Lesson video

Hello there.

My name is Mr. Goldie and welcome to today's maths lesson.

And here is our lesson outcome.

Our lesson outcome is I can subtract to and from 10.

And here are our keywords for today's lesson.

So our keywords are minuend.

Can you say that? Minuend.

Our next keyword is subtrahend.

Can you say subtrahend? Well done.

And our last keyword is difference.

Can you say that? Difference.

So let's look at what those words mean.

The minuend is the number being subtracted from.

A subtrahend is a number subtracted from another.

So in that calculation, the subtrahend is three.

That is the number that is being subtracted from the minuend.

The difference is the result after subtracting one number from another.

So the difference in that calculation is four.

The difference between seven and three is four.

And here's our lesson outline.

So the first part of the lesson, we're going to be subtracting to 10 and in the second part of the lesson, we're going to be subtracting from 10.

So let's start off with subtracting to 10.

In the lesson you'll meet Izzy and Alex.

So Izzy and Alex are going to be helping you today.

Izzy's saying "Number pairs for 10 will be really important in today's lesson".

So if you know your number pairs to 10, you're gonna find this lesson quite a lot easier than if you don't.

Alex is asking, "Do you know all the number pairs that total 10?" I wonder if you do.

Let's start off with our first problem.

There are 15 cakes.

There are 15 cakes.

Five get eaten.

So five of the cakes get eaten.

How many cakes are left? Alex is asking, "What calculation would you do to work out the answer?" What calculation would you do? We'd have to calculate 15 - 5 to find out the answer.

What is 15 - 5? "Let's use a 10s frame and a number line to represent the calculation" says Alex.

Here's our 10s frames with the 15 cakes inside.

And here's our number line.

So if we start from 15 and we count back five, we subtract five, we get to 10.

So there are 15 cakes.

Five get eaten.

We are left with 10.

So 15 - 5 = 10.

Let's look at a different problem.

There are 13 slices of pizza.

"I ate three slices", says Alex.

How many slices are left? What calculation would you do to work out the answer? Our calculation this time would be 13, that's the number of slices we started with, subtract three, that's the number that Alex ate and we'd have to work out the answer.

"Let's use a 10s frame and a number line to represent the calculation" says Alex.

So we've got 13 in our 10s frame with counters representing the pizza slices and there's our number line.

So we start from 13 and we subtract three, we get to 10.

And in our 10s frames, if we subtract the three, we are left with 10.

Let's look at a different problem.

There are 19 slices of pizza.

Some slices get eaten.

We're not going to blame anybody Alex, are we, but I wonder who ate them.

There are 10 slices left.

How many were eaten? So this time we start with 19 slices of pizza, some slices get eaten and there are 10 slices left.

What calculation would you do to work out the answer? So this time we're going to be calculating 19, that's the number of slices we started with, and we subtract something and we're left with 10.

What is our missing number? Wonder how we'd work it out.

"What do I subtract from 19 to get back to 10?" says Alex.

There's our 19 slices of pizza represented in 10s frames and there's a number line to help us work out the answer as well.

So let's start from 19 and count back to get to 10.

What do we have to jump back? We have to jump back nine, we have to count back nine.

19 - 9 = 10.

And if we look at our 10s frames and we subtract the nine, we're left with 10.

So the missing number was nine.

That's how many slices of the pizza were eaten.

The difference is a 10, is a 10s number, when the subtrahend is the same as the ones digit of the minuend.

Now that sounds more complicated than it really is.

There's a calculation, 16 - 6 = 10.

So we've got there the difference being a 10s number, in this case 10.

There's the minuend, it's 16.

There's our subtrahend, it's six.

The difference is 10.

Now Alex has said "The subtrahend is six and the ones digit of the minuend is also six".

So 16 is made out of 10 and six, and if we subtract six, we're left with a 10.

Now here's one to have a look at on your own.

Which calculations give you a difference of 10? So which calculations give you a difference of 10? And Alex is just reminding you to look carefully at the minuend and the subtrahend and see if you can spot anything.

So pause the video.

Have a good look at those six calculations.

Can you work out which ones would give a difference of 10? Welcome back and let's see if you were right.

So our first calculation is 14 - 4.

14 - 4 would be 10.

So our minuend is 14 and the ones number of the minuend is a four.

14 is made out of 10 and four.

If we subtract the four, we're left with a 10.

How about the next one, 16 - 5? 16 - 5 is 11, it's not a 10.

So although that's the right calculation, although that's the right answer, does not give us a 10s number.

What about 17 - 8? Would that give us a difference of 10? It would not, it would give us a nine.

So it is not a 10.

If it was 17 - 7, it would equal 10.

If it was 18 - 8, it would equal 10, but it isn't.

The next one, we've got 12 - 2.

Would that make 10? Yes it would.

Next one, 18 - 8, also makes 10.

And the last one, 11 - 2.

Would that make 10? No it would not.

It would make nine.

So very well done if you've got those ones right.

You can also end up with other 10s numbers.

So not just 10, other 10s numbers as well.

Here's a number line.

What would 23 - 3 be? "The subtrahend is three and the ones digit of the minuend is also three" says Izzy.

We've got three, 23 - 3.

23 - 3 would be 20, would equal 20.

What about 37 - 7? What would that equal? Alex is saying "The subtrahend is seven and the ones digit of the minuend is also seven." So can you work out what 37 - 7 would be? Let's start from 37.

Count back seven, we would get to 30.

37 - 7 = 30.

What happens if there is more than one subtrahend? So let's look at this calculation here.

15 - 3 - 2, what would that equal? "Start with 15" says Izzy.

"Subtract three then subtract two." So we start from 15, we subtract three.

That gives us 12, that equals 12.

Subtract two, that equals 10.

The answer would be 10.

So if there's more than one subtrahend, we can subtract one of them and then subtract the other.

What happens if you change the order of the subtrahends? If you change them around? 27 - 2 - 5, what would that equal? Let's start from 27.

Going to subtract two, that equals 25.

Subtract five, that equals 20.

What about if we did 27 - 5 - 2? So the numbers are the same we're subtracting but the order has changed.

We're subtracting in a different order.

Again, let's use a number line, start from 27.

This time we subtract five first of all.

That gets us to 22 and then we subtract 2.

22 - 2 = 20.

"The order of the subtrahends doesn't change the difference" says Izzy.

Izzy says "You can also add the subtrahends before subtracting them from the minuend." Again, it sounds more complicated than it really is.

Let's look at an example.

28 - 2 - 6.

Now we could do 28 and subtract two and subtract six, but I think there's a different way of doing it.

So Izzy says "I'm going to use a bar model." I've got a number line there as well.

So 28 and we're subtracting two and six.

But Izzy says you could add the subtrahends first.

So you can add the six and two together.

So first I add together two and six.

And 2 + 6 or 6 + 2 = 8.

28 - 2 - 6 is the same as 28 - 8.

It'll equal the same answer.

Then Izzy's going to calculate 28 - 8.

We could use a number line to do that.

So 28, count back eight will give us 20.

28 - 8 = 20.

The answer is 20.

Izzy is trying to work out the missing subtrahend.

So she's trying to work out the number that has been subtracted.

14 - 2 - something = 10.

What is that missing number? Let's use a number line to help us work out the answer.

So first I subtract two from 14.

"What else do I need to subtract?" asks Izzy.

So let's start off with 14 - 2.

14 - 2 = 12.

What else does Izzy need to subtract? She needs to subtract another two.

So 12 - 2 = 10.

The answer would be two.

14 - 2 - 2 = 10.

Izzy is trying to work out another missing subtrahend.

27 - something - 4 = 20.

What would the answer be, I wonder.

Again, let's use a number line to help us work out the answer.

This time the number line goes from 20 to 40.

First I subtract four from 27.

What else do I need to subtract? Remember it doesn't matter which order we subtract the subtrahends.

It still gives us the same answer.

So let's start with 27 and let's subtract 4.

27 - 4 = 23.

What else does Izzy need to subtract? Subtract 3.

23 - 3 = 20.

So our missing subtrahend is 3.

27 - 3 - 4 = 20.

This time Izzy is trying to work out the missing minuend.

What is the missing minuend? Let's use a number line to help us work out the answer.

So the minuend subtract six is equal to 30.

The minuend is six more than 30.

Remember, addition and subtraction are inverses.

"If I add six back onto 30, I'll get the minuend" says Izzy.

So 30, add six, we add the six back on, we get to 36, which means that 36 - 6 = 30.

How could Izzy work out the missing minuend this time? A slightly trickier calculation.

Something - 2 - 5 = 10.

What is our missing number? And Izzy says, "I'm going to add five and two back onto 10 to find the minuend." Remember if we started with this number and we subtracted two, then subtracted five to get 10, if we add those two numbers back on again, we'll get our starting number.

10 + 5 = 15 and then 15 + 2 = 17.

And we could have added them in a different order.

We could have added two first and then added five.

It doesn't matter.

So our missing number is 17.

That's our missing minuend.

And here's one to do on your own.

How could you complete this equation? 16 - something - something = 10.

And here's Izzy asking you a helpful question, just to guide your thinking.

"What do you have to subtract altogether?" So pause the video and have a go trying to find as many different answers as you can.

Now welcome back and here are some possible answers.

It's not all of them, it's just some of them and you may have come up with some different answers too.

So you could have had 16 - 5 - 1 = 10.

So as long as those two numbers you are subtracting total six altogether, doesn't matter what the numbers are and doesn't matter what order they appear in.

You could have tried 16 - 2 - 4 = 10.

You could have had 16 - 3 - 3 = 10.

And Alex is saying "You could also have had 16 - 1 - 5." That's a different answer.

The numbers are in a different order.

So well done if you came up with one solution to that problem.

Very well done if you came up with lots and lots of different solutions.

And here is your task.

So which expressions have a difference that is a 10s number? Which do not? One side of the table says difference is a 10s number and one side of the table says difference is not a 10s number and you are going to be sorting the expressions.

So for example 16 - 6 = 10.

So the answer is a 10s number, it is 10.

23 - 3 = 20.

So the answer is also a 10s number.

20 is a 10s number.

On the other side it says difference is not a 10s number.

So 15 - 6, the answer would not be a 10s number.

21 - 2 would also not make a 10s number.

The answer would be 19.

19 is not a 10s number.

And here are the different expressions that you are going to be sorting and putting onto the table in the correct place.

So think carefully about whether the answer is a 10s number or whether it is not.

And then part two, you've got to make these calculations correct.

So what is the missing number in those calculations? Sometimes one of the subtrahends is missing.

Sometimes it's the minuend that's missing.

On the last task, so part three of task A is how many ways can you make this correct? You've got a calculation there.

18 - something - something else = 10.

What two numbers could go in that calculation? And can you think of more than one way of making that correct? Pause the video and have a go at your tasks.

Welcome back and let's see how you got on with those tasks.

Let's look at the different answers.

So one side of the table are the calculations where the difference is a 10s number such as 25 - 5, that would equal 20 or 14 - 4, that would equal 10.

And on the other side are the calculations where the difference is not a 10s number.

So well done if you managed to sort those correctly.

The next task you had to make these calculations correct.

So there are the answers.

You can see there the missing subtrahends and the missing minuends.

And then your third task, here are the different answers you could have come up with.

Very well done if you managed to get onto part three and managed to find some of those possible answers.

Excellent work.

And let's move on to part two.

Part two is subtracting from 10.

So there are 10 children on the bus.

Three children get off at the next stop.

How many children are on the bus now? "What calculation would you do to work out the answer?" says Alex.

You can use number pairs that total 10 to help you subtract from 10.

So how would you calculate 10 - 3? What would the answer be? What would it equal? "I know 10 = 3 + 7," says Alex.

So here's a 10s frame to help us work out the answer.

And here's the number line to help us represent the calculation.

And we're going to subtract the three.

We have seven left and on our number line, start from 10 and count back three, we get seven.

So the answer is seven, 10 - 3 = 7.

So it's all about using those number pairs that total 10 to help you.

"There would be seven children on the bus", says Alex.

Each number pair gives you several number facts.

Alex is saying "I know 10 = 4 + 6." So what would 10 - 6 be, what would the answer be? So we start with 10, we subtract six, the answer would be four.

What about 10 - 4? We have 10, we take away four, we subtract four.

Our answer would be six, 10 - 4 = 6.

Alex is saying "I know 10 = 8 + 2." That would also give us some subtraction number facts as well.

So what would 10 - 8 be? Let's start with 10.

We're going to subtract eight.

It would equal two.

10 - 2, what would that equal? Let's start with 10 and subtract two and that gives us the answer eight.

And here's one to try on your own.

Use number pairs to find the difference.

So think about a number fact that's going to be helpful for you to work out the answers.

We've got there 10 - 9 and 10 - 1.

Pause the video and work out those two answers.

Welcome back.

Let's see how you got on.

So the useful number pair to 10 would be 9 + 1 = 10.

So 10 - 9 = 1.

10 - 1 = 9.

Well done if you got those two right.

Calculate the missing subtrahends.

So we've got there three calculations with missing subtrahends.

Can you use number pairs that total 10 to work out the answer? Here's Alex to help us.

"What has been subtracted from the minuends?" What has been subtracted? And Izzy's saying, "Use number pairs that total 10 to help you." So in that first calculation, 10 - what = 5? Well our number pair that's gonna be helpful there is 5 + 5 = 10.

So the answer must be five.

Let's look at our next calculation.

The helpful number pair there is 7 + 3 = 10.

So 10 - 3 = 7.

And the last one, a bit of a tricky one this one in some ways.

Our number pair that totals 10 is actually going to be 0 + 10 = 10.

If we start with 10 and we subtract zero, our answer would be 10.

10 - 0 = 10.

Number pairs that total 10 can also be used for other 10s numbers as well.

So Alex is saying, "I know that 10 - 4 = 6." "Use the number pair to 10 to work out the differences in these equations" says Izzy.

So what would be 20 - 4? What would that equal? We have 10 - 4 = 6.

20 - 4 must be 16, equals 16.

What would be the answer to 30 - 4? The answer would be 26, 30 - 4 = 26.

What about 40 - 4? Can you work out what the answer is? The answer would be 36.

You can see there a pattern can't we in our answers? They all end in six.

Izzy is trying to work out the missing subtrahend.

10 - 3 - something = 5.

"First I'll subtract three" says Izzy.

Lets start from 10 and we're going to subtract three, 10 - 3 = 7.

"What else do I have to subtract to get to five?" says Izzy.

Can you work out what the answer is? We'd have to subtract two, 7 - 2 = 5.

So our missing subtrahend is two, 10 - 3 - 2 = 5.

Lets have a go at this problem.

So this time we've got 20 - 4 - something = 13.

"First I'll subtract four" says Izzy.

So this time our number line goes from 10 to 20 and we're gonna count back from 20.

20, let's subtract four.

That equals 16.

What do we now have to subtract, I wonder? "What else do I have to subtract to get to 13?" says Izzy.

So 16 subtract what number makes 13? Three, 16 - 3 = 13.

So our missing subtrahend is three.

How could you complete this equation? This is one for you to try on your own.

So 10 - something - something = 2.

"What do you have to subtract altogether?" says Izzy.

So pause the video and see how many different answers you can find.

Welcome back.

Let's see how you got on.

So here are some possible answers.

And again, it's not all the answers, it's just some of them.

So you could have done 10 - 7 - 1 = 2.

You could have had 10 - 5 - 3 = 2.

You could have had 10 - 3 - 5 = 2.

What did you have to subtract altogether? You had to subtract eight, didn't you? So as long as the two numbers you're subtracting have a total of eight, you'd have the right answer.

"You could also do 10 - 1 - 7" says Alex.

Remember, you can subtract numbers in any order.

And here is the first part of task B.

So make these calculations correct.

So for most of them, the minuend is 10, but for some of them the minuend is 20.

So you've gotta subtract the subtrahend and see if you can work out the difference.

Or sometimes you've got to work out a missing subtrahend.

And then the second part of task B is how many ways can you make this correct? So how many different possible answers can you find? And can you find all of them? Pause the video and have a go at task B.

Welcome back and let's see what answers you managed to come up with.

So here's part one, how to make these calculations correct.

There are our missing numbers.

They got quite tricky as well, didn't they? Especially when you had to find one of the missing subtrahends.

So very well done if you managed to get all those correct.

And here are some possible answers for the second part of task B.

So you could have had 10 - 4 - 1 = 5.

You could have had 10 - 4 - 6 = 0.

And well done if you managed to find lots and lots of different ways.

Excellent work.

And here is our lesson summary for subtracting to and from 10.

So use the minuend and subtrahend to help subtract to 10.

Use number pairs that total 10 to help you subtract from 10.

So if you know that 10 = 7 + 3, 10 - 7 must equal 3 and 10 - 3 = 7.

Very well done in today's lesson.