Lesson video

Hello, I'm Mrs. Cayley, and I'm going to be your teacher for this lesson.

So in this lesson we're going to solve problems involving multiples of 10 in a range of different contexts.

So let's have a look at today's lesson outcome.

Here's the outcome of today's lesson, "I can solve problems involving multiples of 10 in a range of contexts." Here are the key words for today's lesson.

Can you say them after me? My turn, add, your turn? My turn, subtract, your turn? My turn, multiple, your turn? Well done, you might have seen these words before.

Look out for them in today's lesson.

Here's today's lesson outline.

We're going to solve problems involving multiples of 10 in a range of context.

We'll start off looking at multiples of 10, and then we'll move on to solving problems. So let's start with the lesson.

Here are some children that are going to help us today.

We've got Jacob and Laura.

Laura and Jacob are going shopping.

They have some 10 pence coins to spend.

Can you see their 10 pence coins there? Laura's got six 10 pence coins, and Jacob's got six 10 pence coins as well.

I wonder how much they've each got.

Let's see how much Laura's got.

Can you count her coins in tens? 10, 20, 30, 40, 50, 60 pence.

Laura has got 60 pence, and so has Jacob.

Laura said, "I will spend 60 pence on fruit." Jacob said, "I will spend 60 pence on fruit too." In the greengrocers, each piece of fruit costs a multiple of 10.

Can you see the prices of the fruit? Apples are 10 pence each, lemons are 20 pence each, oranges are 30 pence each, and pears are 40 pence each.

So each piece of fruit costs a multiple of 10.

I can see they're multiples of 10 because they end in zero.

What fruit could Laura and Jacob buy? Laura said, "I have 60 pence.

I like apples and pears." So I wonder if she can buy some apples and pears with her 60 pence.

Jacob said, "I have 60 pence.

I love oranges." So I wonder how many oranges he can buy for 60 pence.

Laura said, "I will buy two apples and a pear." Has she got enough money to buy two apples and a pear? Jacob said, "I will buy two oranges." Has he got enough money to buy two oranges? So Laura said, "Two apples cost 20 p, so that's 10 plus 10, and a pear is 40 pence, so 20 pence plus 40 pence is equal to 60 pence." So she can buy two apples and a pear with her 60 pence.

Jacob wants to buy two oranges, and they're 30 pence each.

Jacob said, "I know that double three is six, so double 30 is 60." So he can buy two oranges for 60 pence.

Laura has written an equation for her fruit, "10 pence plus 10 pence plus 40 pence is equal to 60 pence." And Jacob's written an equation as well, "30 pence plus 30 pence is equal to 60 pence." Let's check your understanding.

Does Laura have enough money to buy three lemons? So the lemons are 20 pence each, and here's her money.

Can you see how many 10 pence coins she's got? Does Laura have enough money to buy three lemons, and how do you know? So pause the video while you think about this one.

What did you think about this one? Does Laura have enough money to buy three lemons, and how do you know? Laura said, "I have five 10 pence pieces.

I have 50 pence." Jacob said, "Three lemons would cost 20 p plus 20 p plus 20 p, which is equal to 60 p." Laura said, "I do not have enough money." She only had 50 p, didn't she? And she needs 60 p to buy three lemons.

She would be able to buy two lemons, wouldn't she? But not three lemons.

Jacob said, "You would need another 10 p." Now Laura and Jacob are going to the toy shop.

They have different amounts to spend.

Can you see Laura's money and Jacob's money here? They've both got 10 pence coins.

Laura has got five 10 pence pieces, and Jacob has got eight 10 pence pieces.

How much has Laura got? Should we count them in tens? 10, 20, 30, 40, 50 pence.

How much has Jacob got? Should we count his money in tens? 10, 20, 30, 40, 50, 60, 70, 80 pence.

In the toy shop, each toy costs a multiple of 10 p.

Can you see that we've got a car that costs 60 p, a pig that costs 40 p, a ball that costs 10 p, a teddy that costs 50 p, a boat that costs 30 p, and a robot that costs 20 p.

They all cost a multiple of 10 p.

Which toy is the most expensive? So which toy costs the most money? Laura said, "The car is most expensive because it costs the most money.

It costs 60 p.

Six is the highest number of tens, so 60 p is the highest value, which is the most expensive.

Which toy is the least expensive, or the cheapest? Jacob said, "The ball is the least expensive because it costs the least.

It costs 10 p." Each toy costs a multiple of 10 p.

Which toys could Laura and Jacob buy? Laura said, "I have 50 pence.

I will buy two toys." Jacob said, "I have 80 pence.

I will buy three toys." I wonder which toys they could buy with their money.

Laura has chosen a pig and a ball.

She said, "I have 50 pence.

I will buy a pig and a ball." So here's the pig and the ball.

The pig is 40 pence, and the ball is 10 pence.

I wonder how much that is altogether.

40 pence plus 10 pence is equal to 50 pence.

So she can buy those two toys, can't she? Could she have chosen other toys? Are there any other toys that add up to make 50 pence? Laura said, "I have 50 pence.

I could buy a boat and a robot." So here's the boat for 30 pence and the robot that's 20 pence.

Jacob said, "30 pence plus 20 pence is equal to 50 pence." So she could have bought a boat and a robot.

Are there any other toys that she could have chosen? Jacob has chosen a teddy, robot and a ball.

Jacob said, "I have 80 pence.

I will buy a teddy, robot and a ball." So here's the teddy for 50 pence, a robot for 20 pence and a ball for 10 pence.

Do those three amounts add up to 80 pence? Laura said, "I know that 50 pence plus 20 pence is equal to 70 pence, and 70 pence plus 10 pence is equal to 80 pence.

So 50 pence plus 20 pence plus 10 pence is equal to 80 pence." Could he have chosen other toys? Jacob said, "I could have bought a car and two balls." So here's the car for 60 pence and two balls that are 10 pence each.

Does that make 80 pence? Yes, Laura said, "I know that 10 pence plus 10 pence is equal to 20 pence and 20 pence plus 60 pence is equal to 80 pence.

60 pence plus 10 pence plus 10 pence is equal to 80 pence." Could he have chosen any other toys? Jacob said, "I could have bought a pig and two robots." So here's a pig for 40 pence and two robots for 20 pence each.

Does that make 80 pence altogether? Laura said, "I know that 20 pence plus 20 pence is equal to 40 pence and 40 pence plus 40 pence is equal to 80 pence." So he can buy those three toys for 80 pence.

40 pence plus 20 pence plus 20 pence is equal to 80 pence.

Could he have chosen any other toys? Jacob said, "I could have bought a pig, a boat and a ball." So here's a pig for 40 pence, a boat for 30 pence and a ball for 10 pence.

Does that add up to make 80 pence? Yes, Laura said, "I know that 30 pence plus 10 pence is equal to 40 pence and 40 pence plus 40 pence is equal to 80 pence.

40 pence plus 30 pence plus 10 pence is equal to 80 pence." Let's check your understanding.

Does Jacob have enough money to buy a boat and a ball? So here I can see that a boat is 30 pence and a ball is 10 pence.

And here's Jacob's money.

He's got five 10 pence coins.

Does he have enough money to buy a boat and a ball, and how do you know? Pause the video while you think about this one.

Does Jacob have enough money to buy a boat and a ball, and how do you know? I can see that Jacob has got five 10 pence coins.

How much is that in total? Should we count them in tens? 10, 20, 30, 40, 50 pence.

Jacob said, "I have five 10 pence pieces.

I have 50 pence." Is that enough money to buy a boat and a ball? Laura said, "30 pence plus 10 pence is equal to 40 pence." Jacob said, "I do have enough money." Yes, he did have enough money.

He'll have some money left as well, won't he? How much money will he have left? Laura said, "You would have 10 pence left." Here's a task for you to have a go at.

You have 50 pence to spend.

What fruit would you buy? So here we can see the pieces of fruit all cost a multiple of 10 pence.

The apples are 10 pence each, the lemons are 20 pence each, the oranges are 30 pence each, and the pears are 40 pence each.

What fruit would you buy with 50 pence? Find at least three different ways you could spend all of your money.

Write an equation to show the total cost.

If you've got some coins and some fruit, you could try this out by playing shops.

Here's the second part of your task.

Each toy costs a multiple of 10 pence.

So each toy has got a price next to it showing how much it costs.

Put the toys in order of value from cheapest to most expensive.

So start with the amount that's the least, and then work up to the highest amount.

Which toys can you buy for 50 pence, 60 pence, or 80 pence? And if you've got some toys and some coins, you could try this out to check.

Here's the third part of your task.

Use the toy cards to answer the questions.

So use the toys from before to work out the answer to these questions.

Which is the most expensive toy? Which toys cost more than the robot? Buy two toys and work out the total cost.

Which two toys would cost the least money? Laura bought two toys, which cost 90 pence in total.

What did she buy? Jacob had 80 pence and now he has 60 pence.

What could he have bought? Laura bought two of the same toy and spent 60 pence in total.

What did she buy? Jacob had 90 pence and now he has 50 pence left.

What could he have bought? So pause the video and have a go at your tasks.

How did you get on with the first part of the task? There were lots of different ways to spend 50 pence on fruit.

So you might have tried 40 pence plus 10 pence.

That's equal to 50 pence, so that's a pear and an apple.

30 pence plus 10 pence plus 10 pence is equal to 50 pence, so that's an orange and two apples, 20 pence plus 10 pence plus 10 pence plus 10 pence is equal to 50 pence.

So that's a lemon and three apples.

Or you might have tried five apples, so that's 10 pence plus 10 pence plus 10 pence plus 10 pence plus 10 pence, which is equal to 50 pence.

Which ways did you find to spend 50 pence on fruit? How did you get on with the second part of your task? Did you put the toys in order of value from cheapest to most expensive? So I've put the toys in the correct order.

You can see the cheapest toy is 10 pence.

That's a ball.

And the most expensive toy is a car.

That's 60 pence.

And you can see I've put the other toys in order.

So we've got 10 pence, 20 pence, 30 pence, 40 pence, 50 pence, and 60 pence.

We've got all the multiples of 10 from 10 p up to 60 p.

Which toys can you buy for 50 p? So you might have tried a boat and a robot, so that adds up to 50 pence.

Or a pig and a ball, they add up to 50 pence as well.

What about 60 pence? You might have tried a teddy and a ball, or a pig and a robot, or two boats.

And what about 80 pence? So you might have tried a car and a robot, a teddy and a boat, or two pigs.

What did you find? How did you get on with the third part of the task? Did you use the toy cards to answer the questions? So which is the most expensive toy? I can see it's the car.

That's 60 pence.

Which toys cost more than the robot? Well, the robot is 20 pence, so the boat, pig, teddy and car all cost more than the robot.

Buy two toys and work out the total cost.

So you might have chosen any of the two toys.

You might have chosen a teddy and a robot.

That's 50 pence plus 20 pence, which is equal to 70 pence.

Which two toys would cost the least money? So that's the lowest amount.

A ball and a robot, that would be 10 pence plus 20 pence, which is equal to 30 pence.

Laura bought two toys, which cost 90 pence in total.

What did she buy? So she might've bought a teddy and a pig.

That's 50 p plus 40 p, which is 90 pence.

Or she might've bought a car and a boat.

That's 60 p plus 30 p, which is also equal to 90 p.

Jacob had 80 pence and now he has 60 pence.

What could he have bought? Well, 80 pence minus 60 pence is equal to 20 pence, so he spent 20 pence.

He might have bought a robot or two balls.

Two balls are 10 pence plus another 10 pence, which is 20 pence.

Laura bought two of the same toy and spent 60 pence in total.

What did she buy? So she must have bought two boats.

That's 30 pence plus 30 pence, which is equal to 60 pence.

So double 30 is 60.

Jacob had 90 pence and now he has 50 pence left.

What could he have bought? So 90 pence minus 50 pence is equal to 40 pence, so he spent 40 pence.

He might have bought a boat and a ball, or two robots.

Two robots are 20 p plus 20 p, and that's equal to 40 p.

How did you get on with those? Let's move on to the second part of the lesson, solving problems. We can solve problems using multiples of 10.

We can use known facts to help us.

Part-part-whole models and number lines can help to represent the problem.

Can you see the part-part-whole models here showing the whole in two parts? And we can also use a number line from zero to 100 to help us.

I can see the multiples of 10 have been marked.

Stem sentences can help us as well.

This one says the whole is mm, and one part is mm, so the other part must be mm.

Here's a problem for us to solve.

The ladybird is climbing up the flower.

The flower is 60 centimetres tall, and the ladybird is 10 centimetres up.

How much further does it need to go? Can you see the ladybird has started to climb the flower? He's already 10 centimetres up, but he wants to get to the top of the flower.

So 10 plus something is equal to 60, or 60 minus something is equal to 10.

Here's a part-part-whole model to help us.

Laura said, "The ladybird needs to climb up to 60 centimetres." So 60 is going to be the whole.

The ladybird is at 10 centimetres.

So we know that 10 is one of the parts.

How many more tens to get to 60? Is there a known fact that you know that can help us work this out? Laura said, "I know one plus five is equal to six, so 10 plus 50 is equal to 60." And she said, "I know that six minus one is equal to five, so 60 minus 10 is equal to 50.

The ladybird needs to go up 50 centimetres more." So the missing part is 50.

So you can see on the equations, 10 plus 50 is equal to 60, or 60 minus 50 is equal to 10.

And you can see it's on the number line as well.

The ladybird needs to go up 50 centimetres more, so the ladybird's going to move 50 centimetres more up the flower.

10, 20, 30, 40, 50 centimetres, now the ladybirds at the top of the flower.

Here's another problem for us to look at.

The car has travelled 50 miles along a 100-mile journey.

How much further does it need to go? Here we've got a bar model to help us.

The car needs to travel 100 miles, so that's going to be the whole.

The car has travelled 50 miles, so that's one of the parts.

How many more tens to get to 100? Is there a known fact that you can use to help us work this out? So 50 plus something is equal to 100.

Jacob said, "I know five plus five is equal to 10, so 50 plus 50 is equal to 100." So the missing part is 50.

Jacob said, "I know 10 minus five is equal to five, so 100 minus 50 is equal to 50." So we can also have a subtraction equation to help us.

100 minus 50 is equal to 50.

So the missing part was 50.

So it needs to travel 50 more miles, because 50 plus 50 is equal to 100.

Here's another problem for us to solve.

The spider is climbing up the spout.

The is 80 centimetres tall, and the spider is 60 centimetres up.

How much further does it need to go? Here's a part-part-whole model to help us.

What do we already know? Laura said, "The spider is 60 centimetres up." So that's one of the parts.

"The spider needs to climb up to 80 centimetres." So the whole will be 80.

So we need to work out the other part.

How many more tens to get to 80? Do you know a fact that can help us with this one? Laura said, "I know six plus two is equal to eight, so 60 plus 20 is equal to 80." Laura said, "I know eight minus six is equal to two, so 80 minus 60 is equal to 20." So the missing part is 20.

"It needs to climb 20 centimetres more." Let's see the spider move 20 centimetres up the spout.

10 centimetres, 20 centimetres.

Now it's at the top of the spout.

Let's check your understanding.

The car has travelled 60 miles along a 100-mile journey.

How much further does it need to go? Here's a stem sentence to help us.

The whole is mm, and one part is mm, so the other part must be mm.

What do we know already? Well, we know that the whole is 100 miles and one of the parts is 60 miles.

So what do you think the other part is? Pause the video while you think about this one.

So the whole is 100 and one part is 60, so the other part must be 40.

Jacob said, "I know six plus four is equal to 10.

So 60 plus 40 is equal to 100." Is that what you thought? Here's a task for you to have a go at.

Can you find the missing parts and match to the story? So here you can see some part-part-whole models.

Some of them have got a part missing, and some of them have got the whole missing.

And we've got some stories to match to the part-part-whole models.

The first one says, "A car has travelled 20 miles of a 70-mile journey.

How many more miles does it need to go?" Second story says, "Laura buys an orange for 30 pence and two lemons for 20 pence each.

How much is this in total?" The third story says, "A flower is 70 centimetres tall and a ladybird is 10 centimetres up.

How much further does it need to climb?" And the last story says, "Jacob has 80 pence in total.

He spends 40 pence.

How much does he have left?" See if you can find the missing parts and match to the correct story.

Here's the second part of your task.

Write an equation and solve each story.

So the first story says, "A car has travelled 40 miles of a 90 mile journey.

How many more miles does it need to go?" Can you write an equation to match this story and then solve the problem? You might use an addition or a subtraction equation.

The second story says, "Laura buys an orange for 30 pence and an apple for 10 pence.

How much change will she have from 50 pence?" Can you write an equation to match that story and then solve it? The third story says, "A flower is 90 centimetres tall, and a ladybird is 20 centimetres up.

How much further does it need to climb?" So see if you can write an equation to match this story and then solve it.

The last story says, "Jacob has 90 pence in total.

He spends 10 pence.

How much does he have left?" See if you can write an equation to match that one and then solve it.

So pause the video and have a go at your tasks.

How did you get on with the tasks? Did you find the missing parts and match to the story? So the first part-part-whole model has got one of the parts missing.

I can see we've got 70 as the whole and 10 as a part, and the other part is 60.

Which story does this match to? I can see it matches to the third story, "A flower is 70 centimetres tall, and a ladybird is 10 centimetres up.

How much further does it need to climb?' Well, the answer is 60 centimetres because 10 centimetres plus 60 centimetres is equal to 70 centimetres, or 70 centimetres minus 10 centimetres is equal to 60 centimetres.

Let's look at the second part-part-whole model.

We've got 70 as the whole and 20 as one of the parts.

So the missing part is 50 because 20 plus 50 is equal to 70.

It matches with the first story, "A car has travelled 20 miles of a 70-mile journey.

How many more miles does it need to go?" Well, the answer is 50 miles because 20 plus 50 is equal to 70 or 70 minus 20 is equal to 50.

Let's look at the third part-part-whole model.

I can see the whole is missing.

The parts are 30 and 40.

Well, 30 plus 40 is equal to 70.

I know that because three plus four is equal to seven.

So three tens plus four tens is equal to seven tens.

Which story does that match to? It's the second story, "Laura buys an orange for 30 pence and two lemons for 20 pence each." So 20 plus 20 is equal to 40.

"How much is this in total?" It's 70 pence.

Let's look at the last part-part-whole model.

I can see we've got one of the parts missing.

80 is the whole, and 40 is one of the parts.

So the other part is 40.

And it matches to the last story, "Jacob has 80 pence in total.

He spends 40 pence.

How much does he have left?" The answer is 40 pence.

I know that eight minus four is equal to four, so 80 minus 40 is equal to 40.

How did you get on with the second part of the task? Did you write an equation and solve each story? So the first story said, "A car has travelled 40 miles of a 90-mile journey.

How many more miles does it need to go?" Well, I know that 40 plus 50 is equal to 90 or 90 minus 40 is equal to 50.

So the answer is 50 miles.

The car needs to travel 50 miles more.

The second story says, "Laura buys an orange for 30 pence and an apple for 10 pence.

How much change will she have from 50 pence?" Well, 30 pence plus 10 pence is equal to 40 pence, so she's going to spend 40 pence in total.

How much change will she have from 50 pence? Well, 40 plus 10 is equal to 50 or 50 minus 40 is equal to 10, so it'd be 10 pence change.

The third story says, "A flower is 90 centimetres tall and a ladybird is 20 centimetres up.

How much further does it need to climb?" Well, I know that 20 plus 70 is equal to 90 or 90 minus 20 is equal to 70, so it needs to climb 70 centimetres more.

The final story says, "Jacob has 90 pence in total.

He spends 10 pence.

How much does he have left?" Well, 10 plus 80 is equal to 90 or 90 minus 10 is equal to 80, so he's going to have 80 pence left.

Can you see that we can use addition or subtraction to help with these problems? Well done, we've got to the end of our lesson.

Today we were solving problems involving multiples of 10 in a range of contexts.

We found out that unitizing and known facts can help you to add and subtract multiples of 10.

If three plus two is equal to five, then three tens plus two tens is equal to five tens, which is equal to 50.

If five minus two is equal to three, then five tens subtract two tens is equal to three tens, which is equal to 30.

So we can always use our known facts to help us to add and subtract multiples of 10.

Well done everyone.

See you soon.