Lesson video

Hello, I'm Mrs. Cayley and I'm going to help you with this lesson.

So in today's lesson we're going to solve problems using multiples of 10.

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

Here's today's lesson outcome: I can solve problems involving multiples of 10.

So multiples of 10 are tens numbers like 10, 20, 30, 40, and 50.

They're all made of groups of 10 and they end with a 0.

Here's today's key words.

Can you repeat them after me? My turn, add, your turn? My turn, subtract, your turn? My turn, multiple of 10, your turn? Well done, you might have used these words before.

Look out for them in today's lesson.

Here's today's lesson outline.

We're going to be solving problems involving multiples of 10.

We'll start off with solving problems. And then, we'll move on to addition and subtraction puzzles.

So let's start on the learning.

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

We've got Sam and Lucas.

We can solve problems using addition and subtraction.

Here we've got some bar models.

Can you see the whole has been partitioned into two parts? I wonder if you can think of any addition and subtraction equations to match these bar models? So for the first bar model, we could say 8 is equal to 5 plus 3 or 8 minus 5 is equal to 3.

So we could show addition or subtraction using this bar model.

The second bar model is showing 8 tens is equal to 5 tens plus 3 tens, or we could say 8 tens minus 5 tens is equal to 3 tens.

The third bar model is showing 80 is equal to 50 plus 30 or we could say 80 minus 50 is equal to 30.

Can you think of any other addition and subtraction equations that these bar models are representing? So these bar models can show addition or subtraction.

Sam said, "Addition is the inverse of subtraction." That means it's the opposite.

Lucas said, "We can use known facts to help us." So we can use the known fact in the first bar model to help us work out the facts in the second and the third bar models.

So if we know that 8 is equal to 5 plus 3, then we can work out that 8 tens is equal to 5 tens plus 3 tens or 80 is equal to 50 plus 30.

Sam has 30 pence and Lucas has 40 pence.

How much do they have altogether? Sam is asking, "What calculation do we need to do?" So are we going to add or subtract these amounts? Lucas said, "We need to add the amounts to find the total." Sam said, "I have 3 ten pence coins." Lucas said, "I have 4 ten pence coins." So I wonder what the total is.

Can you use a known fact to help you? Sam said, "We have 7 ten pence coins in total." Lucas said, "3 tens plus 4 tens is equal to 7 tens." Or we could say 30 plus 40 is equal to 70.

Sam and Lucas have shown this on a bar model.

So here's the known fact.

7 is equal to 3 plus 4.

Sam said, "I know that 3 plus 4 is equal to 7." Lucas said, "So 3 tens plus 4 tens is equal to 7 tens." And we can see that on the second bar model.

So 30 plus 40 is equal to 70.

We can see that on the last bar model.

Lucas said, "We had 70 pence in total." So 30 pence plus 40 pence is equal to 70 pence.

Sam and Lucas have 70 pence in total.

They each earn 10 pence more for doing jobs.

How much do they have now? Sam is asking, "What calculation do we need to do?" So are we going to add some tens or subtract some tens? Lucas said, "We need to add the amounts to find the total." Sam is asking, "Do we just add ten pence?" Hmm, if we look at the question again, it said Sam and Lucas have 70 pence in total.

They each earn 10 pence more for doing jobs.

So Lucas said, "We need to add 20 pence.

We earned 10 pence each." Sam said, "We had 7 ten pence coins." Lucas said, "We each earned 1 ten pence more." "So we earned 2 more ten pence coins." So wonder how many ten pence coins they'll have now? 7 tens plus 2 tens is equal to 9 tens.

So that's 70 plus 20 is equal to 90.

So they've got 90 pence in total.

Can you see they've both been given 10 more pence? So there are 9 tens altogether.

Lucas said, "So we now have 90 pence." Sam and Lucas have shown this on a bar model.

Here's a known fact that can help them.

9 is equal to 7 plus 2.

Sam said, "I know that 7 plus 2 is equal to 9." "So 7 tens plus 2 tens is equal to 9 tens." Can you see that on the second bar model? "So 70 plus 20 is equal to 90." Can you see that on the third bar model? "We now have 90 pence in total." Sam and Lucas have 90 pence in total.

Sam has 40 pence.

How much does Lucas have? Sam is asking, "What calculation do we need to do?" Do you think we need to add or subtract? Lucas said, "We need to subtract your money from the total." Sam said, "We have 9 ten pence coins in total." Lucas said, "You have 4 ten pence coins." Sam said, "So I have 40 pence." Lucas said, "I have the rest.

I have 9 tens, subtract 4 tens, and that's equal to 5 tens." "90 minus 40 is equal to 50." "So I have 50 pence." There's Lucas's money.

He's got 5 ten pence coins, that's 50 pence.

Sam and Lucas have shown this on a bar model.

Can you see the known fact here? 9 subtract 4 is equal to 5.

Sam said, "I know that 9 minus 4 is equal to 5." "So 9 tens minus 4 tens is equal to 5 tens." "So 90 minus 40 is equal to 50." Lucas said, "I have 5 tens, which is 50 p." Lucas has 50 pence.

He wants to buy two apples for ten pence each.

How much will he have left? "What calculation do we need to do?" Do you think we're going to add or subtract to work out how much he has left? Lucas said, "We need to subtract 20 p from the total to find what is left." Sam said, "You have 5 ten pence coins in total." Lucas said, "I have 50 pence.

5 tens minus 2 tens is equal to 3 tens." So he is going to have 3 tens left.

That's 50 minus 20 which is equal to 30.

Sam said, "You will have 3 ten pence coins left.

That's 30 p." Lucas said, "I will have 30 pence left." Is that what you thought? So he spent 20 p.

So 2 of his ten pence coins have gone.

He's got 3 ten pence coins left.

That's 30 pence.

Sam and Lucas have shown this on a bar model.

Here's a known fact that they can use to help them.

5 minus 2 is equal to 3.

Sam said, "I know that 5 minus 2 is equal to 3." Lucas said, "So 5 tens minus 2 tens is equal to 3 tens." "So 50 minus 20 is equal to 30." Lucas said, "I had 30 pence left." Let's check your understanding.

Which bar model represents this problem? Sam had 6 ten pence coins and spent 3 of them.

How much did she have left? Here are some bar models.

Can you think about which bar model can help represent this problem? So the first bar model is showing 60 subtract 10 which is equal to 50.

The middle one is showing 6 tens minus 3 tens, which is equal to 3 tens.

And the last bar model is showing 60 minus 20 is equal to 40.

Can you think about which bar model represents this problem? Pause the video while you think about this one.

Which bar model represents this problem? Sam said, "I had 60 pence.

That was 6 ten pence coins and I spent 30 pence.

That's 3 ten pence coins." Lucas said, "60 minus 30 is equal to 30." "So 6 tens minus 3 tens is equal to 3 tens." "You had 30 pence left." 3 tens is equal to 30.

So the middle bar model is going to help us with this one.

6 tens minus 3 tens is equal to 3 tens.

Here's a task for you to have a go at.

Can you use known facts to solve the problems? So the first problem says Sam has 40 pence and Lucas has 20 pence.

How much do they have in total? Can you think of a known fact that will help you? And then, think of an equation that will help you to solve the problem.

The second one says Lucas has 50 pence and finds 50 pence more.

How much does he have now? Can you think of an known fact that will help you? And then, think of an equation to help you solve the problem.

The last one says Sam has 90 pence and spends 40 pence.

How much does she have left? Can you think of a known fact to help with this one? And then, write an equation to help you solve the problem.

Here's the second part of your task.

Use the known facts to fill in the missing numbers in the problems. So here we've got three problems: a, b, and c, and we've got some known facts.

So the first known fact is 5 plus 2 is equal to 7.

Can use that to help you solve part a? Sam has hmm pence and Lucas has hmm pence.

How much do they have in total? The second one, the known fact is 6 plus 4 is equal to 10.

Can you use that fact to help you solve part b? Lucas has hmm pence and he finds hmm pence more.

How much does he have now? And the last one, the known fact is 8 minus 4 is equal to 4.

Can use that to help you solve part c? Sam has hmm pence and spends hmm pence.

How much does she have left? Try to think of multiples of 10 that can go in these gaps.

Here's the third part of your task.

Can you write a problem to match the bar model? Can you see here 90 is the whole and 60 and 30 are the parts? Can you think of a problem to match the bar model? Sam is asking, "Will it be addition or subtraction?" And Lucas is asking, "How can you check?" So pause the video and have a go at your tasks.

How did you get on with the tasks? Did you use known facts to solve the problems? So the first problem had the known fact 4 plus 2 is equal to 5 and you can use that to help you solve the problem.

Sam has 40 pence and Lucas has 20 pence.

How much do they have in total? So 40 plus 20 is equal to 60.

They have 60 pence in total.

The second known fact is 5 plus 5 is equal to 10.

We can use that to help us work out part b.

Lucas has 50 pence and finds 50 pence more.

How much does he have now? So 50 plus 50 is equal to 100.

He has 100 pence now.

That is 1 pound.

The known fact for the last one is 9 minus 4 is equal to 5 and we can use that to help us solve part c.

Sam has 90 pence and spends 40 pence.

How much does she have left? So 90 minus 40 is equal to 50.

She has 50 pence left.

How did you get on with part two? Did you use the known facts to fill in the missing numbers in the problems? So the first known fact was 5 plus 2 is equal to 7.

So we can use that to help us work out part a using multiples of 10.

So Sam has 50 pence and Lucas has 20 pence.

How much do they have in total? Well, 50 plus 20 is equal to 70.

So they have 70 pence in total.

Part b, the known fact was 6 plus 4 is equal to 10 and we can use that for multiples of 10.

So Lucas has 60 pence and finds 40 pence more.

How much does he have now? So 60 plus 40 is equal to 100.

He has 100 pence now.

That is 1 pound.

The last known fact was 8 minus 4 is equal to 4 and we can use that to help her solve part c using multiples of 10.

So Sam has 80 pence and spends 40 pence.

How much does she have left? So 80 minus 40 is equal to 40.

She has 40 pence left.

Here's the third part of your task.

We had a bar model, the whole was 90 and the parts were 60 and 30.

Did you write a problem to match this bar model? You might have said 60 pence plus 30 pence is equal to 90 pence.

Sam said, "I had 60 pence and you had 30 pence, how much is this in total?" So she's added the two amounts to find the total which is 90 pence.

Lucas has written a subtraction problem: 90 pence minus 60 pence is equal to 30 pence.

So he said, "I had 90 pence and spent 60 pence, how much do I have left?" So that's a subtraction problem.

So we can use the bar model to help us write addition or subtraction problems. Let's move on to the second part of the lesson.

We'll look at addition and subtraction puzzles.

This is an addition number pyramid.

Two bricks next to each other add together to make the total above.

So here we can see the bottom layer of bricks.

We've got the numbers 20, 10, and 10.

They're all multiples of 10, aren't they? Two bricks next to each other will add to make the total above.

So I wonder what the missing numbers are going to be.

How can we work out the missing numbers? There are three missing numbers.

What is the equation for each? Sam said, "I will start with the middle left.

This is 20 plus 10." I wonder what 20 plus 10 is equal to.

Can you think of a known fact to help you? Sam said, "I know 2 plus 1 is equal to 3 so 20 plus 10 is equal to 30." So the missing number there is 30.

Lucas said, "I will do the middle right.

This is 10 plus 10." So what is 10 plus 10 equal to? Can you think of a known fact to help you? Lucas said, "I know 1 plus 1 is equal to 2 so 10 plus 10 is equal to 20." So that missing number is 20.

So Sam's going to look at the top brick.

"The equation at the top is addition.

It is 30 plus 20." I wonder what 30 plus 20 is equal to? Sam said, "I know 3 plus 2 is equal to 5 so 30 plus 20 is equal to 50." So the missing number at the top was 50.

Can you see that all of the missing numbers end in a 0? So they're all multiples of 10, aren't they? Here's another addition pyramid.

Can you see we've got some missing numbers here? How can we work out the missing numbers? There are three missing numbers.

What is the equation for each? Sam said, "I will start with the bottom left." Can you see the brick at the bottom left? It's got a question mark in it.

She said, "We could subtract." Lucas said, "Or we could add 20 plus something is equal to 50." Sam said, "50 minus 20 will give us the missing number." Do you know known fact that can help? Sam said, "I know 5 minus 2 is equal to 3 so 50 minus 20 is equal to 30." So the missing number is 30.

We could check by adding like Lucas suggested, 20 plus something is equal to 50.

So is 20 plus 30 equal to 50? Yes it is, isn't it? I know that 2 plus 3 is equal to 5 so 2 tens plus 3 tens is equal to 5 tens.

Lucas is going to find a different missing number.

He said, "I will do the middle right, we could use addition." I wonder what two numbers we're going to add together to work out the missing number? It's 20 plus 10.

Do you know a known fact that can help with this one? Lucas said, "I know 2 plus 1 is equal to 3 so 20 plus 10 is equal to 30." So the missing number is 30.

Let's look at the missing number at the top.

Sam said, "The equation at the top is addition.

It is 50 plus 30." I wonder what that's going to make? Can you think of a known fact that will help? Sam said, "I know 5 plus 3 is equal to 8 so 50 plus 30 is equal to 80." So the missing number is 80.

Can you see that all the numbers in this pyramid are multiples of 10? They all end with a 0, don't they? Let's check your understanding.

What number will be at the top of this addition pyramid? How do you know? How are you going to work it out? And will it be a multiple of 10? Pause the video while you think about this one.

So how are we going to find out the number at the top of the pyramid? Sam said, "I will start by adding 10 and 20 to work out the middle row." So I can see at the bottom we've got 10 and 20 and 20 and 10.

They're going to make the same total, aren't they? So 10 plus 20 and 20 plus 10.

Sam said, "I know 2 plus 1 is equal to 3 so 20 plus 10 is equal to 30." So both of these missing numbers are 30.

How can we work out the missing number at the top? Lucas said, "We can use addition to work out the top number." So this is going to be 30 plus 30.

Lucas said, "I know that 3 plus 3 is equal to 6 so 30 plus is equal to 60.

The top number is 60." Is that what you thought it would be? Here is a magic cross.

Each row and column adds up to the same total.

So the row is going across and the column is going down.

What is the total for each line and how can you check? Can you see that the numbers in the magic cross are all multiples of 10? So we need to add up the multiples of 10 to work out the total for the row and the column.

So here's the numbers in the row and we're going to add 50 and 20 and 30.

So 50 plus 30 plus 20 is equal to? It's equal to 100.

How can we work that out? Sam said, "I know that 5 plus 2 plus 3 is equal to 10 so 50 plus 20 plus 30 is equal to 100." Because 5 tens plus 2 tens plus 3 tens will be equal to 10 tens and that's 100.

Lucas said, "I know that 50 plus 30 is equal to 80, and 80 plus 20 is equal to 100." So he's added up two of the numbers first, and then added the third one.

Let's have a look at the column.

We've got 20 in the middle again and we're going to add 70 plus 20 plus 10.

So 70 plus 10 plus 20 is equal to? That makes 100 as well.

How do you know? Sam said, "I know that 7 plus 2 plus 1 is equal to 10, so 70 plus 20 plus 10 is equal to 100." Lucas said, "I know that 70 plus 10 is equal to 80 and 80 plus 20 is equal to 100." So Sam and Lucas use different strategies to add up the numbers, but they ended up with the same total.

Sam and Lucas are making a magic cross.

Remember the numbers in each row and column add up to the same total.

They put all the multiples of 10 from 10 to 50 in each square to make each row and column add up to 80.

I wonder where they're going to put the numbers.

Sam said, "I will try 10 in the middle." She's put the number 10 in the middle.

How's she going to make the row add up to 80? Lucas said, "I know that 80 minus 10 is equal 70, so the other two numbers will total 70." Can you think of two multiple of 10 to add up to make 70? Sam said, "I know that 50 plus 20 is equal to 70 so 10 plus 50 plus 20 is equal to 80." So she's going to put 50 and 20 in the row with the 10.

So the row is 50 plus 10 plus 20.

We can add them up in any order.

So 10 plus 50 plus 20 is equal to 80.

We know that 50 plus 20 is equal to 70 and 70 plus 10 is equal to 80.

Lucas is going to try to find some multiples of 10 to go in the column so that the column totals 80.

We've already got 10 in the middle.

He said, "I know that 80 minus 10 is equal to 70, so the other two numbers will total 70." Can you think of two multiples of 10 that add up to make 70? Lucas said, "I know that 40 plus 30 is equal to 70," so he's going to put 40 and 30 in the column.

"So 10 plus 40 plus 30 is equal to 80." So there's the column.

We've got 40, 10, and 30.

We can add them up in any order.

Lucas knows that 40 plus 30 is equal to 70 and 70 plus 10 is equal to 80.

So they've made the magic cross and the row and the column add up to make 80.

Have they used all of the multiples of 10, from 10 up to 50? They've used 10, 20, 30, 40, and 50.

Yes, they have.

Let's check your understanding.

Spot the mistake on this magic cross.

And how do you know? And how can you check? Remember that the row and the column need to add up to the same total.

So pause the video and think about this one.

Did you spot any mistakes in the magic cross? I can see that we've got the number 20 in the middle and the total for each row and column is going to be 80.

So the other two numbers in the row or the column are going to add up to 60 because that's 20 less than 80.

Let's have a look at the row.

We've got 10 plus 20 plus 50.

Is that equal to 80? So 10 plus 50 plus 20 is equal to? It is equal to 80.

How do we know? Sam said, "I know that 1 plus 2 plus 5 is equal to 8, so 10 plus 20 plus 50 is equal to 80." Lucas said, "I know that 10 plus 50 is equal to 60, and 60 plus 20 is equal to 80." Let's have a look at the column.

I can see that we've got 20 in the middle.

So the other two numbers are going to total 60.

So 30 plus 40 plus 20.

Does that make 80? No, it makes 90.

Sam said, "I know that 3 plus 2 plus 4 is equal to 9, so 30 plus 20 plus 40 is equal to 90." Lucas said, "I know that 30 plus 40 is equal to 70 and 70 plus 20 is equal to 90." So the column does not add up to 80.

It adds up to 90.

Sam said, "The totals are not the same." Lucas said, "So this is not a magic cross." Here's a task for you to have a go at.

Can you work out the missing numbers in the addition pyramids? Remember that two bricks next to each other add up to make the brick above.

Think about how you can work out the missing numbers in the addition pyramids.

Here's the second part of your task.

Can you use all the multiples of 10 from 10 to 50 to put in each square on the crosses so that each line adds up to the magic number? Can you see on these magic crosses that the first magic number is 90 and the second magic number is 100? So see if you can use all of the multiples of 10 from 10 up to 50 to go in each square so that each line, the row and the column, adds up to the magic number and think about how can you check.

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

How did you get on with the first part of the task? Did you work out the missing numbers in the addition pyramids? So here are the completed pyramids.

How did you work out the missing numbers? Well, on the first pyramid, I can see we've got a number missing at the bottom.

It was the number 10 because 10 plus 10 is equal to 20 which is above.

Then in the middle row, it must be the number 20 because that's 10 plus 10 as well.

And the top row must be 40 because 20 plus 20 is equal to 40.

On the second pyramid, we've got some numbers missing at the bottom, so we need to start from the top and work down.

So in the middle row the missing number is 70 minus 40, which is equal to 30.

And on the bottom row in the middle, the missing number is 20 because 40 minus 20 is equal to 20.

And the other missing number was 10 because 30 minus 20 is equal to 10.

On the next pyramid, I can see that in the middle row, we've got the number 60 missing because 100 minus 40 is equal to 60.

And then on the bottom row, we've got the number 40 missing because 60 minus 20 is equal to 40.

And the other missing number is 20 because 40 minus 20 is equal to 20.

On the last addition pyramid, I can see that we've got a missing number on the bottom row.

Well, that's 50 minus 20 which is equal to 30.

And in the middle row, we've got a number missing.

Well, that's 20 plus 30, so that's equal to 50.

And the brick at the top must be 100 because 50 plus 50 is equal to 100.

How did you get on with that one? Here's the second part of your task.

Did you use all the multiples of 10 from 10 to 50 to put in each square on the crosses so that each line adds up to the magic number? So the first magic cross had the magic number 90.

We need to put 30 in the middle to make this one work.

So if 30 is going to go in the middle, what were the other two numbers total? The other two numbers will total 60 because 60 plus 30 is equal to 90.

So you could have 50 and 10 or 20 and 40.

Let's look at the second magic cross.

The magic number was 100.

50 will need to be in the middle to make this one work.

So the other two numbers will total 50 because 50 plus 50 is equal to 100.

Can you think of two multiples of 10 total 50? So we could have 10 and 40 or we could have 20 and 30.

They make 50 as well.

How did you get on with those? We've come to the end of our lesson.

Today, we were solving problems involving multiples of 10.

This is what we found out: Unitizing and known facts help you to add and subtract multiples of 10.

So if 3 plus 2 is equal to 5, then 3 tens plus 2 tens is equal to 5 tens, which is equal to 50.

If 5 minus 2 is equal to 3, then 5 tens subtract 2 tens is equal to 3 tens, which is equal to 30.

Well done, everyone.

See you next time.