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.

Hello, and in this lesson we're going to be adding and subtracting to and from a two digit number crossing the tens boundary.

So this time, we're going to be working outside of our decades and thinking about numbers as they go from the twenties to the thirties, the thirties to the forties and so on.

So are you ready to do some adding and subtracting across the tens boundary? Let's get ready.

We've got lots of keywords in our lesson today.

We've got one more, one less, difference, decade and regroup.

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

So are you ready? My turn, one more, your turn.

My turn, one less, your turn.

My turn, difference, your turn.

My turn, decade, your turn.

My turn, regroup, your turn.

Wow, lots of words there, but I'm sure there's some you've used before.

So look out for them as you go through our lesson, they're going to help us with our learning.

There are two parts to our lesson today.

We're going to add and subtract one in the counting sequence, and then we're going to add and subtract one to and from a multiple of 10.

So let's make a start.

And we've got Alex and Sam helping us in our lesson today.

Alex and Sam are drawing a number line to help them to add and subtract one.

Can you see their number line's gone all the way from 40 up to 49? Sam says, "What is one more than 49?" Alex says, "I know when we add one to a two digit number, "the tens stays the same.

"One more must be 40-something," he says.

"So is one more than 49 40-10?" What do you think? Sam says, "There's no such number.

"When we're counting in ones and a two digit number ends in nine, "it is the end of the decade," ah.

So here are the forties.

That's what they've got on their number line, all the way from 40 up to 49.

"The next number will start the next decade." So what's the next decade? Oh, Alex says, "The decade after the forties is the fifties.

"So one more than 49 must be 50," the beginning of the fifties.

And there they are on the number line.

Both the tens and the ones digits change when we cross the tens boundary.

Let's use this learning to complete the stem sentences and write some equations.

So we can say that 50 is one more than 49.

50 is equal to 49 plus 1.

49 plus one is equal to 50.

And we can write our stem sentences and our equations each way round.

Alex says, "If 50 is one more than 49, "then 49 must be one less than 50." So let's complete the stem sentences, thinking about one less and some subtraction.

49 is one less than 50.

49 is equal to 50 minus one.

50 minus one is equal to 49.

And Alex says, "We can also say that 49 and 50 have a difference of one." They're next door to each other on the number line.

They are one more and one less than each other.

They have a difference of one.

So let's use the patterns on the number line to help us find one more and complete the stem sentences.

So we've got some gaps here.

Something is one more than 49.

49 is at the end of the forties, so one more must start the fifties decade.

We've looked at this one, haven't we? So 50 is one more than 49.

49 plus one is equal to 50.

50 is equal to 49 plus one.

What about the next one? Something is one more than 59, and we've got 59 on our number line.

So what's one more? That's right, it's 60.

60 is one more than 59.

59 plus one is equal to 60.

60 is equal to 59 plus one.

We've moved on into that next decade.

The decade after the fifties is the sixties.

What about the bottom number line then? Something is one more than 89.

So we're going to move to that next decade.

And the next decade starts with 90.

So 90 is one more than 89.

89 plus one is equal to 90.

90 is equal to 89 plus one.

So what do we notice when we add one more to a number with a ones digit of nine? Alex says, "When we add one to a number ending in nine, "we always reach the next multiple of 10." There's multiples of 10 for the 50, 60, 70, 80, 90, the decade numbers with a zero in the ones.

And that's the number we get when we add one to a number with a nine in the ones.

Let's see if we can use the pattern to find one less.

So we've got our number lines here ending in 50, 60 and 90.

So what is one less than 50? So we're going to go back into the decade before, aren't we? The decade before 50 is the forties.

So we can say that 49 is one less than 50.

50 minus one is equal to 49, and 49 is equal to 50 minus one.

What about the next number line? What is one less than 60? What's the decade before the sixties? Well, the decade before 60 is the fifties, and there are the fifties on our number line.

So we're thinking of one less than 60, and that must be 59.

59 is one less than 60.

60 minus one is equal to 59.

59 is equal to 60 minus one.

What about our last number line? We've got 90 on there.

What is the number that is one less than 90? Well, the decade before 90 is the eighties.

So there are our eighties written on.

Ooh, what's our missing number? That's right, 89 is one less than 90.

90 minus one is equal to 89.

89 is equal to 90 minus one.

So what do we notice when we subtract one from a multiple of 10? And Sam says, "One less than a multiple of 10 "always has a ones digit of nine." And we've gone back into the decade before the multiple of 10 we started on.

Time to check your understanding.

Can you complete the stem sentences and write the addition and subtraction equations to match? Pause the video and have a go, and we'll get back together for some feedback when you are ready.

How did you get on? So did you spot that 80 is one more than 79? 80 is equal to 79 plus one.

79 plus one is equal to 80.

And we can record that with an equation.

So what about thinking with subtraction? What is one less than 80? Well, 79 is one less than 80.

79 is equal to 80 minus one, and 80 minus one is equal to 79.

And there they are as equations.

And we can say that 79 and 80 have a difference of one, they are neighbours on the number line.

They may be in different decades, but they still have a difference of one.

So there's a pattern when we subtract one and we cross the tens boundary.

Let's look at the pattern on the Gattegno chart to help us.

Sam says, "What is one less than 90?" So remember, we're going to have a number with a nine in the ones, and we're going to be in the previous decade, the decade before.

And Alex says, "One less than a multiple of 10 always ends in a nine, "so it must be 89." And did you see how the Gattegno chart changed there? We had a tap on 90 and then a tap on 80 and nine.

90 minus one is equal to 89.

So Sam says, "What is one less than 80?" Well, 80 minus one is equal to 79.

One less than a multiple of 10 always ends in a nine, so it must be 79.

"What's one less than 70," then, says Sam.

Can you work this one out? One less than a multiple of 10 always ends in a nine, so it must be 69.

70 minus one is equal to 69.

One less than 70 is 69.

So perhaps you could continue this pattern on the Gattegno chart.

Time to check your understanding.

You're going to tap the number that is one less than the number shown, and then you're going to write an equation to represent it.

So tap the number that's one less and write an equation.

Pause the video, have a go.

And when you're ready, we'll get together for some feedback.

How did you get on? Did you remember that one less than a multiple of 10 always ends in a nine, and that the forties are before 50, so it must be 49? 50 subtract one is equal to 49, or you may have said 49 is equal to 50 subtract one or 50 minus one.

Sam is thinking of two numbers that have a difference of one.

She writes down one of the numbers.

So let's see if we can work out the other number.

So the number Sam writes down is 70.

And Alex says, "Any pair of numbers "that are one more or one less than each other "have a difference of one.

"I must find the number "that is one more or one less than 70." So he's tapped 70 on the Gattegno chart.

"One more than 70 is 71, "so your number could be 71.

"But one less than 70 is 69.

"Your number could be 69," he says.

And Sam says, "My other number is 69." So her number was one less than 70.

Time to check your understanding.

Which pair of numbers have a difference of one? Is it A, B or C? Pause the video, have a go.

And when you're ready, we'll get together for some feedback.

So which pair of numbers have a difference of one? That's right, it was C, wasn't it? 50 and 59, ooh, they look about right, but they don't have a difference of one.

If we counted 50 all the way up to 59, we've almost counted into the next decade.

And 69 and 79, well, the ones digits are the same there, so we haven't got to change in the ones, have we? But for C, 60 and 59, we can say that those numbers have a difference of one.

60 is one more than 59 and 59 is one less 60, so they have a difference of one.

Time for you to do some practise.

In part one, we'd like you to find the missing numbers.

So you're given one number of a pair, and you've got to find either the one that's one more or one less, depending on which way the arrows are going.

And you might want to use a number line, a Gattegno chart or a 100 square to help you.

And in question two, how many ways can you complete the following correctly? So we've got numbers there with the tens digits missing.

So how many different ways can you complete those? And remember, if you work systematically and in an order, then you might be able to find all the possible solutions.

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

And when you're ready, we'll get together for some feedback.

How did you get on? So for 1A, we were given 29 and we had to work out what was one more than 29.

And one more than 29 is 30.

We're adding one, we're going into the next decade.

Now we've got a number of something and one more is 40.

So we're looking at the number that's one less than 40.

So remember, we're going to end with a nine, but we're gonna go back to the previous decade.

So 39 is one less than 40.

What about 59? Can we find one more than 59? Well, we're at the end of a decade, aren't we? So one more is going to push us up into the next decade, which will be 60.

So 59 is one less than 60, 60 is one more than 59.

So for number two, you had to fill in the tens digits to create two numbers that had a difference of one.

So you could choose any pair of numbers where the tens digit had a difference of one.

So the tens digit with our nine had to be one less than the tens digit with the zero because we knew that that was the number that was one less than the next multiple of 10.

So we could have had 19 and 20, 29 and 30, 39 and 40, 49 and 50, 59 and 60, 69 and 70, 79 and 80, 89 and 90.

We couldn't go on any further because we only had tens and ones numbers, two digit numbers to work with.

So well done if you've got all of those correct.

And on into the second part of our lesson, and we're going to be adding and subtracting one to and from a multiple of 10.

So let's cross the tens boundaries without a number line.

We've got a bead string here.

And let's look closely at what happens.

So what is one more than 29? So we've got 29 beads on our string here, and then we've got a bar showing us where the next one comes in, one more.

So 29 is the same as two tens and nine ones.

When we add one to the nine ones, it makes a new 10.

Nine add one is equal to 10.

So we make one more whole group of 10.

So now we have three tens, which is 30.

So when we add one to a number ending in a nine, it will make a new 10.

That means one more than a number ending in a nine will always be a multiple of 10.

Let's explore the number patterns that we see on a number line.

So here, we've got nine and one more, and that will equal 10.

19 and one more will equal 20.

29 and one more will equal 30.

39 and one more would equal 40.

49 and one more would equal 50.

Sam's going to use the Base 10 blocks to show that one more than 29 is equal to 30.

So let's see if she's right.

So she's got 29, and she's going to add one more.

So you can see she's added one more to the set on the right hand side of the screen.

So now she's got 10 ones, and the 10 ones she can regroup as one 10.

So she's gone from two tens and nine ones to three tens.

29 plus one is equal to 30.

"When I added one to the nine," she says, "It made a new 10." And she regrouped the 10 ones into one 10.

"So now I have three tens," she says, "Which is 30." Time to check your understanding.

Which number will be one more than 39? And you might want to use Base 10 blocks to prove that you've got the correct answer.

So pause the video and decide whether A, B or C is the number that is one more than 39.

And when you're ready, we'll get together for some feedback.

How did you get on? Which number do you think is one more than 39? Well, there's 39.

We've added in one more.

We regroup our 10 ones as one 10, and we've got four tens, which is 40, so B was the correct answer.

Sam's going to use a bead string to find one less than 30.

So we can see she's got 30 here on her bead string.

So 30 is the same as three tens, but we're going to subtract one from one of the tens when we find one less.

So 10 subtract one is equal to nine.

So now we have two tens and nine ones or 29.

So the number that is one less than a multiple of 10 will always have a ones digit of nine.

And there, we can see the bead popping off as well.

So we started with three tens.

We took away one one from one of those tens, and we've ended up with two tens and nine ones.

So one less than 30 is 29.

Alex says, "One less than 70 will be 69." And he uses Base 10 blocks to prove it.

So he says, "70 is the same as seven tens.

"To subtract one, "first we regroup one 10 for 10 ones." So he's got his seven tens, but he's going to regroup one of those tens for 10 ones.

Now he can subtract his one.

So 10 minus one is equal to nine.

So now we have six tens and nine ones or 69.

So 70 minus one is 69.

One less than 70 is 69.

Time to check your understanding.

Which number will be one less than 60? And can you use the Base 10 blocks to prove it? Pause the video, have a go.

And when you're ready, we'll get together for some feedback.

How did you get on? So did you remember how Alex had used the Base 10 blocks to help him? So 60 is six tens.

If we exchange one 10 for 10 ones and then subtract one, we'll have five tens and nine ones left.

So 60 subtract one is equal to 59.

So the correct answer was C.

One less than 60 is 59.

All the children are playing a game with some number cards.

They have to find pairs with a difference of one, and the person with the most pairs wins.

So let's help them.

Sam says, "80 is one more than 79, "so 79 and 80 have a difference of one." Is she right? That works, doesn't it? One more than 79 is 80, one less than 80 is 79.

I wonder what Alex is going to choose.

What would you choose next? Oh, Alex says, "59 is one less than 60, "so 59 and 60 have a difference of one." They sit next to each other on a number line if we're counting in ones, don't they? So 59 is one less than 60.

60 is one more than 59.

They have a difference of one.

What would you choose next for Sam? Oh, Sam says, "The difference between 90 and 89 is one." So she spotted those two numbers.

I wonder what Alex is going to choose.

Oh, he says, "69 plus one is equal to 70, so they have a difference of one." 69 and 70.

70 is one more.

Sam says, "I can see 49 and 40." Are those a pair of numbers with a difference of one? Alex says, "One less than 40 would be 39, "so that's not correct.

"But 49 and 50 have a difference of one," he says.

"Oh, well done," says Sam, "You have the most pairs, you've won." I don't think there are any other pairs we can make of numbers that have a difference of one now, are there? So Alex found three pairs and Sam found two.

So Sam says a two digit multiple of 10, and Alex has to write the number that is one less.

So let's see if we can predict the number he'll write.

Sam says 70, and he's got to write the number that's one less.

He says, "The sixties are before 70, "so it must be 69." Did you get that too? Sam says 30 now.

Oh, what's Alex gonna say? He says, "The twenties are before 30, "so it must be 29." 29 is one less than 30.

Sam says 40.

What do you say? What's the number that's one less than 40? Alex says, "The thirties are before 40, "so it must be 39." He's getting good at this, isn't he? Are you getting good at this too? Perhaps you could try this game with a partner.

And time to check your understanding.

Alex says, "50 minus one is equal to 39." Is he right? Use the bead string or Base 10 blocks to prove it.

Pause the video, have a go.

And when you're ready, we'll get together for some feedback.

So was Alex right? Well, to subtract one from 10, we must exchange the 10 for 10 ones.

So we're going to regroup them.

So our one 10 becomes 10 ones.

Now we've got four tens and 10 ones.

We've still got 50.

But we've got some ones, and we can take away a one.

So 10 ones minus one is equal to nine ones.

So we'll have four tens and nine ones left, so 49.

So Alex wasn't correct this time.

50 subtract one or one less than 50 is 49.

Alex wants to use his knowledge to try and find the missing number in these equations.

He draws a number line to help him.

He says, "Something is equal to 71 subtract one." So there's 71, and he's shown that he's jumped back one on the number line, he's subtracted one.

Where would he land? Ah, he says, "One less than 71 is 70." So 70 must be equal to 71 subtract one.

What about 70 plus one? He says, "I think I can use the same number line "to solve the next equation.

"If 70 is one less than 71, "then 71 is one more than 70." So the answer to our next equation must be 71.

He needs a new number line this time, doesn't he? He says, "79 minus one means one less than 79." So what is one less than 79? We can use our knowledge of one less than nine, can't we, because we know that we're within a decade, so the tens digits won't change.

Ah, it's 78.

One less than 79 is 78.

And then he says, "79 plus one means one more than 79." And he's just done lots of work on that.

He says, "That will be 80." One more than 79, we're into the next decade, which is the eighties.

So 79 and one more is equal to 80.

Well done, Alex, was really good use of a number line to help you solve those.

Time for you to do some practise.

So use what you know to find the missing numbers, and you might want to draw a number line to help you as well.

Pause the video, have a go.

And when you're ready, we'll get together for some feedback.

How did you get on? So for A, we had 40 in the middle, and we had to find one less and one more.

Well, one less than 40 is 39.

We know that one less than a multiple of 10 will have a nine in the ones and will go back into the previous decade.

So the decade before the forties is the thirties, so it'll be 39.

And one more than 40 will be 41.

So something is equal to 40 minus one.

Well, that's the one less, isn't it? So that must be 39.

And 40 plus one is equal to something.

Well, that's the one more, so that's 41.

So we've just written equations to match the thinking we'd done to fill in those missing numbers.

So what about B? Something is equal to 30 plus one.

Well, 30 plus one, that's one more than 30, so it must be 31.

And then something is equal to 30 minus one.

30 minus one must be one less than 30.

So we think back to the next decade, and nine in the ones, 29.

So next, we've got 49 plus one.

So one more than 49 is equal to 50.

And then 49 minus one, one less than 49.

So we don't have to think about another decade here.

We can use our fact that nine minus one is equal to eight, so 49 minus one must be equal to 48.

So the next one is something is equal to 61 minus one.

Or 61 minus one, we're taking away one, so it's one less than 61, which is 60.

And then we've got 60 plus one, so we're thinking one more, which is 61.

So for C, 60 is equal to something minus one.

Ooh, so something minus one, so we've gone for a one less.

So 60 must be one less than 61.

61 minus one is equal to 60.

Something minus one is equal to 59.

So we know the sort of two parts here, we don't know the whole.

So something minus one is equal to 59.

So the answer must be one more than 59, which is 60.

And we can use the same thinking for something minus one equals 70.

So our whole must be one more than 70, which is 71.

And 71 is equal to something minus one.

Ooh, so 71 and one are our parts, so our whole must be 72.

71 is equal to 72 minus one.

80 is equal to 79 plus, well, 80 is one more than 79, so it must be plus one.

And if 79 plus one is equal to 80, then 80 minus one must be equal to 79.

One less than 80 is 79.

I hope you were able to use all your thinking about one more, one less and about crossing decades.

And maybe you used a number line to help you with those, but I hope you were successful.

Well done if you were.

And we've come to the end of our lesson.

We've been adding and subtracting one to and from a two digit number, crossing a tens boundary this time.

What have we learned about? We've learned that finding one more is the same as adding one, and finding one less is the same as subtracting one.

And numbers that are one more or one less than each other have a difference of one.

When we add one to a number with a ones digit of nine, we will reach the next multiple of 10.

And when we subtract one from a multiple of 10, the number we reach will have a ones digit of nine.

And it'll be from the decade before, won't it? And when we change one 10 for 10 ones or 10 ones for one 10, it's called regrouping.

And that was really useful when we were adding to a number with a nine in the ones or subtracting from a multiple of 10.

Thank you for all your hard work and your mathematical thinking in this lesson.

I've really enjoyed it.

I hope you have too.

And I hope I get to work with you again soon, bye-bye.