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 adding and subtracting 10 to and from a two digit number.

We've got one key word today and that's efficient.

So I'll take my turn, then it'll be your turn.

My turn efficient, your turn, well done.

So look out for the word efficient as we go through our lesson today.

It'll help us to describe the way that we're working.

We've got two parts to our lesson today.

In the first part, we're going to be thinking about patterns when adding and subtracting 10.

And in the second part, we're going to be understanding the equations that we write down.

So let's make a start on part one.

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

Alex wants to use a 100 square to solve this equation.

We've got 17 plus 10 is equal to something.

Alex says, "I will count on 10 to solve this." So he started with 17, shall we help him to count on 10? 18, 19, 20, 21, 22, 23, 24, 25, 26, 27.

You might have used your fingers to help you count on.

But Sam says, "I think there is a more efficient way." It took quite a long time to count on in ones, didn't it? And do you notice something about where we've landed? We know that when we find 10 more, the tens digit increases by one, but the ones digit stays the same.

We see this in the pattern when we count on in tens.

When we find 10 more, it is the same as adding 10 says Sam.

So 17 and 10 more is the same as 17 plus 10.

She says, "I think I can write some equations to represent this sequence." So there's our 17, 17 plus 10.

So 17 and 10 more is 27.

27 plus 10 is 37.

37 plus 10 is 47.

47 plus 10 is equal to 57.

57 plus 10 is equal to 67.

67 plus 10 is equal to 77.

77 plus 10 is equal to 87 and 87 plus 10 is equal to 97.

Alex says, now I know how to solve this equation more efficiently.

Adding 10 is the same as 10 more.

So when we add 10, the tens digit will increase by one.

So he is thinking about it now with a place value chart.

17 is one 10 and seven ones and we want 10 more.

So that will increase to two tens and seven ones.

So 17 plus 10 is equal to 27.

We know that when we find 10 less, the tens digit decreases by one, but the ones digit states the same.

We see this pattern when we count back in tens.

And Sam says, when we find 10 less, it is the same as subtracting 10.

So 10 less than 97 is the same as 97, subtract 10.

Let's write the equations to represent this sequence.

So this time we're gonna start on 97.

97 Subtract 10 is equal to 87.

87 subtract 10 is equal to 77.

77 subtract 10 is equal to 67.

67 subtract 10 is equal to 57.

57 subtract 10 is equal to 47.

47 subtract 10 is equal to 37.

37 subtract 10 is equal to 27.

27 subtract 10 is equal to 17, and 17 subtract 10 is equal to seven.

So we can use this pattern to solve this equation.

57 subtract 10.

Let's try; when we find 10 less, the tens digit decreases by one.

So there's our 57, 5 tens and seven ones.

So we've decreased our tens digit by one.

We've subtracted one 10.

We've now got four tens and seven ones.

So we've got 47; 57, subtract 10 is equal to 47.

And Alex says, "I will check you are right by counting back 10 ones, are you ready?" 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47.

"I was right!" says Sam.

So over to you to check your understanding.

Can you use a 100 square to solve the equations? 38 plus 10 is equal to something and 29, subtract 10 is equal to something.

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 there was our 38 and we were doing 38 plus 10, but we weren't going to count on in ones were we because that wasn't an efficient method.

We knew that adding 10 is the same as finding 10 more.

So we had three tens and eight ones.

10 more are tens digit increases by one.

So we've got four tens and eight ones.

48, 38 plus 10 is equal to 48.

When we add 10, the tens digit increases by one, but the ones digit stays the same.

And we can see that in our place value chart.

We had three tens and eight ones and we added another 10.

We now have four tens and eight ones, 48.

What's about our subtraction? We've got 29 and we are subtracting 10.

And we know that subtracting 10 is the same as finding 10 less.

So we've taken away one 10.

When we subtract 10, the tens digit decreases by one, but the ones digit stays the same.

So there's our 29 in our place value chart, our tens digit is going to decrease by one.

And we've got 19; 29 subtract 10 is equal to 19.

Let's use base 10 blocks to show this pattern.

We've got 34 and we're going to add 10.

So we add 10, our tens digit increases by one, our ones digit stays the same.

And we saw that just happen in our place value chart.

So 34 plus 10 is equal to 44.

What about 44 plus 10? 54.

Let's predict the next equations.

What do you think's coming next? 54 plus 10 will be equal to 64.

64 plus 10 will be equal to 74.

74 plus 10 will be equal to 84 and 84 plus 10 will be equal to 94.

While Alex says when we add 10, the tens digit increases by one and the ones digits stays the same.

And we could see that in our base 10 blocks and in our place value chart.

Time to check your understanding.

Can you use base 10 blocks to write the next equation in the pattern and then solve it.

So here's some base 10 blocks and here's the number in a place value chart.

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

So we could see there 76 had been increased by 10 already to make 86, 8 tens and 6 ones.

So what would come next? Well, 86 and 10 more would be equal to 96.

One more base 10 block representing 10.

And our number in our place value chart are tens digit has increased by one.

When we add 10, the tens digit increases by one and the ones digit stays the same.

That's really useful to remember.

This time we're subtracting 10.

We've got 94 and we're going to subtract 10.

Let's explore how the pattern changes this time.

So 94, subtract 10, we can take one 10 away, decrease our number of tens by one and it's equal to 84.

What about 84 subtract 10, one 10 removed, one 10 fewer in our place value chart.

So it's equal to 74.

Let's predict the next equations.

74 subtract 10 is equal to 64.

64 Subtract 10 is equal to 54.

54 subtract 10 is equal to 44.

44 subtract 10 is equal to 34.

What do you notice this time? When we subtract 10, the tens digit decreases and the ones digit stays the same.

Sam solves this equation like this.

What mistake has been made? Sam's equation says 83 subtract 10 is equal to 82.

Can you see what's happened there? Alex says, we know that when we subtract 10 the tens digit changes, but the ones digit stays the same.

Is that true in Sam's equation? So here's 83.

83 is eight tens and three ones.

So when we subtract 10, there should still be three ones.

When we subtract 10, the tens digit changes.

So we subtract one 10.

And Sam says, "I subtracted one one and not one 10.

I should have decreased the tens digit by one.

So 83, subtract 10 is equal to 73.

Well done Sam.

Well corrected.

Time to check your understanding.

Can you use base 10 blocks to write the next equation in the pattern? We've got 62, subtract 10 is equal to 52 and there's the 52 and there's 52 represented in our place value chart.

So use that information to write the next equation in the pattern.

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

How did you get on? Well the next one will be 52 subtract 10, which is equal to 42.

We've removed one base 10 block and our tens digit has decreased by one.

When we subtract 10, the tens digit decreases by one and the ones digit stays the same.

Time for you to do some practise.

Can you fill in the missing numbers in these sets of equations? And for part two, can you fill in the missing numbers here? How many possible solutions are there for each equation? 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 a, you had lots of missing numbers to fill in, but we were adding 10 each time for a.

45 plus 10 is equal to 55.

The tens digit increases by 1, 55 plus 10 is equal to 65.

65 plus 10 is equal to 75.

75 plus something is equal to 85 or what's happened? Our seven tens have become eight tens.

Our ones haven't changed, so we must have added 10 and something add 10 is equal to 95.

So our tens digit must have increased by one.

So we must have started with 85.

In b, we were subtracting 10.

So 81 subtract 10.

So our 10 digit is getting one fewer.

So that must be 71 or one stays the same.

71 subtract 10 must be 61.

61 subtract 10 must be 51.

51 subtract something is equal to 41.

Well what's happened? Our tens digit has decreased by one.

So we must have subtracted 10 and then something subtract 10 is equal to 31.

We've taken away a 10.

So our tens digit must have been one larger to start with.

So we must have started with 41.

What about C? Something is equal to 67, subtract 10.

Well we know that 67 subtract 10 will be 57 and something is equal to 77 subtract 10.

77, subtract 10 or tens digit will decrease by one.

Our ones will stay the same.

So it must be 67 is equal to 77 subtract 10.

What about d? We've got 27 is equal to 17 plus something.

Well we need an extra 10, don't we? So we must be adding 10.

47 is equal to something plus 10.

We must have started with 37 and 87 is equal to something plus 10 and that must be 77.

So what about question two? Well our solution is 43 plus 10 is equal to 53.

Why is that true? Well, there is only one possible solution here.

The missing ones digit must be three because when we add 10, ones digit stays the same, the missing tens digit must increase by one.

So the missing tens digit can only be five.

What about b? Well we know the missing tens digit must be eight because when we add 10, the 10s digit increases by one and we had seven.

So seven plus one is equal to eight.

So seven tens and one more 10 is eight tens.

The ones digit can be any digit from zero to nine.

As long as both ones digits are the same because we know that the ones don't change.

So two examples are given, but there were 10 possible examples.

So we could have had 71 plus 10 is equal to 81 and we could have had 72 plus 10 is equal to 82.

But as long as those one digits were the same, we could have had any digits from zero all the way up to nine.

I wonder if you found that out.

And on into the second part of our lesson, we're going to be understanding equations.

Sam wants to solve this equation.

10 plus 48 is equal to, this means 10 and 48 more.

It'll take me a long time to add 48 says Sam.

Alex says, "I've spotted something to help us work more efficiently." Oh, jolly good Alex.

He says addition is commutative.

We can combine the addends in any order and the sum will stay the same.

Instead of thinking 10 plus 48 more, we can think of 48 and 10 more.

So our two parts are 10 and 48.

So we can swap them and we can combine them in any order.

So we can think of 48 and 10 more.

Sam wants to solve this equation, so she's going to use the stem sentences to help her.

One part is 10 and the other part is 48 and the whole is 58, 10 more than 48.

This can be written as 10 plus 48 is equal to 58 or 48 plus 10 is equal to 58.

So 48 plus 10 is equal to 58 and 10 plus 48 is equal to 58 because addition is commutative.

So can you draw a part, part whole model to help you solve this equation? 10 plus 26 is equal to.

And then can you complete the stem sentences to help solve the problem? Pause the video, have a go and we'll get back together when you're ready for some feedback.

How did you get on? So here is a part-part-whole model to help you.

So our parts are 10 and 26.

So one part is 10 and the other part is 26.

The whole is 36, so we can think of 10 more than 26.

This can be written as 26 plus 10 is equal to 36 or 10 plus 26 is equal to 36.

And there are our two equations representing the stem sentences.

The children think they can use the same part-part-whole models to write a subtraction equation.

So here we've got a part-part-whole model where our whole is 58 and our parts are 10 and 48.

Let's use the stem sentences to help us.

The whole is 58, 1 part is 10 and the other part is 48.

This can be recorded as 58 minus 10 is equal to 48.

So we can think about that idea of 10 less than 58.

58 subtract 10 is equal to 48, it's 10 less.

Over to you to check your understanding, use the part-part-whole model to write a subtraction equation.

Use the stem sentences to help you.

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 see that the whole is 62 and one part is 10? So the other part is 52.

This can be recorded as 62 minus 10 is equal to 52.

62 subtract 10 is equal to 52, and we can think about using 10 less to solve the problem.

Alex wonders how he can find the missing part in this part-part-whole model.

He says I notice that the ones digits in the part and the whole are the same.

We've got 63 as our whole and 53 as our part.

So yes, well spotted Alex, the ones digits are the same.

He says the tens digits have a difference of one.

That's right, six tens and three ones and five tens and three ones.

63 is 10 more than 53 and 53 is 10 less than 63.

So they have a difference of 10.

So our other part must be 10.

53 plus 10 is equal to 63, and 63 subtract 10 is equal to 53 and he's shown that on a little part of a number line as well.

Sam uses a base 10 block to explore numbers with a difference of 10 on a number line.

So we've got a base 10 block representing 10 there on the number line.

Sam says 34 is 10 more than 24 and 24 is 10 less than 34.

So 24 and 34 have a difference of 10.

24 plus 10 is equal to 34 and 34 subtract 10 is equal to 24.

So our base 10 block represents that difference of 10.

Sam slides the base 10 block along to find two more numbers with a difference of 10.

Oh, our base 10 block's moved.

She says 35 is 10 more than 25 and 25 is 10 less than 35.

So 25 and 35 have a difference of 10.

25 plus 10 is equal to 35 and 35 subtract 10 is equal to 25.

Alex says, I knew that by looking at the digits, the tens digits has a difference of one and the ones digits are the same.

So there must be a difference of 10 overall, only the tens digits has changed.

The two numbers must have a difference of 10 he says.

Alex is thinking of two numbers with a difference of 10.

He taps one of them on the Gattegno chart.

What could the other one be? So he's tapped 60 and eight, 68.

He says the ones digits must be the same.

So the number must have eight ones.

The tens digit must be one greater or one smaller.

They must have a difference of one for the tens digits.

So it could be 68, subtract 10, which is 58, or it could be 68 plus 10, which is 78.

So those are the two numbers which could have a difference of 10 from Alex's starting number of 68.

Over to you to check your understanding.

Can you use a base 10 block on a number line to find some other numbers with a difference of 10? And can you use the stem sentence to record your numbers? Pause the video, have a go, and when you're ready for some feedback, we'll get together again.

How did you get on? What did you find? So you could have chosen any two numbers with the same ones digit as long as the tens digits have a difference of one.

So here are some examples.

You could have had 20 and 30 and they have a difference of one because the tens digits have a difference of one and the ones digits are the same.

And you could write those equations to prove it.

You could have had 21 and 31 for the same reasons.

You could have had 22 and 32 for the same reasons and you might have gone on all the way along the line up to 30 and 40 on this particular number line.

I hope you had fun exploring those numbers with a difference of 10.

So the children play a game with some number cards.

They have to find pairs that have a difference of 10.

The person with the most pairs wins.

So let's help them.

Sam says 79 plus 10 is equal to 89.

So 79 and 89 have a difference of 10.

Well then Sam, good start.

Alex says 69, subtract 10 is equal to 59.

So 59 and 69 have a difference of 10.

Well done Alex.

Sam says 75 subtract 10 is equal to 65, so 75 and 65 have a difference of 10.

Another pair.

And Alex says, "I could also say that the difference between 96 and 86 is 10 because 96 subtract 10 is equal to 86." Another pair for Alex, well done.

Is that last pair, a pair with a difference of 10.

It is 57, subtract 47 is equal to 10.

Ooh Sam, that's a different way of thinking about it.

If I take four tens and seven ones away from 57, I will have 10 left.

So 57 and 47 have a difference of 10 as well.

Well done.

"Oh, well done," says Alex, "You won this time." I think it depended on who started the game, didn't it? 'cause all the cards could be made into pairs.

Perhaps you could play this game with a friend.

Think carefully about who starts the game.

Time for you to do some practise.

For question one, you're going to fill in the missing numbers.

And then for question two, you're going to complete the equations using an addition or a subtraction symbol.

In three, you are going to use the part part whole model to complete some equations and you're going to fill in the stem sentence.

And then in part four you're going to fill in the missing numbers to make the equation correct and think about what you notice about the missing numbers.

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 first you had to fill in some missing numbers.

So 68, subtract 10 was equal to 58, 27 plus 10 was equal to 37.

61 plus 10 was equal to 71 and 78 subtract 10 was equal to 68.

10 plus 65 or we could use our knowledge of adding in any order to realise that that was 10 more than 65 or 65 plus 10 was 75.

And the same for the next one.

10 plus 48 is equal to 58.

73 is equal to 63 plus 10 and 63 is equal to 73 subtract 10.

So onto question two, you had to complete the equations using addition or subtraction.

So 45 and something with 10 is equal to 35.

Well our tens number has decreased by one, so we must have subtracted.

What about the second one? 29 something to 10 is equal to 39.

So our tens digit has increased, so we must be adding 10 this time.

93, oh, we've got this one where we're comparing the two numbers.

93 and something with 83 is equal to 10.

Well, if we take away eight tens and three ones from 93, we're left with 10.

So that must be a subtraction.

And 67 plus 10 is equal to 77.

We've got 10 more there haven't we? For question three, our part-part-whole model showed our whole is 43, 1 part is 10 and one part is 33.

So the equations we can write are 10 plus 33 is equal to 43 or 33 plus 10 is equal to 43.

43 subtract 33 is equal to 10 and 43, subtract 10 is equal to 33, because we know that if we subtract a part from the whole, we can find the other part.

The difference between 33 and 43 is 10.

And what about four? Well, 19 plus 10 is equal to 39.

Subtract 10, 19 plus 10 is equal to 29 and 39 subtract 10 is equal to 29 as well.

Ooh so what do we notice here? We could also have had 29 plus 10, which is 39 is equal to 49 subtract 10, which is also 39.

21 plus 10 is equal to 41, subtract 10.

And we've realised that the missing numbers must have the same ones digits, and the tens digits have a difference of two because for both sides to be equal, one side has to have 10 added and the other side has to have 10 subtracted.

So 21 and 41 have a difference of two tens to make our equations balance and to make both sides of the equal sign exactly the same.

And we can show it on a number line as well.

21 plus 10 is equal to 31 and 41 subtract 10 is also equal to 31.

So we can imagine that little set of numbers going up and down the number line and seeing that our missing numbers had to have a difference of two tens so that they would meet in the middle to be equal.

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

We've been adding and subtracting 10 to and from a two digit number.

So what have we learned about today? Well, when adding or subtracting 10, the ones digit does not change.

When adding 10, the tens digit increases by one and when subtracting one 10 the tens digit decreases by one.

If two numbers have the same ones digit and the tens digit has a difference of one, then the two numbers will have a difference of 10.

You might need to think about that 10 block on the number line to think about that one.

And understanding the patterns when we add and subtract 10 can help us to solve equations efficiently.

Remember, Alex realised he didn't have to count on and back in ones to add and subtract 10.

I hope you've enjoyed adding and subtracting 10 to two digit numbers.

I've certainly enjoyed working with you and I hope we get to work again sometime soon.

Bye-Bye.