Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in today's maths lesson.

It's from our unit, "Adding And Subtracting Ones And Tens To And From Two-Digit Numbers." So we're going to be looking at two digit numbers, and we're going to be thinking about adding and subtracting and hopefully using our known facts to help us.

So if you're ready, let's make a start.

So in this lesson, we're going to be using our number bonds to add and subtract one-digit and two-digit numbers.

So how are your number bonds? Have you been practising them? I hope so, 'cause we're going to be using them a lot in our lesson today.

We've got two key words.

We've got sum and difference.

So I'll take my turn to say them, and then it'll be your turn.

So my turn, sum, your turn.

My turn, difference, your turn.

Well done.

I'm sure you've used those words before.

Look out for them in today's lesson though, 'cause they're going to be really useful when we are talking about our additions and subtractions.

There are two parts to our lesson today.

In the first part, we're going to be using number bonds to add, and in the second part, we're going to be using number bonds to subtract.

So let's make a start on part one.

And we've got Alex and Sam helping us with our learning today.

So the children use a 10 frame to represent this equation.

Can you see we've got 7 + 3? We've got 7 blue counters, and we've added 3 red counters, so our sum is 10.

Alex is going to add another full 10 frame.

I wonder what the equation would be now.

Can you think? How many has he got? Well, Sam says, "Now, there are 17 blue counters and 3 red counters." And Alex says, "We would represent this as 17 + 3." And we can see that it's equal to 20.

We've got two full 10 frames, so we've got 20.

We know we can use known facts to help us solve new facts.

So here's our 7 + 3, which is equal to 10.

Let's look at the pattern we see when we add 10 to our known fact.

So what have we got now? We know that 7 + 3 is equal to 10, so we also know that 17 + 3 is equal to 20.

We've got 17 blue counters and we're adding those 3 red counters.

And there it is as an equation.

"We found a new fact," says Sam.

"Let's keep exploring." There's another whole 10.

What have we got now? Well, if we know that 7 + 3 is equal to 10, we also know that 27 + 3 is equal to 30.

We've got 27 blue counters and 3 red counters.

We've added another 10 blue counters.

27 + 3 is equal to 30.

Let's keep going.

There's another 10.

What have we got now? Well, we've now got 37 + 3 is equal to 40.

37 blue counters plus 3 red counters is equal to 40 counters in total.

And we can see those four full 10 frames.

What's the same and what's different? Well, Sam says, "The ones digits stay the same.

There are 3 ones and 7 ones each time, but the tens digits are changing." First, well, we have no tens, then 1 tens, then 2 tens, then 3 tens.

But we know that 7 + 3 is equal to 10, so we're always going to get to that next multiple of 10.

Let's look at the sum in each equation.

Let's use a bead string.

What do you notice now? Sam says, "In each equation, the sum is a multiple of ten." It's a whole number of tens.

We could see that in our 10 frames.

Alex says, "I wonder why." Do you know why? Let's find out.

So we've got 7 beads and we're adding three beads, and 7 + 3 is equal to 10.

Well, now we've got 17 beads, 1 whole ten and 7 ones, and we're going to add those three extra ones.

And what do you notice? The 7 + 3 of our red beads completes another ten, so 17 + 3 must be equal to 20.

2 whole tens.

What's gonna happen when we add in another ten? Now, we've got 27 beads and we're going to add in the extra three.

And can you see again we've completed that ten.

So 27 + 3 is equal to 30.

Sam says, "Each time 3 is added to 7, it makes a new ten, so the sum is always a multiple of ten." A whole number of tens.

Over to you to check your understanding.

Can you use a bead string or some ten frames to find an equation that would follow the same pattern in the ones digits as the equation below? So we've got 37 + 3 equals something.

So pause the video, have a go, and see if you can create another equation that would follow the same pattern.

Have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Well, you could have had any equation that had 3 ones added to 7 ones.

So for example, you could have had 37 + 3 is equal to 40.

Can you see that 7 in the 37 and the 3 that we're adding? So what else could we have had? Well, we could have had 47 + 3 is equal to 50.

47 has that 7 ones added to 3 ones to make another 10.

57 + 3 is equal to 60, 67 + 3 is equal to 70, 77 + 3 is equal to 80, 87 + 3 is equal to 90, and you might even have had 97 + 3 is equal to 100.

10 lots of ten.

Let's explore the pattern on a number line.

So can you see we've got our 7 + 3 is equal to 10? We're on 7 on the number line, and we've jumped on another 3, and we've landed on 10.

17 + 3.

So there's 17 + 3 and we're going to land on 20, the next whole 10.

27 + 3 is equal to 30.

37 + 3 is equal to 40.

47 + 3 is equal to 50.

What stays the same in each equation? Sam says, "I noticed that in each equation, there are 7 ones, and then 3 ones are added." Can you see the 7 ones in each of our first addends? And then the second addend is always a 3.

She says, "In each equation, the ones digits sum to ten, so the sum is always a multiple of ten." 7 + 3 is equal to 10.

What changes in each equation? Sam says, "The number of tens changes in each equation." We went from having no tens in our addends to having 1 ten and 7 ones, 2 tens and 7 ones, 3 tens and 7 ones, and 4 tens and 7 ones to make our first addends.

The sum in each equation is always the next multiple of ten after the first addend.

So let's look at 27 + 3.

27 + 3 is going to take us to the next multiple of ten.

We had 2 tens for though we were in the twenties, so our next multiple of ten is 30.

And there we can see them highlighted on the number line.

Let's use this pattern to calculate 57 + 3.

So there's 57, and we're going to add 3, we're going to end up on the next multiple of ten after 57, which is 60.

57 + 3 is equal to 60.

Over to you to check your understanding.

Can you tick the equation that correctly completes the following? So we've got, "I know that 7 + 3 is equal to 10, so I know that.

." So which one completes the following? A, B, or C? Pause the video, have a think, and when you're ready, we'll get together for some feedback.

How did you get on? Which one was it? Did you remember that you could imagine a number line to help you? That was it.

It was A, 97 + 3 is equal to 100.

We can see that 7 ones in the 97 plus 3 ones, and the next multiple of ten after 90 is 100.

Well done if you got that right.

Sam thinks about these patterns and realises something new.

She says, "If a number has a ones digit of 6 and 4 is added, the sum will always be a multiple of ten." Is she right? What do you think? She says, "I'll try some different examples to find out." Good idea, Sam.

46 has a ones digit of six.

There's 46.

4 tens, 40, and 6.

And she's represented it with base 10 blocks.

4 tens for 40 and 6 ones for the 6.

She says, "I will add 4 to the 6 ones.

So 6 + 4, you know what that's going to make, don't you? So if we've got 46 + 4, she says, "I know that 6 + 4 is equal to 10, so I know that 46 + 4 must be equal to 50." She's made another whole 10 by adding 6 and 4, hasn't she? So instead of 4 tens, we've now got 5 tens.

46 + 4 is equal to 50.

She says, "86 has a ones digit of 6." And there it is, 86 represented in a part-part-whole model and with her base 10 blocks, 8 tens, and 6 ones.

I will add 4 to the 6 ones.

6 + 4.

She says, "I know 6 + 4 is equal to 10, so I know that 86 + 4 must be equal to 90." When she adds on those extra 4 ones to the 6 ones, she creates another ten.

So instead of having 8 tens, she has 9 tens.

So 86 + 4 is equal to 90.

"I was right," she says.

"6 + 4 = 10, so a number with 6 ones added to a number with 4 ones will always sum to a multiple of ten." Well done, Sam.

Great exploring.

The children are trying to find the missing digits in this equation.

So we've got something 2 plus something equals something with a zero in the ones.

Hmm, I wonder if you can think what's going on here.

Sam says she knows what the second addend must be.

Ooh, do you know what the second addend must be? You might want to have a little think before Sam tells us.

I wonder how she knows.

Ah, she's thinking about how we would partition that first number.

It's a two-digit number.

So we've got some tens and 2 ones.

And there we have a bead string, and our mystery box is covering up however many tens we've got, but we can see our 2 ones.

Ah, Sam says we need 2 + 8.

2 + 8 is equal to 10.

She knows that, and I expect you know that too.

Why is that important? She says, "If there are 2 ones in one addend, the other addend must have 8 ones if the sum is a multiple of ten." Let's just think about that again.

If there are 2 ones in one addend, the other addend must have 8 ones if the sum is a multiple of ten.

And we know the sum is a multiple of ten because we can see, after the equal sign, we've got a two-digit number with a zero in the ones column.

Good thinking, Sam.

I wonder if you've got that thinking too.

She says, "I would use the known fact 2 + 8 is equal to 10 to help me solve this equation.

"Now, I'll pick a tens digit to show one possible correct solution." Because she's realised there could be more than one possible solution here.

Which tens digit would you pick? Ah, Sam's picked 20.

So she knows her first addend must be 22 and she's adding 8 so her sum will be 30.

And we can see that on the bead string.

Over to you to check your understanding.

Can you find another possible solution to the equation that Sam was working on? Pause the video, have a think, and when you're ready, we'll get together for some feedback.

How did you get on? So we know that 2 + 8 = 10, so the ones digit must be an 8 that we're adding.

So we can put our 8 in.

And we can see there, 2 + 8 is equal to 10.

The tens digit in the whole must be one more than the tens digit in the first part.

Ah, so because we are adding 8, we're going to get to that next multiple of ten.

So the tens number in our first addend has got to be 1 ten less than the ten in our sum or in our whole.

So we could have had 12 + 8 is equal to 20, 22 + 8 is equal to 30, 32 + 8 is equal to 40, 42 + 8 is equal to 50, 52 + 8 is equal to 60, 62 + 8 is equal to 70, 72 + 8 is equal to 80, 82 + 8 is equal to 90.

That's as far as we can go 'cause we've only got a two-digit number as our sum.

Great thinking.

I wonder if you found all of those possible answers.

Time for you to do some practise.

So for question one, you're going to use a 10 frame, a Base 10 blocks, or a bead string to help you to find the numbers to complete the pattern.

And you can see we've got some part-part-whole models there with some gaps.

You are going to complete those gaps.

I wonder if there's a pattern you can use.

And remember to use the stem sentences we've been using.

If I know that hmm plus hmm is equal to 10, I know that hmm plus hmm is equal to.

Another multiple of ten.

For the next part, you're going to complete these part-part-whole models.

And then for question two, you're going to use a known fact and you're going to draw part-part-whole models to show a pattern.

So pick a known fact to 10 that you know and see if you can work it out with some numbers that are above 10.

And for question three, you're going to fill in the missing numbers in these equations and think about the fact that you use to help you.

So pause the video, have a go at all your tasks, and when you're ready, we'll get together for some feedback.

How did you get on? So for question one, you had to fill in the missing gaps.

So what was the fact we were using? So for A, we knew that 1 + 9 is equal to 10.

So 1 + 19 was equal to 20, 1 + 29 was equal to 30, and 1 + 39 was equal to 40.

So the known fact we'll be using was 1 + 9 is equal to 10.

What about B? Well, we've got a 2 and a 10.

So the 2 is a part and 10 is a whole.

So if 2 is a part and 10 is the whole, the other part must be 8.

So we can use that stem sentence.

I know that 8 + 2 is equal to 10, so I know that 2 + 18 is equal to 20, 2 + 28 is equal to 30, and 2 + 38 is equal to 40.

Question two is over to you.

I wonder which number bond you used to help you.

We've used 3 + 7 is equal to 10.

So if we know that, we also know that 3 + 17 is equal to 20, 3 + 27 is equal to 30, 3 + 37 is equal to 40, 3 + 47 is equal to 50, and all the rest of those facts right up to 3 + 97 is equal to 100.

I wonder which fact you chose.

And for question three, you had to fill in the gaps.

So we've got 41 + 9 is equal to 50.

Oh, can you see what's happened now? Now, we've got 42 + 8 is equal to 50.

So we're using a different number bond to 10 each time to help us.

We've used 1 + 9 is equal to 10, 2 + 8 is equal to 10, and we know that 3 + 7 is equal to 10, so 43 + 7 is also equal to 50.

What about the next set in A? 10 is equal to 5 + 5, 20 is equal to 15 + 5, and 30 must be equal to 25 + 5.

We're making that next multiple of 10.

So let's have a look at B.

50 is equal to something plus five.

Hmm.

So we've got to think of the two-digit number now.

Were adding five to it so there must be a 5 in the ones, and the tens must be 1 ten less than our sum so it must be 45 + 5.

So can we use that same thinking for 60? 60 is equal to 55 + 5.

Now, we've got some missing wholes to fill in.

Something is equal to 65 + 5.

Oh, that's 70, isn't it? 80 is equal to 75 + 5, 90 is equal to 85 + 5, and 100 is equal to 95 + 5.

We were using our known fact 5 + 5 is equal to 10 for all of those.

And what can we see in C here? Ah, this was the one Sam was exploring.

54 + 6 must be equal to 60.

So that was using 4 + 6 is equal to 10.

Now we've got 55, so what are we going to add to 55 to get to our next multiple of ten? Well, we know that 5 + 5 is equal to 10, so 55 + 5 must be equal to 60.

And 56, well, we know that 6 + 4 is equal to 10, so 56 + 4 must be equal to 60.

Now, in our next set, our sum, our whole is 60 each time.

So we've got to think about the other part of our number that goes with our number fact.

So we've got three plus something.

Well, it must be a 3 + 7, so it must be 57 + 3.

And if it was 57 + 3, it must be 58 + 2 and 59 + 1 that give us a sum of 60.

And all the number bonds to 10 were useful to solve different equations.

And on into the second part of our lesson.

We're going to use number bonds to subtract.

So the children draw a part-part-whole model to represent the counters on the 10 frame.

We're thinking subtraction this time.

So we've got 10 as our whole, 7 is a part, and 3 is a part.

Alex thinks he can also represent them as a subtraction equation.

He says, "We would represent this as 10 - 3 is equal to 7." He's thought about those 3 red counters as the 3 that we are subtracting.

We could have written 10 - 7 = 3, but he's thinking about taking away, subtracting the 3 red counters, so 10 - 3 is equal to 7.

Sam adds another full 10 frame.

What would the subtraction equation be now? What's our whole and what are we subtracting? Ah, so we've now got 20 in our whole and we're subtracting those 3 red counters again.

And 20 - 3 is equal to 17.

We've got 1 whole ten left and 7 ones.

Let's look at these equations.

So 10 - 3 was equal to 7.

We know that 10 - 7 is equal to 3, we've added another whole ten in now, so we also know that 20 - 3 is equal to 17.

Sam says, "We've found a new fact.

Let's keep exploring." We've added another whole 10 frame.

So what have we got now? We've got 30 as our number that we're starting with.

30 is our minuend.

So if we know that 10 - 3 is equal to 7, we also know that 30 - 3 is equal to 27.

Can you see if we take away those 3 red counters, we've got 2 whole tens and 7 ones, 27.

Add another whole 10 frame, what have we got now? Well, we know also that 40 - 3 must be equal to 37.

What's the same and what's different? Well, the ones digits stay the same.

3 ones are subtracted from each multiple of ten, so there's 7 left in the ones each time.

But the tens digits are changing.

That's what's different, isn't it? Let's look at this on a bead string.

So let's look at the whole in each equation.

What do you notice? So we've got 10 as our whole in our first equation.

And in each equation, the whole is a multiple of ten.

And Sam says, "If we subtract 3 from 10, it will leave 7 each time." So 10 - 3 is equal to 7.

20 - 3 is equal to 17.

If we subtract 3 from 20, there will be 1 ten and 7 ones left.

And if we subtract 3 from 30, there will be 2 tens left and 7 ones, 27.

"If we subtract 3 from a multiple of ten," Alex says, "there will always be 7 ones left." Time to check your understanding.

You might want to use a bead string or some 10 frames, and you're going to find an equation that would follow in the same pattern with the ones digits as the equation below.

40 - 3 is equal to.

So pause the video, have a go, and when you're ready, we'll get together for some feedback.

So you could have had any equation that had 3 ones subtracted from a multiple of ten.

I hope you got all those.

I wonder if you worked systematically to find them all.

So let's explore this pattern on a number line.

We've got 10 - 3 is equal to 7.

What if we start on 20? 20 - 3 is equal to? Well, it's got to have a 7 in the ones and it's in that next decade back, so it's 17.

20 - 3 is equal to 17.

What about 30- 3? Well, we've gone back into the twenties and we know there's going to be a 7 in the ones of our answer.

30 - 3 is equal to 27, 40 - 3 must be equal to 37, and 50 - 3 must be equal to 47.

What stays the same in each calculation? Ah, in each calculation, 3 is subtracted from a multiple of ten, so there are always 7 left in the ones.

And we can see that with those numbers highlighted on the number line.

What changes in each calculation? All the number of tens changes in each calculation.

We start on a multiple of ten and we end up in the previous decade, so with one less in our multiple of ten and 7 ones.

Well, let's use this pattern then to calculate 60 - 3.

So there's 60, and if I subtract 3 from a multiple of ten, Alex says there must be 7 ones left and I've gone back into my previous decade.

So 60 - 3 must be equal to 57.

Over to you to check your understanding.

What other equations could you write that follow the pattern? Pause the video, have a go, and when you're ready, we'll get together for some feedback.

What did you think? Well Alex says, "When the whole is a multiple of ten, there are always 7 ones left in the ones when you subtract 3." I wonder if you found all of those.

Sam thinks about these patterns and realises something new.

She says, "When 4 is subtracted from a multiple of ten, there will always be 6 left in the ones." Is she right? She's going to try some different examples to find out.

50 - 4.

Well, 50 is made of 40 and 10.

So there's our 40 and 10 more.

She says, "I must subtract 4 ones, but there are no ones, so I must regroup 1 ten into 10 ones." So there we go.

She's regrouped her ten into 10 ones.

So we've still got 5 tens, we've just regrouped one of them.

She says, "I know that 10 - 4 is equal to 6, so I know that 50 - 4 must be equal to 46." So if she takes away 4 ones, she's got 4 tens and 6 ones remaining, 46.

She's going to try it with 90 - 4 now.

She says, "90 is made of 80 and another 10." Partitioning into 80 and 10 is quite important because she's got to subtract four and she hasn't got any ones on their own, so she's going to regroup that 10.

She knows that 10 - 4 is equal to 6, so she knows when she subtracts four, she's going to have 8 tens and 6 ones, so she must have 86.

So 90 - 4 must be equal to 86.

She says, "I think I'm right.

There will always be 6 left in the ones when I subtract 4 from a multiple of ten." The children write some equations and give each other clues to help them find the missing ones.

So Sam says, "My minuend was a multiple of ten and my difference had 3 ones.

What can you tell me about the subtrahend?" There's her equation.

And Alex says, "I know 10 - 7 is equal to 3, so 7 must have been subtracted from a multiple of ten to leave 3 ones in the difference." Great thinking, Alex.

Well done.

Right, Alex's turn.

He says, "I subtract 9 from a multiple of ten.

What can you tell me about the difference?" Hmm.

Well, Sam says, "I know that 10 - 9 is equal to 1, so when I subtract 9 from a multiple of ten, the difference will have a ones digit of 1." Excellent thinking, Sam.

Well done.

Did you get that too? Time for you to do some practise.

So you are going to use a 10 frame, or Base 10 blocks, or a bead string to help you to find these missing numbers to complete the pattern.

And remember to use the stem sentences.

In B, again, you're going to find the known fact that will help you to complete the missing numbers in these part-part-whole models.

For two, you're going to choose a known fact of your own and draw the part-part-whole models to show the pattern.

And then question three, you are going to fill in some missing numbers and think about which facts you used.

So lots to get on with there.

Pause the video, have a go at your tasks, and when you're ready, we'll get together for some answers and feedback.

How did you get on? So for question one, we had the known fact there that if 10 is the whole, 1 is a part, and 9 is a part, so we might have thought 10 - 1 is equal to 9.

And we can use that to fill in the missing numbers in our part-part-whole models.

So if 1 + 9 is equal to 10, then 1 + 19 must be equal to 20.

If 30 is the whole and 29 is a part, we must have subtracted a 1.

So one is our other part.

And if 1 is a part and 40 is a part, we know that 1 + 9 is equal to 10, so 1 + 39 must be equal to 40.

And in B, we knew that 10 - 2 was equal to 8.

So we also knew that 20 - 2 would be equal to 18, 30 - 2 would be equal to 28, and 40 - 2 would be equal to 38.

I wonder what fact you chose.

We chose 10 - 7 is equal to 3, so we were able to complete all of these part-part-whole models.

So if 10 - 3 is equal to 7, then 20 - 3 must be equal to 17, 30 - 3 must be equal to 27, and 40 - 37 must be equal to 3.

And we can also carry on that pattern and complete all the rest of our part-part-whole models using our known fact 10 - 7 is equal to 3.

And for question three, you had some missing numbers to fill in.

So for A, 10 - 3 is equal to 7, so 20 - 3 must be equal to 17 and 30 - 3 must be equal to 27.

What fact were we using for B? Well, we've gotta subtract eight equals two, so 10 - 8 = 2, so we must be starting with multiples of ten here.

70 - 8 is equal to 62, 80 - 8 is equal to 72, and 90 - 8 is equal to 82.

What about C? Well, we've got some subtract fives here.

We know that 10 - 5 is equal to 5, so we are looking for ones digits of five.

So 50 - 5 is equal to 45 and 60 - 5 is equal to 55.

Now, we've got that missing subtrahend, the missing number we're taking away, but we can see those fives again.

So 70 - 5 is equal to 65, 80 - 5 is equal to 75, 90 - 5 must be equal to 85, and 100 - 5 must be equal to 95.

And those were the known facts that helped with these equations.

Then we had to continue some patterns in D.

So we were thinking about 10 - 1 = 9.

So this time, we knew that all our differences would have a 9 in the ones, and so we could have continued the pattern like that.

And for E, our pattern was slightly different.

Did you notice that the difference was one less each time? So we were doing 60 subtract something and we were using our different number facts each time.

So 56 is equal to 60 - 4, so we can complete the pattern like this.

Each time we were subtracting one more and so our difference was getting one less as well.

Wow, you've done some really hard work in this lesson and we've come to the end of it.

We've been using number bonds to 10 to add and subtract one-digit and two-digit numbers.

So what have we learned about? We've learned that when the ones digits in an equation sum to ten, the sum in the equation will always be a multiple of ten.

So for example here, we know that 2 + 8 is equal to 10, so 42 + 8 must be equal to a multiple of ten.

50 in this case.

And that when subtracting a one-digit number from a multiple of ten, you can use your number bonds to ten.

The number being subtracted and the ones digit in the difference will be a number bond to ten.

So here we can see 50 - 8 is equal to 42.

We know that 8 + 2 is equal to 10, so we know that when we subtract eight from a multiple of ten, there will always be a 2 in the ones digit.

Thank you for all your hard work and your mathematical thinking today.

I hope you've enjoyed the lesson and I hope I get to work with you again soon.

Bye-bye.