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

It's from our unit, Adding and Subtracting Ones and Tens To and From Two-Digit Numbers.

So we're going to be looking at two-digit numbers and we're going to be thinking about adding and subtracting, and hopefully using our known facts to help us.

So if you're ready, let's make a start.

So in this lesson, we're going to be using our number facts to solve problems in measures and data context.

So we're going to be looking at some length measurements and we're going to be looking at some graphs, and we're going to be finding the information from there and using our number facts to help us to solve the problems. So if you're ready, let's get started.

We've got three key words.

We've got difference, whole, and part.

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

So, my turn, difference.

Your turn.

My turn, whole.

Your turn.

My turn, part.

Your turn.

Excellent.

I'm sure they're words that you've come across before, but listen out for them 'cause they're going to be really useful in talking about our work and our learning today.

So there are two parts to our lesson.

In the first part, we're going to be looking at problems involving measures.

And in the second part, we're going to be looking at problems involving data and statistics.

So let's make a start on part one and some measures.

And we've got Alex and Sam helping us with our learning today.

So we can use known facts to solve difference problems. So we've got some sunflower growing going on here, haven't we? Sam's sunflower is 42 centimetres tall.

"Alex's sunflower," it says, "Was taller than Sam's, and the difference between them was five centimetres.

So how tall was Alex's sunflower?" So there's Sam's sunflower at 42 centimetres and Alex's sunflower is taller, and there's a difference of five centimetres.

Hmm.

Let's represent this on a bar model.

Oh, and Alex says he's going to draw his bar model the other way round to represent the heights of the sunflowers.

But he says, "When we combine the parts to find the whole, it's addition." Because it's looking like Sam's Sunflower and another bit is equal to Alex's sunflower.

Let's see.

So 42 is a part, and five, the difference, is a part, and part plus a part is equal to whole.

So we need to combine our parts.

So 42 plus five.

Oh, now let's think about our known facts.

Which one should we use to solve this efficiently, so we don't need to count on in ones? So let's look at the ones themselves.

So Sam says, "I will partition 42 so that I can see the tens and the ones." And Sam says, "I can see that there are 4 tens and 2 ones.

And I know I have to add 5 ones." That difference we're adding on.

Ah, she says, "I can use the known fact 2 plus 5 is equal to 7." And if she knows 2 plus 5 is equal to 7, then 42 plus 5 must be equal to 47.

So Sam's sunflower must be 47 centimetres tall.

Let's have a look at this again.

Sam's sunflower was shorter than Alex's.

Alex's sunflower was 47 centimetres tall.

The difference between the heights of the sunflowers was five centimetres.

How tall was Sam's sunflower? So the numbers are familiar, aren't they? I think they might have swapped sunflowers at this point, but let's have a think about what this information is telling us.

So Alex's sunflower is 47 centimetres tall, and Sam says, "Mine is shorter," and the difference is five centimetres.

So can you see how that would relate to our bar model? So the whole is Alex's sunflower and that's 47.

And Sam says, "Alex's sunflower is 47 centimetres tall, mine is shorter and the difference is five centimetres.

That means my sunflower is five centimetres shorter than Alex's." So 47 subtract 5 will get us our missing part, which is the height of Sam's sunflower.

Which known fact should you use? So Sam says, "I will partition the 47 so I can see the tens and ones.

And I can see that there are 4 tens and 7 ones.

And I know I have to subtract 5 ones, that difference between the height of Alex's sunflower and the height of her sunflower." And she says, "I can use the known fact 7 subtract 5 is equal to 2." And Sam says, "We know that 7 subtract 5 is equal to 2.

So we know that 47 subtract 5 will be equal to 42." So that means that her sunflower must be 42 centimetres tall.

So what's different about the equation for this problem? Sam's sunflower's 42 centimetres tall and Alex's sunflower was 47 centimetres tall.

What is the difference between the heights of their sunflowers? So Sam says, "I will draw a bar model to represent my sunflower and a bar to represent Alex's sunflower." So there's her sunflower and there's Alex's sunflower and we can see that there's a difference in their heights.

So Sam says, "I know I must find the difference between 42 and 47." She says, "I could write an equation, 42 plus something is equal to 47.

Or I could write the equation 47 subtract something is equal to 42." It works either way.

That difference is the same whether we add it onto the smaller number or subtract it from the larger number.

And Sam says, "Can we use known facts to solve these equations?" Hmm, let's have a look.

So Sam says, "42 Has 2 ones.

How do I know how many ones I need to add to reach 7 ones?" So there we can see, 42 plus something is equal to 47.

The 40 doesn't change so we're looking at the ones.

She says, "I can use the known fact 2 plus 5 is equal to 7.

I know that 2 plus 5 is equal to 7, so I know 42 plus 5 must be equal to 47." Or we could think about the subtraction, 47 subtract something is equal to 42.

She says, "I could say 47 has 7 ones, so how many do I need to subtract to reach 2 ones?" She says, "I know that 7 subtract 5 equals 2.

So I know that 47 subtract 5 is equal to 42." That difference is still five centimetres between the heights of the two sunflowers.

So over to you to check your understanding.

What is the same and what's different about these two ways that we've calculated the difference? Pause the video, have a talk about the two ways, and then when you're ready, we'll get together and discuss our thoughts.

What did you think? Sam says, "There is a step of five if we add or if we subtract.

The difference between 42 and 47 is five.

And we can calculate that by thinking about adding or subtracting." Time for you to do some practise.

You've got three problems here.

Your first task is to draw a bar model to represent each problem, and the second one is to write down the known fact that you would use to solve it, and then solve the problem.

So pause the video, have a go at solving the problems, and when you're ready, we'll get together for some feedback.

How did you get on? So here's A, Sam's shoelace measured 35 centimetres.

Alex's was longer.

The difference between them was three centimetres.

How long was Alex's shoelace? So in our bar model we know that Sam has a shoelace of 35 centimetres and the difference is three.

So Alex's lace must be three centimetres longer than Sam's.

So 35 centimetres is Sam's shoelace, three centimetres is the difference.

So we are increasing 35 by three.

So we need to write an addition equation.

35 Plus 3 is equal to.

Ah, and we can use the known fact 5 plus 3 is equal to 8 'cause we can see that in the ones.

So I know that 35 plus 3 must equal 38.

So Alex's shoelace was 38 centimetres long.

In B, Sam and Alex each had a shoelace.

Sam's was 35 centimetres and Alex's was 38 centimetres.

What is the difference between the lengths of their shoelaces? So this time, our longest shoelace is our whole and the smaller shoelace is a part.

And we know that to find another part we can work out what the missing part is by doing an addition.

So we know that the short shoelace is 35 centimetres and the long one is 38 centimetres.

And what we don't know is the difference.

So we could say 35 plus something is equal to 38.

So there are 5 ones in 35 and 8 ones in 38.

We need to add 3 ones to 5 ones to reach 8 ones, and we can use that known fact, 5 plus 3 is equal to 8.

So we know that 35 plus 3 must be equal to 38.

So the difference between the lengths of the shoelaces was three centimetres.

And for C, Sam's shoelace was shorter than Alex's.

Alex's was 38 centimetres long.

The difference between the length of the laces was three centimetres.

How long was Sam's shoelace? So this time, we know the whole length and we know a small part.

And so actually subtracting that small part from the whole works well for us this time.

We're trying to find that other part.

So we knew that the difference was three centimetres and that Sam's shoelace was shorter, but Alex's was 38 centimetres.

So we need to write a subtraction equation, 38 minus 3, or subtract 3.

So we know that there are 8 ones and 3 ones are subtracted.

So we could use the known fact, 8 subtract 3 is equal to 5.

So if that's true, then 38 subtract 3 is equal to 35.

So Sam's shoelace was 35 centimetres long.

And onto the second part of our lesson, and we're going to be solving problems involving data.

So Alex records the number of goals scored in a football tournament, and he's used a bar chart.

Let's use the bar chart to answer some questions.

How many goals were scored by Class 1 and Class 2 altogether? We can see them on the bar chart.

Alex says, "The numbers on the bar chart look like a number line, so I'll use them to help me." "So Class 1," he says, "Scored four goals." So if we line up the height of Class 1's bar with our number line, then we can see that it's four.

And Class 2, if we line them up, scored 25 goals.

So we want to know how many they scored altogether.

And Alex says, "To find out how many they scored altogether, I must add four and 25.

Which known addition fact will help me to solve this?" He says.

Well, he says, "I know that 4 plus 5 is equal to 9, so I know that 4 plus 25 must be equal to 29." So they must have scored 29 goals altogether.

Oh! Here's another chart.

What's the difference between the number of goals scored by Class 2 and Class 4? Let's have a look.

Oh, they were the highest goal scorers, weren't they? So Class 2 scored 25 goals.

We can look and use that number line to help us see how long the bar is.

And Class 4 scored 28 goals.

Hmm.

So what's the difference between them? Oh, Alex says.

"The bars remind me of a bar model." Let's see if we can do a bar model.

Here we go.

So we took the bars and turned them into a bar model.

So Class 4 scored 28 goals and Class 5 scored 25 goals.

So we've got to look and find that difference, haven't we? And Alex says, "To find the difference, I can think 25 plus something is equal to 28.

Which known fact will help me to solve this?" He says.

Ah, he says, "I know that 5 plus 3 is equal to 8.

So I know that 25 plus 3 must be equal to 28.

So the difference between the number of goals scored was three.

Time to check your understanding.

Sam used a known fact to answer this question, but which fact did she use? The question is, what is the difference between the number of goals scored by Class 3 and Class 4? So, can you use the bar chart to find out those values and then decide which known fact would help you? Pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Well, there were 21 goals scored by Class 3 and 28 by Class 4.

So to find the difference, we need to think 21 plus something is equal to 28.

And 1 plus 7 is equal to 8, so that's going to help us to work out that the difference in the goals scored was seven goals.

The difference between 21 and 28 is seven.

And then we can see the bar models.

1 Plus 7 equals 8, so I know 21 plus 7 equals 28.

So the difference must have been seven.

There were seven goals scored that was the difference between Class 3 and Class 4.

Another check.

Sam used a known fact to answer this question.

Which fact did she use? How many goals were scored by Class 1 and Class 3 altogether? So pause the video, have a look at the bar chart, and decide which known fact she used.

And when you're ready, we'll get together for some feedback.

So how did you get on? Well, Class 1 scored four goals and Class 3 scored 21 goals.

So we had to do 4 plus 21.

And there they are.

And we can bring them together to make a bar model.

This time we knew the two parts and we wanted to combine them to make the whole.

So 4 plus 21, or 21 plus 4.

So the fact we could use was 1 plus 4 is equal to 5 or 4 plus 1 is equal to 5.

So if we know that, we know that 4 plus 21 must be equal to 25.

So there were 25 goals scored altogether by Class 1 and Class 3.

So Sam's carried out a survey to find the favourite colours of the children in Year Two and she's recorded it in a bar chart.

How many more children chose red than green? Can you see red and green on the chart? And we can use that number line to help us work out the values, can't we? So let's have a look.

27 Children chose red as their favourite colour and 21 children chose green.

Let's use the bars to help us draw a bar model.

So there are our bars.

21 And seven, and we want to find that difference, that missing part.

"So how many more must I add to 21 to reach 27?" says Sam.

"To find out how many more, I must find the difference between 21 and 27." So which known fact can help us to solve it? And can you explain how you know? Sam says, "I will use 1 plus 6 equals 7.

I've got the one and I've got to add something to equal seven.

So if 1 plus 6 equals 7, I know that 21 plus 6 must equal 27." So the difference must be six.

Six more children chose red than green.

Oh, how many fewer children chose green than red? Hmm.

Can you spot something here? 21 Children chose green and 27 children chose red as their favourite colours.

So let's draw the bar models again.

So we've still got that same difference to find, but this time, Sam's thinking about how many must she subtract from 27 to reach 21.

"To find how many fewer," she says, "I must find the difference between 27 and 21." So she could think 27 subtract something is equal to 21.

And what fact can she use? Yes, that's right.

7 Subtract 6 is equal to 1.

So she says, "I know that 7 subtract 6 equals 1, so I know that 27 subtract 6 is equal to 21." So we found out how many more by adding to 21, and how many fewer by subtracting from 27.

In both cases, the answer was the same because they both involved finding the difference between 21 and 27.

There were six fewer children that chose green than red and six more children that chose red than green.

I think I might have chosen red if I'd been asked.

Okay, so let's have another look.

Two more children chose purple than chose blue.

How many children chose purple? And can you draw the bar to show this? Ooh, that's an interesting one.

Let's have a think.

Two more children chose purple than chose blue.

So let's have a think.

"26 Children chose blue," says Sam, "As their favourite colour and two more children chose purple.

So I must find two more than 26.

I must add 26 and two." She says, "I could use a bar model to help me." There's the 26 that chose blue and we need an extra two people.

Which addition fact can help us answer this? Ah, she says, "I know that 6 plus 2 is equal to 8, so I know that 26 plus 2 must be equal to 28.

So the bar for purple must reach 28." And it does.

28 Children chose purple.

Time to check your understanding.

Sam's bar chart shows Year Two's favourite pets.

And the question is, how many more children chose a dog than a cat? Use the bar chart to answer the question, draw a bar model, and explain which known fact will help you answer the question.

So pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Well, Sam says, "22 Children chose a cat as their favourite pet, and 29 children chose a dog.

To find out how many more, I must find the difference between 22 and 29." So we could think 22 plus something is equal to 29.

And there are the bars to show us.

Sam says, "I know that 2 plus 7 is equal to 9, so I know that 22 plus 7 must be equal to 29.

So the difference is seven.

Seven more children chose a dog than a cat.

Ooh, let's have another look.

So now we know that six more children chose a guinea pig than a cat.

Draw the bar to show how many children chose a guinea pig.

Use the bar chart, draw a bar model, and explain which known fact will help you to answer the question, and work out how long the bar for a guinea pig must be.

Pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Well, 22 children chose a cat as their favourite pet and it said that six more children chose a guinea pig.

"So to find out how many children chose a guinea pig, I must add six to 22," says Sam.

So there's the bar model to show us that 22 children chose a cat and six more chose a guinea pig.

So we need to add those two together to find our whole for the guinea pigs.

She says, "I know that 2 plus 6 is equal to 8, so I know that 22 plus 6 must be equal to 28." There we go.

So 28 children chose a guinea pig.

And there it is on the bar chart added in as its own bar.

And a final check.

How many children chose either a cat or a rabbit as their favourite pet? Pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? "Well, 22 children chose a cat and six chose a rabbit, so I must add 22 and six," says Sam.

We know the two parts and we must combine them to make the whole.

So there are the six and the 22, and we can create our bar model from that.

I know 2 plus 6 equals 8, so I know 22 plus 6 must equal 28.

So there we are.

28 Children chose either a cat or a rabbit.

Time for you to do some practise.

So can you use the bar chart to answer the questions that are on the next slide? For each of them, draw a bar model and then write an equation for each.

And part two says, "Explain which known fact you would use to solve the equation and then to answer the problems." So here are the problems. Pause the video, have a go at solving the problems using the information in the bar chart, and when you're ready, we'll get together for some answers and feedback.

How did you get on? So A asked how many people visited the park on Tuesday and Wednesday altogether? So on Tuesday, there were 25 visitors, and on Wednesday, there were three visitors.

So to find out how many altogether, we must add 25 plus 3, and that's equal to 28.

There were 28 visitors on Tuesday and Wednesday altogether.

So part B, how many more visitors were there on Thursday than Tuesday? Let's have a look at those bars.

So on Tuesday there were 25 visitors, and on Thursday there were 28 visitors.

So how many more must be added to 25 to reach 28? 25 Plus something is equal to 28.

How can we find that missing number? Well, it's three, isn't it? 25 Plus 3 is equal to 28 because we know that 5 plus 3 is equal to 8.

So there were three more visitors on Thursday than on Tuesday.

For C, how many fewer visitors were there on Tuesday than Thursday? Mmhmm.

Ah! I noticed that once again, we're finding the difference between the number of visitors to the park on Tuesday and Thursday, 28 and 25.

And it's going to be three, isn't it? So in answer to this question, there were three fewer visitors on Tuesday, there were three more visitors on Thursday.

It's the same question, we're just looking at it from a different day of the week.

So D says, "Saturday had two fewer visitors than Tuesday.

Can you draw the bar to show how many visitors there were on Saturday?" Two fewer than Tuesday.

So there were 25 visitors on Tuesday and Saturday had two fewer.

So we had to subtract 2.

25 Subtract 2.

We know that 5 subtract 2 is equal to 3, so 25 subtract 2 is equal to 23.

So Saturday had 23 visitors.

And there it is on the bar chart.

And for E, on Sunday, there were more visitors than on Friday.

The difference between the number of visitors was two.

So can we draw the bar to show the visitors on Sunday? So the difference between Friday and Sunday was two, and there were more visitors than on Friday.

So there were 24 visitors on Friday, and Sunday was two more, so we need two more.

We know that 4 plus 2 is equal to 6, so we know that 24 plus 2 is equal to 26.

So Sunday had 26 visitors.

And there's our bar showing the 26 visitors on Sunday.

Wow.

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

What a lot of thinking you've been doing in that lesson.

Well done all of you.

We've been using number facts to solve problems in measures and data contexts.

What have we learned? We've learned that we can use known addition and subtraction facts to help us solve problems, and that we can draw a bar model to help us to understand the problem.

We've looked at some problems where the answer was the same, it just depended whether we were looking at how many more between two numbers or how many fewer there were between two numbers.

So, interesting to look and realise that some problems you can solve using addition and subtraction, especially when we're finding the difference.

Thank you for all your hard work and I hope I get to work with you again soon.

Until then, bye-bye.