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 1s and 10s 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 today's lesson, we're going to be adding and subtracting one to and from a two-digit number within a decade.

So are you ready to make a start? Let's get going.

We've got three keywords in our lesson today.

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

So I'll take my turn to say them, and then you can repeat them.

Are you ready? My turn, one more.

Your turn.

My turn, one less.

Your turn.

My turn, difference.

Your turn.

Excellent.

Watch out for those words as we go through our lesson today.

They're going to be really useful, and they're going to help us to think about the numbers we're working with.

So there are two parts to our lesson today.

In the first part, we're going to be thinking about one more and one less in the counting sequence, so as we're counting.

And in the second part, we're going to be thinking about patterns in the one digits when we're adding and subtracting 1.

So let's get started with part one.

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

So Sam is counting along the number line from different starting points.

When she stops counting, Alex has to say the number that is one more or one less than the number she's got to.

Shall we have a go with Sam? Let's start counting.

40, 41, 42, 43, 44, 45, 40, oh, 46.

Sam stopped there.

So she says to Alex, "What is one more than 46?" I wonder if you know.

Alex knows.

Alex says, "47 is one more than 46.

47 is equal to 46 plus 1.

46 plus 1 is equal to 47." And he's shown that jump of one more with his arrow on the number line.

Sam says, "So what is one less than 47?" "Oh," says Alex, "46 is one less than 47.

46 is equal to 47 minus 1, and 47 minus 1 is equal to 46." And he's shown that with one jump backwards down the number line, a jump of one.

He says, "I could also say that the difference between 46 and 47 is 1." There's a count of 1 to go forwards from 46 to 47 or backwards from 47 to 46.

So the difference is 1.

Sam picks another number.

Ooh, what's she picked this time? Well, she says, 'What is one more than 56?" I wonder if you know.

Alex says, "57 is one more than 56.

57 is equal to 56 plus 1, and 56 plus 1 is equal to 57." And there he's shown that jump of one more with his arrow on the number line.

Ah, but Sam says, "So what is one less than 57?" Do you know? Alex says, "56 is one less than 57.

56 is equal to 57 minus 1.

57 minus 1 is equal to 56." And he's shown his jump subtracting 1, showing -1 one going backwards from 57 to 56 on the number line.

I think Alex is quite good at this, isn't he? Oh, he says, "I could also say that the difference between 56 and 57 is 1." You have to count on one more to get from 56 to 57 and one less to count back from 57 to 56.

Well done, Alex.

So let's look at the number pairs that Alex and Sam chose.

What's the same, and what's different? I wonder if you can see anything there.

So Alex said that 47 is one more than 46, and he also said that 57 is one more than 56.

Do you spot something there? Let's have a think about the less than.

Alex said that 46 was one less than 47 and that 56 is one less than 57.

He also talked about the difference, didn't he? So the difference between 46 and 47 is 1, and the difference between 56 and 57 is 1.

And we can see that jump of one shown by the arrow on the number line.

Is there something you've spotted? Well, Sam says, "I noticed that in each pair of numbers, the ones digits follow the same pattern.

7 is one more than 6.

So 47 is one more than 46." And Alex says, "And 57 is one more than 56." So if we know that 7 is one more than 6, we know those other facts as well when we're looking at numbers in the 40s and numbers in the 50s.

I wonder if it will work for other decades as well.

What about the one less bit? Ah, Alex says, "6 is one less than 7, so 46 is one less than 47." "And," says Sam, "56 is one less than 57." Let's find out if the same pattern happens in other decades.

We were looking at the 40s and the 50s.

Now we've got some other decades to look at.

So we've still got our 6 and 7 on our number line from 0 to 10.

7 is one more than 6.

So that means that 37 is one more than 36.

And can you predict what it's going to be on our bottom number line? And 87 is one more than 86.

Well done if you spotted those.

So let's complete the stem sentences and think about those as addition sentences.

So 7 is equal to 6 plus 1.

So 6 plus 1 is equal to 7.

What's that going to look like for our number line when we're in our 30s decade? 37 is equal to 36 plus 1.

36 plus 1 is equal to 37.

And what about for our numbers in our 80s decade? 87 is equal to 86 plus 1.

86 plus 1 is equal to 87.

So what do we notice when we add one more to a number in each decade? What changes, and what stays the same? Well, Alex says, "When we add one more, the tens digit stays the same, but the ones digit changes." Time to check your understanding now.

Can you use the ones digit on the number line to find one more than 78? And then complete the stem sentences thinking about addition.

So 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 spot that it was 79, that 79 was one more than 78? So let's think about the stem sentences.

79 is equal to 78 plus 1.

78 plus 1 is equal to 79.

If we know that one more than 8 is 9, then we know that one more than 78 will be 79.

I wonder if we can use the pattern to find one less.

We've talked about one more.

Let's think about one less.

6 is one less than 7.

So that means that 36 is one less than 37 and that 86 is one less than 87.

So let's complete the stem sentences, and let's think about subtraction.

We're going to think about minus one each time this time.

6 is equal to 7 minus 1.

7 minus 1 is equal to 6.

What about when we're in the 30s? 36 is equal to 37 minus 1.

37 minus 1 is equal to 36.

And what about when we are in the 80s? 86 is equal to 87 minus 1.

87 minus 1 is equal to 86.

Well done if you got those.

Really useful to be able to think about one more, one less and relate it to our addition and subtraction.

So what do we notice when we subtract 1 from each number in the decade? Alex says, "When we find one less, the tens digit stays the same, but the ones digit changes." And that will happen when we are working within a decade.

Over to you to check your understanding, Use the ones digit on the number line to find one less than 78 and then complete the stem sentences.

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

How did you get on? So we were looking at using the fact that 7 is one less than 8, and we were going to think about how we could think about 78.

So we can say that 77 is equal to 78 minus 1.

78 minus 1 is equal to 77.

8 minus 1 is 7, so 78 minus 1 is 77.

Now do you remember Alex talking about this earlier in the lesson? When numbers are one more or one less than each other, we say they have a difference of 1.

So 9 is one more than 8, and 8 is one less than 9.

8 and 9 have a difference of 1.

Which other two numbers have a difference of 1? You might want to have a think.

Well, Sam says, "59 is one more than 58, and 58 is one less than 59.

58 and 59 have a difference of 1, just like 8 and 9 did." And we can show that on the number line.

What do you think that will look like on our last number line? Ah, yes, we can use the same pattern.

89 is one more than 88, and 88 is one less than 89.

So 88 and 89 have a difference of 1.

Well done if you spotted that.

I wonder if you can find any other numbers on the number line with a difference of 1.

Do you think you can see any? Let's have a look.

We've got a number line here from 70 to 80.

So we're looking at the decade of the 70s.

Can you find two numbers on the number line that have a difference of 1? And can you explain how you know? Pause the video, 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 lots of possibilities.

You could have had 70 and 71 that have a difference of 1, or 71 and 72, 72 and 73, 73 and 74, 74 and 75, 75 and 76, 76 and 77, 77 and 78, 78 and 79, and 79 and 80.

Any pair of numbers that are one more or one less than each other have a difference of 1.

So there were all those different possible pairs of numbers that have a difference of 1.

Sam decides to show the pattern when we add one more on her Gattegno chart.

"I will tap a number from the 70s and then tap the number that is one more." So she's going to tap something that has seven 10s.

And she says, "I think only the ones digit will change." Let's have a look.

So she's tapped 70 and 2, and 70 and 3, ah.

And Alex says, "3 is one more than 2, so 73 is one more than 72.

You were right," he says.

"Only the ones digit changed." 72 changed to 73.

Let's think about that with our stem sentences.

73 is equal to 72 plus 1.

72 plus 1 is equal to 73.

Alex taps the pattern to show one less.

He says, "I will tap a number from the 70s and then tap the number that is one less.

I think only the ones digit will change." If it stays in the 70s, Alex, I think you might be right.

So he's tapped 73, and he's going to tap one less, 72.

And Sam says, "2 is one less than 3, so 72 will be one less than 73." And yes, Alex was right.

She says, "Only the ones digit changed." So let's complete the stem sentences.

72 is equal to 73 minus 1.

73 minus 1 is equal to 72.

And you could also say 72 and 73 have a difference of 1.

Time for you to do some practise.

Can you find the missing numbers? We've given you one number and then a one more, one less arrow, and you've got to fill in the missing number.

You could use a number line, a Gattegno chart, or a hundred square to help you if you would like.

And so for question two, how many ways can you complete the following correctly? Remember to work systematically.

Try and find all the possible solutions.

What are we going to be looking at? So for A, we've got two numbers in the 40s, and you're going to complete those to find a number that is one more or one less.

And for B, we know what our ones digits are.

We've got a 7 and an 8.

So can you fill in the tens digits to make those true so that one number is one more or one less than the other one? Pause the video, have a go at your tasks, and we'll get together for some feedback.

How did you get on? So for A, you had to fill in the missing numbers.

There was just one answer for each question here.

So we knew 65, and we were asked to find one more.

So one more than 65 is 66, and we can check that.

66 and one less will take us to 65.

So this time we were given 66, and we needed to find the number that was one less than 66, and that was 65.

Ooh, did you spot something there? That's right.

We were working in the other direction from A, weren't we? What about C? This time we were given 66, and we had to find one more.

That's right.

One more than 66 is 67, and 67, one less will give us 66.

What about two? There were lots of different ways of filling this in.

Did you notice that? So we have two numbers in A that were 40 something and 40 something.

Do you remember that number line we looked at earlier in the lesson? So you could choose any pair of numbers where the ones digits had a difference of 1.

So let's have a look.

We could have 40 and 41, 41 and 42, 42 and 43, 43 and 44, 44 and 45, 45 and 46, 46 and 47, 47 and 48, 48 and 49.

We can't go anymore 'cause if we had 49, ooh, we wouldn't be in the 40s anymore, so that wouldn't work.

So for B, you could choose any tens digits as long as they were the same.

So we could have had 17 and 18, 27 and 28, 37 and 38, 47 and 48, 57 and 58, 67 and 68, 77 and 78, 87 and 88, 97 and 98.

We couldn't go any higher because we only had space for one tens digit.

Well done if you got all of those right.

I hope you enjoyed it.

And into the second part of our lesson, and we're going to be looking at patterns in the ones digits when we're adding and subtracting one.

Alex represents one more than 65 on a bead bar.

So we can see he's got 65 beads and one more.

So there's his 60, and he's got five extras, and he's going to add in one more.

And he says, "66 is one more than 65." And he says, "I've noticed that the 10s have stayed the same, and the 1s are different." So let's use the bead bar to complete the stem sentences.

66 is one more than 65, and 65 plus 1 is equal to 66.

And we could see that little one bead being added to the 65 to equal 66.

Can we think about the one less as well? We could say that 65 is one less than 66.

We've taken away our one, and 66 minus 1 is equal to 65.

So if we take away the one bead, we go from 66 down to 65.

Sam represents two numbers using base-10 blocks.

What numbers can you see? Let's think about what's the same and what's different.

Well, Sam says, 'Both numbers have the same number of 10s." They've both got three 10s, haven't they? But the number of ones are different in each case.

We've got three 10s and three 1s, 33, and we've got three 10s and four 1s, 34.

Ooh, do you spot something there? 34 is one more than 33.

There's one more 1, isn't there? Let's see if we can complete the stem sentences.

34 is one more than 33.

33 plus 1 is equal to 34.

And we can represent this as an equation, ooh.

33 plus 1 is equal to 34.

It's that second stem sentence written out with numbers and symbols.

And we can look at it in the place value chart as well.

There's our 33, three 10s and three 1s, and we've added one more 1, three 10s and four 1s.

33 plus 1 is equal to 34.

The 10s have stayed the same.

The 1s are different.

We can also write a subtraction equation.

33 is one less than 34.

So let's use the stem sentences.

33 is one less than 34.

So 34 minus 1 is equal to 33, and we can record that as an equation.

Let's think about it in the place value chart.

We've got 34, and we're going to take away one, so 34 minus 1.

Take away one of the 1s.

It's equal to 33.

The 10s have stayed the same.

The 1s are different because we're still within that decade, aren't we? Time to check your understanding.

Use the base-10 blocks to complete the stem sentences.

What do you notice about the 10s and the 1s in each number? 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 spot that 44 is one more than 43? 43 plus 1 is equal to 44, and we can record that with an equation.

43 plus 1 is equal to 44.

What about the subtraction side? 43 is one less than 44.

44 minus 1 is equal to 43.

And we can record that with a subtraction equation.

44 minus 1 is equal to 43.

The 10s have stayed the same, the ones are different, and we can see that in our place value chart.

43 changes to 44.

Let's think about how the 1s change when we find one more here.

What can we see? What is one more than 48? We should be getting quite good at this now.

To find one more, we add one more 1.

So 48, four 10s and eight 1s, becomes 49, four 10s and nine 1s.

48 and one more will be 49.

And Sam says, "I will draw the 10s and 1s." So there she's drawn four lines to represent her four 10s, and now she's got nine little dots to represent her nine 1s.

And she said, "I noticed that the ones digit increased by one." We can see that in the place value chart.

And she's now shown that in her drawing of 49.

"It's the same as adding 1," she says.

One more than 48 is 49.

48 and 1 is equal to 49.

Now let's think about how the ones change when we find one less, so we've got our 49, and we're going to see what is one less.

Sam says, "To find one less, we subtract 1." And we can see that in the place value chart.

We've gone from four 10s and nine 1s.

We've taken away a 1, four 10s and eight 1s.

49 subtract 1 will be 48, and Sam's going to draw the tens and ones.

So she's got her four 10s and eight 1s because she subtracted a 1.

"I noticed," she says, "that the ones digit decreased by one." It went from nine 1s to eight 1s.

49 subtract 1 is equal to 48.

And there we go, "It's the same as subtracting 1." And we can also say that 48 and 49 have a difference of 1.

They'd be next door to each other on a number line if we were counting in 1s up from 40 up to 50.

So can you draw the base-10 blocks to represent the number that is one more and the number that is one less than the number shown? So the number we've got is 68.

Pause the video, and we'll get back together for some feedback when you're ready.

So if we subtract 1 from 68, the tens digit will stay the same, but the ones digit will decrease by one.

So we will have 67, six 10s and seven 1s, and if we add 1 to 68, the tens digit will again stay the same, but the ones digit will increase by one.

So we'll have six 10s and nine 1s, 69.

Well done if you got that correct.

Alex draws base-10 blocks to make a number sequence and then hides some of the numbers from Sam.

Oh, gosh, that's a bit sneaky, isn't it? Sam draws one of the missing numbers and explains how she knows she's right.

So she's starting with the one she knows is 61.

So she's going to find that next missing number.

And she says, "The missing number is 62.

I know this because 62 is one more than 61.

61 plus 1 is equal to 62." And she's shown that with an addition equation.

So she can draw in the base-10 blocks to show six 10s and two 1s.

"The ones digit increases by one," she says.

61 becomes 62.

And she says, "I also know this because 62 is one less than 63.

63 minus 1 is equal to 62." And she's shown that with an equation as well.

The ones digit decreases by 1.

So we've got 63 in our place value chart.

Subtract 1, and we get to 62.

So she's checked her missing number both ways.

Over to you, can you draw the missing number in the number sequence that's left now and explain how you know you are right? Write an addition and a subtraction equation to represent what you did.

So 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 spot that the missing number was 65? 65 is one more than 64.

64 plus 1 is equal to 65.

And there's our equation.

And there are our base-10 blocks drawn in, six 10s and five 1s.

64 add 1 is equal to 65.

But we can also say that 65 is one less than 66.

66 minus 1 is equal to 65.

And we can represent that with an equation.

And if we think about our place value chart, 66 subtract one 1 is equal to 65.

So we've checked our answer from both directions.

Well done if you got that right.

Sam represents two more numbers with base-10 blocks, but she draws a part-part-whole model to represent this but hides one of the numbers.

We can't see her base-10 blocks either, can we? So her whole is 87, and one part is 1, and we don't know the other part, but we do know that to find a missing part, we subtract the part we know from the whole, so whole subtract known part is equal to our unknown part.

"87 is the whole and one is a part, so the other part must be one less than 87." And she says, "I know the tens digit will stay the same, but the ones digit will change.

The missing number must be still in the 80s.

7 minus 1 is equal to 6, so 87 minus 1 is equal to 86.

So the missing number is 86." And there it is.

Alex wants to find the missing number in these equations.

He draws a part-part-whole model to help him.

So what can you see that's the same in there? We've got lots of 63s, and we've got lots of 1s, haven't we? So he's drawn his part-part-whole model, and he says, "63 is the whole, and 1 is a part.

The other part must be one less, so it's 62." So now he can start to fill in the missing numbers in his equations.

63 is equal to 62 plus 1.

He says, "Now the add-ins can be combined in any order, and the sum remains the same." So 63 is equal to 1 plus 62.

And we can rearrange the equation to write the addends first.

So 62 plus 1 is equal to 63, and 1 plus 62 is equal to 63 as well.

What about the subtractions? Ah, well done, Alex.

He's realised that, if our whole is 63, then if we subtract 1 from it, we get our other part of 62 as well.

So 63 subtract 1 is equal to 62, and 62 is also equal to 63 subtract 1 or 63 minus 1.

So his part-part-whole model really helped him to fill in the missing gaps in his equations.

Over to you for some practise, you're going to use Sam's idea to draw base-10 blocks to show the number that is one more and one less.

So use the column on the left to show one less and the column on the right to show one more, and draw your base-10 blocks.

And then for question two, use what you know to find the missing numbers.

So we've got some part-part-whole models, and we've got some equations with missing numbers.

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

How did you get on? How did your base-10 blocks look? So we know when we add or subtract 1 within a decade, the tens digit stays the same.

So here the number that is one less must be in the 40s for the first one.

One less than 5 is 4, so one less than 45 is 44.

One more than 5 is 6, so one more than 45 is 46.

Again, we know that our 10s numbers are not going to change.

So these numbers must both be in the 50s.

One less than 5 is 4, so one less than 55 is 54, and one more than 5 is 6, so one more than 55 is 56.

Did you spot that our 1s were the same each time? What about the last one then? This time we've got six 10s.

We've got 65 as our starting number.

So the number that is one more or one less must still be in the 60s.

One less than 5 is every, so one less than 65 is 64.

And one more than 5 is 6, so one more than 65 must be 66.

Okay, now onto our missing numbers.

Well, if 64 is the whole, and 1 is a part, then our other part must be one less than 64, which is 63.

And for B, did you spot, we had 94 as our whole and 93 as a a part? And we know that two numbers next to each other on the count must have a difference of 1.

So our other missing part must be 1.

94 subtract 1 is equal to 93.

93 plus 1 is equal to 94.

So with C, we started off with having our whole first in our equation.

So we know that our parts are 25 and 1.

We know we can swap the addends around, and the sum remains the same, or swap the parts around, and the whole remains the same.

So the whole must be 26 in both of those.

For the second pair, we can see that we've got our parts of 35 and 1 or 1 and 35.

Again, we can swap them around, and the sum remains the same.

So the sum must be 36 in each case, one more than 35.

in the next ones, our whole is 46.

It appears at the beginning of our first equation and at the end of our next equation.

One part is 45.

Ooh, 45 and 46, they've got a difference of 1.

So our missing part must be 1.

45 plus 1 is equal to 46.

So in D, again, we've got our whole first here at the top.

Something is equal to 67 minus 1.

Ah, so we're finding one less, so 66 is one less than 67.

And then we've got another number with a 7 in the 1s, 87 minus 1.

Well, that must be equal to 86.

So we've got a subtraction next, and we're starting with our whole, and we know that our whole subtract 1 is equal to 37, so our parts must be 37 and 1, so our whole must be 38.

And for the next one, did you spot, we've just reordered the equation? We've started with the part.

37 is equal to 38 subtract 1.

So in the next one, we've got a number subtract 1 is equal to 27.

So again, we've got a missing whole.

So our whole must be 28.

Our parts are 27 and 1.

And this time, we've started with one of our parts, 77 is equal to 78 subtract, oh, we can see that they are numbers next door to each other, so they must have a difference of 1.

So 77 is equal to 78 subtract 1.

I hope you were able to use your knowledge of parts and wholes and maybe even picturing numbers on a number line to help you there.

And I hope you were successful.

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

So in our lesson, we've been adding and subtracting 1 to and from a two-digit number within a decade.

So we haven't been crossing those boundaries yet.

We've learned that finding one more is the same as adding 1.

Finding one less is the same as subtracting 1.

Numbers that are one more or one less than each other have a difference of 1.

And we know that when we add or subtract one within a decade, the tens digit will stay the same.

We know that when we add 1 within a decade, the ones digit increases by one.

And when we subtract 1 within a decade, the ones digit decreases by 1.

Thank you for all your hard work today and all your mathematical thinking, and I hope I get to work with you again soon.

Bye-bye.