Lesson video

Hello, my name's Mrs. Cornwell, and I'm going to be helping you with your learning today.

I'm really looking forward to today's lesson.

I know you're going to work really hard, and we'll do really well.

So, let's get started.

So, welcome to today's lesson, which is called Use Number Pairs to Ten in Subtraction Contexts, and it comes from the unit Addition and Subtraction Facts within Ten.

So, in our lesson today, we're going to use our number pairs to 10 in subtraction equations and problems, and we're going to see how what we know about the pairs that sum to 10 can help us when we are subtracting.

And by the end of today's lesson, you should feel much more confident with spotting those pairs and using them to subtract.

So, let's get started.

So, our keywords for today are subtract.

My turn: subtract.

Your turn.

And difference.

My turn: difference.

Your turn.

And subtrahend.

My turn: subtrahend.

Your turn.

And minuend.

My turn: Minuend.

Your turn.

Excellent.

Well done.

Okay, so in the first part of our lesson today then, we're going to use those number pairs to 10 to find a missing difference in a subtraction.

In this lesson, you will meet Sam, and you will also meet Jacob.

They're going to be helping us today.

So, here's Sam.

Sam has collected 10 conkers.

6 still have their shells; we can see them there, can't we? Jacob wonders how many do not have their shells.

How can he find out, I wonder? Should he use addition or subtraction? He says, "When we know the whole and we know one part, we can subtract to find the other part." And so, Sam says, "This must be a subtraction problem." That's right.

"There are 10 conkers in the whole group, so we can use our number pairs to 10," can't we? Let's represent the problem on a part-part-whole model.

We know 10 is the whole, 6 is a part, and mm is a part.

So, if 10 is the whole, then the parts will sum to 10, won't they? So, we can use our number pairs to 10.

So, we know 10 is the whole, 6 is a part, and 4 is a part.

There are 4 conkers without shells.

There they are.

Let's represent the problem as an equation.

10, so 10 is the minuend; it represents the whole group.

Minus 6, 10 minus 6.

So, 6 is the subtrahend.

It represents the part to be subtracted from the whole.

And then, 4 is the difference; it represents the part of the whole that remains.

10 minus 6 is equal to 4.

Okay, so well done.

Jacob has 10 pencils in his pencil case.

He gives 2 to Sam.

He wonders how many pencils he has left.

How can he find out, I wonder? "Is this still a subtraction problem?" Oh, Sam's reminding us there, "Decreasing the amount in a story is a type of subtraction." So, Jacob says, well, "I think I can tell a 'First, then, now' story." We know we can tell those to decrease the amount.

First I had 10 pencils, then I gave 2 pencils to Sam.

How many pencils do I have left? We can represent the story on a part-part-whole model to help us, can't we? So, there's our part-part-whole model.

First I had 10 pencils; 10 is the whole.

Then I gave 2 pencils to Sam, so 2 is a part.

How many pencils do I have left? "If 10 is the whole, then the parts will sum to 10." 2 and 8 sum to 10.

The other part must be 8.

So, let's represent our problem as an equation.

There's Sam, and she's saying "I think the equation will be 8 plus 2 is equal to 10." Hmm, I wonder if she's right.

"We started with the whole and decreased the amount.

We must subtract," says Jacob.

First I had 10 pencils.

"This is the minuend; it represents the whole amount." Then I subtracted 2.

"This is the subtrahend; it represents the part to be subtracted." Now there are 8 pencils.

This is the difference; it represents the part that remains.

I know 2 and 8 sum to 10, so when I subtract 2 from 10, the remaining part must be 8.

Sam wants to solve this equation using an number line: 10 minus 9 is equal to mm.

She says, "I will start at 10 and count back 9." I wonder if that's a good idea.

So, there's 10, and she counts back 1, 2, 3, 4, 5, 6, 7, 8, 9 jumps, and she can see that it gets her to 1.

But Jacob has noticed, "That will take a long time, and you could make a mistake when counting," couldn't you? And it would be a bit tricky to do if you didn't have your number line there.

So, he says, "Why don't you use your number pairs to 10?" We know 10 is the whole.

If 9 is a part, we can subtract the subtrahend of 9 in one step, and there will be one remaining.

So, 10 minus 9 is equal to 1.

And there's Sam.

She's saying, "I don't think I need the other numbers on the number line." We didn't use those, did we, 'cause we did one jump of 9.

We can call this an empty number line, because it only shows the numbers we need.

Now we can easily see that 10 minus 9 is equal to 1, can't we? So, well done.

Sam uses a number line to solve this equation: 10 minus 3 is equal to mm.

So, she's drawn her empty number line, hasn't she? Because she's only putting on the numbers she needs.

So, she needs 10.

Okay, if 10 is the whole, the parts will sum to 10.

"3 is the subtrahend, so I will subtract 3 in one step," and there we go.

So, 10 minus 3 is equal to.

I know that 3 and 7 sum to 10, so 10 minus 3 is equal to 7.

There it is.

Okay.

So, now, it is time to check your understanding.

Find the difference in each equation by subtracting the subtrahend in one step on each number line.

Okay? So, have a look at the equations, as well, and remember to put the difference in, in the number line, and the equation.

So, pause the video now while you try that.

Okay, and let's see how we got on with that.

So, the first number line has 10 as the whole amount, and then the part that is subtracted, the subtrahend, is 4.

So, 10 minus 4 is equal to 6.

That's right, because we know 6 and 4 sum to 10.

Okay, the next equation is 10 minus 5.

That's right; it's equal to 5, isn't it? Because if 10 is the whole, 5 and 5 must sum to 10.

Okay, we've got 10 minus 6 is equal to 4.

That's right.

So, well done if you did that.

We can use what we know about odd and even numbers to help us spot a mistake, can't we, in an equation.

So, there, we've got 10 minus 3 is equal to 6.

And Sam is saying, "I know that cannot be correct." 10 is an even number.

It can only partition into two odd numbers or two even numbers.

So, then, we've got 10 minus 3, so we've got 10 is the whole amount, and we know one part is 3; 10 minus 3.

Okay? You can see that 3 is odd, isn't it? So, we need another odd number to be the other part of the whole amount of 10, don't we? Now, 6 is an even number, so this cannot be correct.

And there, we can see it should have been 7, shouldn't it? So, now it's time to check your understanding of that.

Use your knowledge of odd and even numbers to spot which equation cannot be correct.

So, we've got A: 10 minus 3 is equal to 7; B: 10 minus 4 is equal to 5; or C: 10 minus 8 is equal to 2.

Okay, so think about what we've learned, okay? And pause the video while you try that.

Okay, and let's see what we thought then.

Okay, so did you spot it? 10 minus 4 is equal to 5.

That cannot be correct, can it? I know 10 cannot partition into an odd and an even number, and we know 4 is even and 5 is odd.

So, that cannot be correct.

So, well done if you noticed that.

Okay, so Sam thinks she can use her pairs to 10 to solve this equation: 9 minus 1 is equal to mm.

Is she right, do you think? So, Jacob has noticed the minuend is 9.

That means there are 9 in the whole group, and he's put the 9 into the whole part of the part-part-whole model, hasn't he? We can only use our number pairs to 10 if there are 10 in the whole group.

If 10 is the whole, then the parts will sum to 10, but 10 isn't the whole there.

The parts there would sum to 9, wouldn't they? Okay, so well done if you noticed that.

Jacob wants to use his number pairs to 10 to solve some subtraction equations.

Let's help him.

So, 8 minus 2.

"Can I use my number pairs to 10," he asks.

The minuend is 8, so that means 8 is the whole amount, so the parts there would sum to 8, wouldn't they? So, he cannot use his number pairs to 10.

What about 10 minus 4? Could he use his number pairs to 10 to help with that? That's right.

The minuend is 10.

So, the parts will sum to 10.

He can use his number pairs to 10.

What about 10 minus 7? Could he use his number pairs to 10 there? The minuend is 10.

10 is the whole amount, so the parts will sum to 10.

So, he can use his number pairs to 10.

And 6 minus 4.

What do we think about that? That's right.

The minuend is 6, so the whole amount is 6.

So, the parts would sum to 6 there.

So, he cannot use his number pairs to 10 there, can he? So, well done if you noticed that.

If the minuend is 10, we can use our number pairs to 10, can't we, because the parts will sum to 10.

Okay, so time to check your understanding of that now.

Which of these equations will your number pairs to 10 help you solve? So, you've got A: 8 minus 2 is equal to; B: 7 minus 3 is equal to; or C: 10 minus 4 is equal to.

Okay, so pause the video now while you think about that.

Okay, so what did you think? That's right: 10 minus 4.

So, 10 is the minuend; it is the whole, so the parts will sum to 10.

So, well done if you noticed that.

If we can spot where we can use our number pairs in subtraction equations, we can use them to solve equations more quickly, can't we, which is really helpful.

Let's practise using our number pairs to quickly solve equations.

Hold up the correct number of fingers to show the difference for each equation.

Okay, are you ready? 10 minus 5.

That's right, you should have five fingers held up, shouldn't you? 10 minus 6.

That's right, you should have four fingers held up.

10 minus 4.

That's right, you should have six fingers held up.

10 minus 2.

That's right, you should have eight fingers held up.

10 minus 8.

That's right, you should have two fingers held up, shouldn't you? 10 minus 1.

That's right, you should have 9 fingers held up, shouldn't you? So, well done.

Hopefully you're getting quicker and quicker at remembering those pairs of numbers that sum to 10.

So, here's our task for the first part of today's lesson.

Use your number pairs to 10 to find the missing numbers and write the equation for each.

Okay? So, pause the video now while you try that.

Okay, and then here's the second part of our task.

Use your number pairs to 10 to solve the following.

So, we've got some equations there, okay, and we can see the minuend is 10 in each one; that's the whole amount, so we can use our number pairs to 10.

So, pause the video now while you try that.

Okay, and then the next part of our task is to write two subtraction equations for each part-part-whole model, and use the counters to help you.

Okay, so pause the video now while you try that.

So, let's see how we got on here.

Okay, so we've got 10 minus 6 is equal to.

That's right, if 10 is a whole and 6 is a part, then 4 must be the other part.

The equation is 10 minus 6 is equal to 4.

Then we've got 10 minus 7.

That's right, that's equal to 3, and there's our equation there.

Then we've got 10 minus 8 is equal to 2, and there's our equation.

And we've got 10 minus 9 is equal to 1, and there's our equation.

So, well done if you did that.

Okay, for the second part of our task here, we've got 10 minus 3 is equal to 7, 10 minus 4 is equal to 6, 10 minus 5 is equal to 5, and so on.

So, you can see that the difference in each equation is the other part of the whole, isn't it? It's the other part that sums to 10.

So, well done if you noticed that.

And then, for part 3 here, we've got 10 is the whole, 2 is a part, and 8 is a part.

So, you could have had 10 minus 2 is equal to 8, or you could have had 10 minus 8 is equal to 2.

And then, for the next one here, we've got 10 is the whole, and 1 is a part, and 9 is a part.

So, we've got 10 minus 1 is equal to 9, 10 minus 9 is equal to 1.

So, well done if you did that.

Excellent work.

So, now we're going to use pairs to 10 to find a missing subtrahend in an equation.

Here is a different subtraction problem.

There were 10 bananas.

We don't know how many had been peeled, but the three remaining bananas were not peeled.

This is different to our previous problems. This time we do not know how many were subtracted.

We don't know the subtrahend, do we? 10 is the whole, so the parts must sum to 10.

And we know the part that was remaining was 3.

So, the other part must have been 7.

7 bananas had been peeled.

There must have been 7 subtracted.

Well done.

Let's represent this as an equation.

Mm, so let's have a think.

There were 10 bananas.

10 is the minuend.

We don't know how many had been peeled, so we don't know the subtrahend, so 10 minus mm.

The part remaining, the difference is 3.

So, 10 minus mm is equal to 3.

And there's our part-part-whole model.

10 is the whole, 3 was the part remaining.

"If 10 is the whole, the parts must sum to 10." So, "The subtrahend must be 7." And there it is in the equation.

Now, Sam tells a 'first, then, now' story with a missing subtrahend.

Okay, and we can see the equation there: 10 minus mm is equal to 2.

So, I wonder what story she tells to go with this.

Let's help her find the amount that was subtracted.

First, I had 10 sweets in the box, so here's her story.

And there's 10 is the whole.

Then some sweets were eaten.

We don't know how many, do we? Now there are 2 sweets left in the box.

So, 2 is the part remaining.

So, 10 minus mm is equal to 2.

If 10 is the whole, the parts must sum to 10.

We know 2 was the part that was remaining, so the other part must be 8.

That's right.

So, Jacob wants to use his number pairs to 10 to solve some subtraction equations.

Let's use the number shapes to help him.

10 minus mm is equal to 7.

And there's Sam.

She's saying, "If 10 is the whole, then the parts will sum to 10." Jacob says, "If I know the part remaining, the difference, then I can work out the parts subtracted." He can work out the subtrahend, can't he? So, there we go.

We can see there are 7 remaining in the equation; that's the difference.

So, the other part must have been 3.

Okay, so let's try a different equation then.

So, 10 minus mm is equal to 4.

Okay, so we've got 10 is the whole, and the part remaining, the difference, is 4 this time, isn't it? So, what will the subtrahend be? 10 minus 6 is equal to 4.

That's right.

Excellent.

Okay, and let's try another equation.

10 minus mm is equal to 2.

So, we've got there 10 is the whole, there were 2 remaining, so the parts subtracted must have been, that's right, 8.

Well done.

So, time to check your understanding of that.

Which of the following is the missing subtrahend in the equation? 10 minus mm is equal to 9.

Okay, is it 1, is it 0, or is it 2? Pause the video now while you decide.

Okay, and what did you think? That's right, it was 1.

10 minus 1 is equal to 9.

If 10 is the whole, then the parts must sum to 10.

We know 1 and 9 sum to 10, don't they? Okay, so Sam wants to solve this equation using a number line.

We can see she's got an empty number line there, hasn't she? 10 minus mm is equal to 5.

We know that the minuend is 10.

When a part is subtracted, we know the part remaining is 5.

When 10 is the whole, the parts will sum to 10.

So, the subtrahend end must be 5 because 5 and 5 sum to 10, don't they? They're the parts of 10.

Okay, so now it's time to check your understanding again.

Match the following to the missing subtrahend.

So, you've got two number lines there, but it doesn't tell us how many were subtracted, what the subtrahend was on each number line, does it? Okay? And you can see that the possible choices are it could be 6 or 7.

So, pause the video now while you match those to the correct choice.

Okay, and let's see how you got on.

So, the first number line has 10 as the whole.

And when we subtract some, the remaining part is 3.

So, it would be 7 that would be the subtrahend.

10 minus 7 is equal to 3.

Well done if you spotted that.

So, the other one, we had 10 as the whole, and the remaining part was 4, so it must have been 6 subtracted in this case; 10 minus 6 is equal to 4.

So, well done if you did that.

Now, we know our number pairs to 10 can help us find a missing subtrahend.

So, let's practise using these quickly, okay? Because the more we practise, the more confident we feel with it.

Okay? Are you ready? So, look at each equation and hold up the fingers to show the missing subtrahend.

10 minus mm is equal to 9.

Okay, so what do we think? That's right, we know 9 and 1 sum to 10, don't they? So, 10 minus 1 is equal to 9, okay? 10 minus mm is equal to 7.

That's right, the missing part will be 3 because 3 and 7 sum to 10.

10 minus mm is equal to 6.

That's right, you should have 4 fingers held up.

10 minus mm is equal to 2 this time.

2 is the part remaining.

So, that's right.

The other part should have been 8, shouldn't it? 10 minus 8 is equal to 2.

And what about 10 minus mm is equal to 8? That's right, this time 8 are remaining, aren't they? So, the other part must be 2.

That's right.

You might have used the equation before to help you with that.

8 minus mm is equal to 1.

That's right, if 1 is the part remaining, the other part of 10 must be 9.

Well done.

So, here is a task for the second part of our lesson.

Use your number pairs to 10 to find the missing subtrahends and write the equation for each.

Okay? And what do you notice? So, you're going to be a pattern spotter again.

See what you notice when you solve those.

Okay? So, pause the video now while you try that.

Okay? And here's the second part of our task.

Use your number pairs to 10 to solve the following.

So, we've got some equations with missing subtrahends.

So, we know the whole amount, okay, the minuend is 10; and we know the part remaining, don't we, the difference, which is at the end of the equation there, isn't it? Okay? And while you're solving these, I want you to think very carefully: can you use any of these equations to help you solve the next equation? Okay? So, you might be able to spot some patterns that can help you there.

So, have a think about that.

So, pause the video now while you try those.

Okay, and then here's the third part of our task, okay? So, choose 2 of the equations above to represent on a part-part-whole model.

Okay? So, pause the video now while you do that.

Okay, so let's see how you got on.

Okay, so if we have a look here, 10, and we don't know what was subtracted, but the remaining part of 10 was 1, so it must have been 9 that was subtracted.

10 minus 9 is equal to 1.

And there, we can see the equation there, can't we? And then, we've got here 10 minus, that's right, 8 is equal to 2, and there's the equation.

10 minus 7 is equal to 3.

There's the equation.

And 10 minus, that's right, 6 is equal to 4.

And there's the equation.

So, well done if you did that.

You may have noticed that, as the subtrahend decreases by one, the difference increased by one.

So, we were taking one less off every time, weren't we? So, the difference, the part remaining, was one more every time.

So, well done if you spotted that.

Okay, so the second part of our task now, let's see how you did.

So, we're using our number pairs to solve these subtractions.

So, we've got 10 minus 3 is equal to 7.

That's right, because 10 is the whole, and we know those are the parts.

Okay, 10 minus 7 is equal to 3.

10 minus 4 is equal to 6, and 10 minus 6 is equal to 4.

Are you spotting a pattern with these? 10 minus 2 is equal to 8; that's right, so 10 minus 8 is equal to 2.

10 minus mm, that's right, 10 minus 0 is equal to 10.

So, 10 minus 10 is equal to 0.

What did we notice there? Could we use anything to help us? You may have noticed that you can change the order of the subtrahend and the difference if the minuend is the same.

So, you can take away one part, and it leaves the other part, so it doesn't matter which part you take away, does it? Okay, and now let's have a look at part 3 then.

So, you may have chosen to do these 2 equations.

10 minus is equal to 7.

So, 10 is the whole, we know 7 is the remaining part, so the part subtracted must be 3.

Well done.

And then, on the other part-part-whole model, perhaps you did 10 minus mm is equal to 3, so the parts just subtracted in a different order.

So, that would've been 10; this time the part remaining was 3, and so the part subtracted was 7.

Okay? So, well done if you did that.

You've worked really hard in today's lesson, haven't you? You've done a really good job, so well done.

Okay, so let's think about what we've learned in today's lesson then.

We can use what we know about pairs that sum to 10 to help us solve subtraction equations.

That's what we've been doing, isn't it? And quickly remembering these number pairs is important for later work.

So, hopefully you'll be feeling much more confident with remembering and recognising those pairs now and knowing how to use them.

So, well done.

I've really enjoyed working with you today.