Lesson video

Hello everybody.

My name is Mrs. Johnson.

I am so excited to be here today to help you with some of your maths learning.

I hope that you are ready to work hard and have lots of fun.

Let's have a look at what we are going to be learning about today.

This lesson is called Solve Addition and Subtraction Problems Involving Length.

It comes from the unit number zero to 20 in different contexts.

By the end of this lesson, you will be able to solve addition and subtraction problems involving length.

You are going to use what you already know about addition and subtraction to help solve some different types of problems that involve looking at length.

There are two important keywords in this lesson today.

You're going to practise saying them now.

It will be my turn first and then your turn, ready? My turn, part.

Your turn.

My turn, whole.

Your turn.

Well done.

Listen out for those words today because they are really important throughout this lesson.

There are going to be two parts to this lesson.

To begin with, you are going to learn about addition problems and then in a little while you are going to move on and learn about subtraction problems. Let's start by learning about addition problems. There are two friends in this lesson who are going to help.

Their names are Lucas and Sam.

Look out for them throughout this lesson because they have lots of helpful information to share.

Lucas and Sam are building towers from blocks.

I wonder if you've ever made towers out of blocks before.

Here is Lucas' Tower and here is Sam's Tower.

What do you notice about their towers? Let's see what they've noticed.

Lucas says, "My tower is taller than Sam's Tower", and Sam says, "My tower is shorter than Lucas' Tower." They want to measure how tall their towers are.

Lucas says, "My tower is three blocks tall." What do you think Sam's going to say? Sam says, "My tower is five blocks tall." Hmm, that doesn't seem right, does it? We know that Lucas' tower is taller, but three is less than five.

Something can't be right here.

Do you think you've spotted what it is? Lucas has spotted what it is.

Let's see what he says.

"Our blocks are different sizes, so we can't use them to compare height." Sam's got an idea.

"I think I know what we could use to measure the height of each tower." What do you think we could use to measure the height of each tower? Let's see if you are thinking the same as what Sam is thinking.

Sam thinks that they could use a ruler and they could measure how many centimetres tall.

Instead of measuring in blocks, they're going to measure in centimetres.

Lucas can use the ruler to see that his tower is 10 centimetres tall.

Sam can use the ruler to see that her tower is five centimetres tall.

Lucas wants to know what would happen if they joined their two towers together.

How tall would it be then? Let's see what that looks like.

Lucas and Sam joined their towers together.

There's Lucas' part and there is Sam's part.

So they've joined them together to make one taller tower.

What is the total height of their tower now that they've joined their two parts together? Let's have a look.

Lucas' tower was 10 centimetres tall.

That means 10 centimetres is a part.

Sam's tower was five centimetres tall.

That means five centimetres is a part.

I'm going to think about that on a number line.

10 centimetres is a part and five centimetres is a part.

Now on my number line, I am on the number 15.

That means that 15 centimetres is the whole.

I can show that here on my tower.

15 centimetres is the whole.

Sam says, "The total height of the tower is 15 centimetres because 10 plus five is equal to 15." If you know that 10 plus five is equal to 15, you know the total height of this tower must be 15 because 10 is a part and five is a part, 15 is the whole.

Let's have a look at that as an equation.

We could write that 10 centimetres plus five centimetres is equal to 15 centimetres.

Lucas and Sam have built some more towers and joined them together.

This time, two centimetres is a part and 10 centimetres is a part.

Let's have a look at that on the number line.

Wonder if I should show two centimetres or 10 centimetres first on my number line.

Sam has remembered something important.

She says, "I know I can change the order of the addends and the sum will stay the same." That means I don't have to write two centimetres on my number line first, just because it is the first part of the tower.

I can choose the order of my addends.

I am going to put 10 centimetres on my number line first because I can see where the 10 is on the number line.

Here is 10 centimetres.

Here is two centimetres.

Now I am at the number 12 on my number line.

That means that 12 centimetres is the whole.

I can show that next to my tower here.

Sam says, "The total height of the tower is 12 centimetres because 10 plus two is equal to 12." Let's have a look at that as an equation.

Two centimetres plus 10 centimetres is equal to 12 centimetres.

Let's check if you can think about the total height of a tower.

Lucas and Sam have built some more towers and joined them together, but some of the numbers are missing.

Pause the video and have a think about what the missing numbers are.

Well done for thinking really carefully about that.

The first missing number is one of the parts.

It says, mm centimetres is a part.

The second line says four centimetres is a part.

If I look at the tower, I can see that the bit at the top is four centimetres.

That's the part that's already written down.

That means the missing part must be the part at the bottom, which is 10 centimetres.

I can say 10 centimetres is a part.

The next missing number says, mm, centimetres is the whole.

I can look at my tower to help me find the whole.

I can see that the bottom part is 10 centimetres tall and the top part is four centimetres tall and I know that next to that there is a box that shows the whole that is the total height of the tower.

That means my next missing number is 14.

14 centimetres is the whole.

Now I'm going to think about the number line.

I can see on the number line that one of the parts is 10.

I need to see what the other part is.

If I read those sentences again, it says 10 centimetres is a part, four centimetres is a part.

That means that my next missing number on my number line is four.

To find my next missing number, I'm going to think about what I can see on the number line.

I can see 10 and then I can see four.

I know that 10 plus four is equal to 14, so the next missing number is 14.

Finally, I'm thinking about the equation at the bottom.

10 centimetres plus four centimetres equals mm centimetres.

I know 10 centimetres is a part and four centimetres is a part.

I am missing the whole and the whole is 14 centimetres.

14 is my last missing number.

Well done if you found all of those missing numbers too.

Good work.

Lucas and Sam have carried on building towers and joining them together.

Here is another one that they've made.

The first part is six centimetres.

Six centimetres is a part.

The next part is six centimetres.

That means we've got the same sentence again.

Six centimetres is a part.

What do you notice about those two parts? They are the same, aren't they? Even though they use different colours and different bricks, both parts are six centimetres tall.

When both addends are the same, I know that I am doubling.

Sam is going to think about what she knows and what she can remember about doubling.

I wonder if you can remember anything about doubling the number six.

Sam says, "The total height of the tower is 12 centimetres because double six is 12." That means 12 centimetres is the whole.

If we wrote that as an equation, this is what we would write.

Six centimetres plus six centimetres equals 12 centimetres.

What is the total height of these towers? Let's have a look.

This time, eight centimetres is a part and eight centimetres is a part.

Do you think we are doubling again? I think you are right.

The total height of the tower is 16 centimetres because double eight is 16.

That means we can say 16 centimetres is the whole.

Let's show the whole next to our tower, 16 centimetres.

How would we write this as an equation? Let's have a look.

Eight centimetres plus eight centimetres is equal to 16 centimetres.

Here is another check for you to do.

Lucas and Sam have been trying to work out the total height of this tower, but some of the numbers are missing.

Pause the video and see if you can think about what those numbers might be.

Well done.

Let's have a look and see if you have found the missing numbers this time.

Let's think about the parts and the wholes first.

Mm centimetres is a part.

Mm centimetres is a part.

I can look at the tower and find the two parts.

Seven centimetres is a part.

Seven centimetres is a part.

Both parts are the same, aren't they? They're both seven centimetres.

What about the whole? Again, I can look at the tower and I can see that 14 centimetres is the whole.

What do you think was missing in Sam's sentence? The total height of the tower is 14 centimetres because double mm is mm.

What number are we doubling? Well done if you said double seven is 14.

Finally, let's find the missing numbers in the equation.

Mm centimetres plus mm centimetres is equal to mm centimetres.

Well done if you have said seven centimetres plus seven centimetres is equal to 14 centimetres.

You had to think really carefully about that.

Well done for trying really hard.

Now it's time for you to go and do a little bit of practise.

I would like you to have a look at these towers that Sam has built.

Sam has put a ruler next to her towers.

I would like you to write the measurement for each of Sam's towers.

Then have a look at what Lucas has done.

He's taken some of Sam's towers and he's joined them together.

Can you use the measurements of Sam's towers to find the total height for each of Lucas' towers? For each tower, I want you to see if you can say the stem sentences.

Mm centimetres is a part.

Mm centimetres is a part.

Mm centimetres is the whole.

Then once you've worked out how tall Sam and Lucas' towers are, you are going to have a go at completing these stem sentences and the equations to show the height of each tower.

You are going to be thinking carefully about your doubles here.

Make sure you've got everything you need because it's time to go and do your first piece of work.

Off you go.

Let's have a look at these towers.

How tall were Sam's towers? Let's see if you've measured them correctly.

Her first tower is three centimetres tall.

The next one is six centimetres tall.

The next one is nine centimetres tall and her final tower was 10 centimetres tall.

Now that we know how tall each of Sam's towers are, we can use those measurements to help find the total height for Lucas' towers.

For the first one, 10 centimetres is a part, three centimetres is a part, 13 centimetres is the whole.

For the second tower, 10 centimetres is a part, six centimetres is a part and 16 centimetres is the whole.

And for Lucas' last tower, 10 centimetres is a part, nine centimetres is a part and 19 centimetres is the whole.

Well done if you were able to find the height of all of those towers, excellent work.

Now let's have a look at this work on doubles.

Have you managed to complete the stem sentences and the equations for each tower? Let's see.

For the first tower you needed to say the total height of the tower is six centimetres because double three is six.

For the equation you would write three plus three is equal to six.

For the second tower, the sentence would be completed by saying the total height of the tower is 12 centimetres because double six is 12 and the equation would look like this.

Six plus six is equal to 12.

For the last tower, you would say the total height of the tower is 18 centimetres because double nine is 18 and this is how you would write the equation.

Nine plus nine is equal to 18.

Well done if you completed the sentences and the equations correctly.

Now it's time to start looking at the next part of our lesson, which is subtraction problems. Sam has been rolling some snakes from playdough, have you ever done that? It's really fun, isn't it? Sam has rolled lots of snakes from her playdough.

Lucas has come along and he wants to know if he could have some playdough to play with.

Sam has used all the playdough to make these snakes but Lucas would like a bit to play with.

Do you think she should give him some of her playdough and be kind? I do too.

Sam says, "You could snip some playdough off each of the snakes that I made." If Lucas takes a piece off the end of each snake, then he will have some playdough to play with and Sam will still be able to keep her snakes, won't she? The snakes will just be a little bit shorter than they were before.

Let's see what happens.

Lucas is going to snips some playdough off this snake.

Can you see how long the snake is before Lucas snips any playdough off? That's right.

The snake was 14 centimetres long.

That means 14 is the whole.

Lucas snipped four centimetres off.

Are you ready to watch Lucas snip the playdough away? There it goes.

Lucas snipped four centimetres off.

Four is a part.

The snake that is left behind is 10 centimetres long.

10 is a part.

Can you hear that we are still using the same words that we were using when we looked at addition? We still have a part, a part, and a whole.

This time 14 is the whole, four is a part and 10 is a part.

Let's write this story as an equation and see what it looks like.

The snake was 14 centimetres long.

14 is the whole.

In my equation, I am going to start with 14 centimetres.

In my part-part-whole model, I'm going to put 14 here to show that 14 is the whole.

What happened next in the story, can you remember? That's right.

Lucas snipped four centimetres off.

Four is a part.

There it goes.

That means in my equation I can say minus four centimetres.

In my part-part-whole model, I know four is one of the parts.

Now the story can be finished.

There is a snake that is left behind which is 10 centimetres long.

That means 10 is a part.

In my equation I can say that 14 centimetres minus four centimetres is equal to 10 centimetres, and in my part-part-whole model I can show that 10 is the other part.

Lucas says, "I know that 14 is equal to 10 plus four, so 14 minus four must be equal to 10." Let's watch Lucas snip some playdough off another one of these snakes and see what happens this time.

The snake was 17 centimetres long.

Lucas snipped some playdough off.

There it goes.

We are not going to look at the ruler this time.

We're going to think about the numbers and see if we notice anything about this story.

The snake that is left behind is seven centimetres long.

Sam says, "I wonder what length playdough Lucas snipped?" If you look carefully at the story, do you notice that's the missing piece of information? We know the snake was 17 centimetres long and we know that Lucas snipped some playdough but it doesn't tell us how much.

If we write it as an equation, I wonder if we can work out how much playdough did Lucas snip.

Let's have a look.

The snake was 17 centimetres long.

17 is the whole.

That means I'm going to start with 17 centimetres in my equation.

In my part-part-whole model I'm going to put 17 as the whole.

Then Lucas snips some playdough off.

There it goes.

At the moment I can't write that in my equation.

I know it's going to be minus but I don't know how much.

In my part-part-whole model, I know that it's one of the parts but I can't write the number in yet because I don't know what it is, so I'm going to carry on with the story and see if it helps me.

The snake that is left behind is seven centimetres long.

Seven is a part.

Oh, that means that I can finish my equation by saying it is equal to seven centimetres and in my part-part-whole model I know that one of the parts is seven.

Let's look at that part-part-whole model.

I wonder if now we could work out the missing part.

We know 17 is the whole and seven is a part.

Lucas is going to help us.

Lucas says, "I know that 17 is equal to 10 plus seven, so 17 minus 10 must be equal to seven." If we know that 17 is equal to 10 plus seven, can we find the missing part and write it into our part-part-whole model? That's right, it's 10.

The missing part is 10.

If we know the missing part is 10, that means I can change the story.

Instead of saying Lucas snipped some playdough off.

I could say Lucas snipped 10 centimetres off 10 is a part.

That means I can now complete my equation.

Instead of saying 17 centimetres minus something centimetres is equal to seven centimetres, I'm going to finish my equation by saying that 17 centimetres minus 10 centimetres is equal to seven centimetres.

Finally, Lucas is going to snip some playdough off this snake.

Let's see what happens.

The snake was 19 centimetres long.

Lucas snipped nine centimetres off.

There it goes.

There is a snake left behind.

Hmm, I wonder how long that snake is.

Let's write the story as an equation and see if we can work it out.

The snake was 19 centimetres long.

19 is the whole.

That means my equation will start with 19 centimetres and I can write 19 in my part-part-whole model.

Lucas snipped nine centimetres off.

Nine is a part.

Let's watch Lucas snip the playdough off.

That means in my equation I know that I need to write minus nine centimetres because that is how much playdough Lucas snipped off and took away.

In my part-part-whole model, I know that nine is a part.

There is a snake left behind.

I don't know how long this snake is so I can't complete my equation yet and I can't complete my part-part-whole model.

Let's think what we know about 19 and nine and a missing part.

Lucas can help us.

Lucas knows that 19 is equal to 10 plus nine, so 19 minus nine must be equal to 10.

Do you agree with that? 19 is equal to 10 plus nine.

That is right, isn't it? So I know that my missing part is 10.

Now that I know my part is 10, I can improve the story.

I can say the snake that is left behind is 10 centimetres long.

10 is a part.

That means I can finish my equation.

19 centimetres minus nine centimetres is equal to 10 centimetres.

Let's check if you can find the equation and the part-part-whole model for a subtraction story.

Watch really carefully and then have a go at finding the missing numbers, ready? The snake was 16 centimetres long.

16 is the whole.

Lucas snipped some playdough off.

The snake that is left behind is 10 centimetres long.

10 is a part.

I know that 16 is equal to mm plus mm, so 16 minus mm must be equal to 10.

Have a go and see if you can find the missing numbers.

Pause the video and have a think about that now.

Well done.

Let's have a look at what these missing numbers are this time.

Let's start with Lucas' sentence.

I know that 16 is equal to mm plus mm.

You might have said 10 plus six or you might have said six plus 10.

Both ways round would be correct.

That means that 16 minus mm must be equal to 10.

16 minus six must be equal to 10.

Now that we've completed Lucas' sentence, that can help us to complete the equation and the part-part-whole model.

So your missing numbers were six in the part-part-whole model and six in the equation.

Well done if you were able to work those out.

Really good thinking.

Did you notice that now you can improve the subtraction story and you can make it a little bit better? We don't want to say Lucas snipped some playdough off.

What do you think we could say to make this story better? Well done for thinking about it.

We could say Lucas snipped six centimetres off.

Six is a part.

Good job.

Now it's time for you to do a little bit of practise at telling subtraction stories.

You're going to use these part-part-whole models to tell your own stories about playdough snakes.

The story will be the same each time, except the numbers in the story will be different.

You need to use the numbers in the part-part-whole models to tell your story.

Try and use these sentences every time.

The snake was mm centimetres long.

Mm is the whole.

Lucas snipped mm centimetres off.

Mm is a part.

The snake that is left behind is mm centimetres long.

Mm is a part.

If you finish telling all of those stories, maybe you could use a ruler and some of your own playdough and have a go at trying to act out some of these stories.

You could make the snakes and then be like Lucas and snip some of the playdough off.

See if you can act out these stories.

Go and have a try at that now for me, off you go.

Well done everybody.

This is what your stories should have sounded like for each part-part-whole model.

The snake was 12 centimetres long.

12 is the whole.

Lucas snipped 10 centimetres off.

10 is a part.

The snake that is left behind is two centimetres long.

Two is a part.

You might have written your parts the other way round.

You could have said Lucas snipped two centimetres off.

The snake that is left behind is 10 centimetres long.

On the second part-part-whole model, you needed to say the snake was 18 centimetres long.

18 is the whole.

Lucas snipped eight centimetres off.

Eight is a part.

The snake that is left behind is 10 centimetres long.

10 is a part.

Again, you could have swapped your parts around and said them the other way round and that's okay.

The next part-part-whole, you should have said the snake was 15 centimetres long.

15 is the whole.

Lucas snipped 10 centimetres off.

10 is a part.

The snake that is left behind is five centimetres long.

Five is a part.

If you swapped your five and your 10 around, that is okay.

If you did have time to use playdough to make your own snakes, this is what it might have looked like.

And the final part-part-whole model, you needed to say that the snake was 13 centimetres long.

13 is the whole.

Lucas snipped three centimetres off.

Three is a part.

The snake that is left behind is 10 centimetres long.

10 is a part.

You could have swapped your three and your 10 around and you would still be correct.

Well done for thinking really carefully about how you could tell those subtraction stories.

Now that you are at the end of the lesson, you have learned that addition and subtraction problems both involve parts and a whole.

One part plus the other part is equal to the whole and the whole minus one part is equal to the other part.

You've been thinking about addition and subtraction stories that involve length and you can find the parts and the wholes in these stories.

Well done for all of your excellent work today.

You have done a really good job.

I hope that I will see you again soon for some more maths learning.

Bye everybody.