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I can use known facts to find complements to 100 efficiently.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Number facts to 10 can be applied to multiples of 10
Using pairs to 10 and pairs to 100 we can find pairs to 100
If we have a pair to 10 then the tens have to total 90 for the whole to be 100
A number line can represent the complements to 100

Common misconception

Pupils may be less efficient if they are not fluent with bonds within 10 e.g. 3 + 6 = 9

Provide additional scaffolding as appropriate including examples of pairs that total 9 and 10

Keywords

Complement to 100 - Pairs of numbers which total 100
Total - The result of adding.

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Hi, my name is Miss Co.

I'm really looking forward to learning with you today and I know that you're going to try really hard and also really enjoy this lesson.

If you're ready, let's get going.

So, the outcome for this lesson today is that you'll be able to use known facts to find compliments to 100 thinking about efficiency.

So we're going to be working today to try and be efficient in our calculations.

Our keywords for this lesson are compliments to 100 and total.

I'm going to say them, and I'd like you to say them back to me.

My turn compliments to 100.

Your turn.

My turn, Total.

Your turn.

Great job.

See if you can spot when I'm using those words in this lesson.

Now let's think about what our keywords mean.

Compliments to 100 are pairs of numbers, which total 100.

The compliments to 100 is the number that we add to make 100.

So for example, 30 and 70 are compliments to 100, because 30 plus 70 is equal to 100.

You might already be able to think of some compliments to 100 that you know.

A total is the result of adding.

Our lesson today focusing on being efficient when finding compliments to 100 has two cycles.

The first cycle we're going to look at two digit number compliments to 100, and then we're going to move on to my favourite thing, solving problems with numbers that total 100.

So let's get started with our first lesson cycle.

In this lesson today, you are going to meet Izzy and Jacob, and they're going to be helping you with your learning and asking you some tricky questions to deepen your understanding.

Let's get going.

Take a look at the 100 square here.

This 100 square represents a pair of two digit numbers, which total 100.

We know that compliments 100 are pairs of numbers that total 100.

The dark purple squares represent 32.

So we can see 32 there coloured in the dark purple squares.

There are three tens and two ones which make 32.

So, what is the missing compliments to 100? Or in other words, what do the grey squares represent? How many grey squares are there? Well, we can use partitioning to help us find the missing compliments to 100 for 32.

So we know that 32 plus something is equal to 100.

And we're going to start by partitioning 32 into its tens and ones.

32 is 30 and two, or three tens and two.

When we combine two, two digit numbers that total 100, the ones digits in those numbers always total 10.

So, we know that the ones digits in 32 is two.

Hmm.

What number do I add to two to make 10? Well hopefully you should know your number pairs to 10 and know that two plus eight is equal to 10.

So we don't know what our missing number is yet in total, but we do know that the ones digits in our missing number is going to be eight because two plus eight is equal to 10.

And we know that when two, two digit numbers total 100, their ones digits total 10.

Let's move on to the tens digits.

When two, two digit numbers total 100, the tens digits total 90.

So we can see here that we've partitioned 32, and we know that there are three tens or 30 in 32.

Hmm.

I need to make 90.

What do I have to add to 30 to make 90? Well, I know that three plus six is equal to nine, so therefore 30 plus 60 is equal to 90.

So my missing tens number must be 60.

If we recombine those parts, 60 and eight, we have 68.

So we can say that 32 plus 68 is equal to 100.

The missing complement to 100 for 32 is 68.

We can see here that in this case the tens digits total 90, the ones digits total 10.

We know that 90 plus 10 is equal to 100.

So these two numbers must total 100.

32 and 68 are compliments to 100.

Let's look at an example that is incorrect, where the two numbers are not compliments to 100 and think about why that's the case.

Jacob is saying that 36 and 74 are not compliments to 100, so they do not equal or total 100.

Let's have a look at why he is correct.

When two, two digit numbers total 100, they're ones digits total 10.

So 36 can be partitioned into 30 and 6 74 can be partitioned into 70 and four.

Hmm.

Six plus four does equal 10.

I know that six plus four totals 10.

So, so far Jacob might be correct or incorrect, because the ones digits do total 10.

Let's have a look at the tens digits.

Now can you remember what they need to total if we have a compliment to 100? That's right.

When two, two digit numbers total 100, the tens digits total 90.

So we have 36 which is three tens or 30, and we have 74, which is 7 tens or 70.

Hmm.

I know that three plus seven totals 10, therefore, 30 plus 70 totals 100 not 90.

Therefore, Jacob is absolutely correct.

36 and 74 are not compliments to 100.

Because if we combine these two parts we have 100 and 10, which makes 110, not 100, which is the total that we are looking for.

Well spotted Jacob.

If the ones digits total 10, and the tens digits total 100, there'll be an extra 10.

So these numbers are not compliments to 100.

So, what is the compliment to 100 for 36? Well again, we're going to show this with partitioning.

As before we've partitioned 36 into tens and ones.

36 is equal to 30 and six.

We're going to add something to it to make 100.

We know that when two, two digit numbers total 100, the ones digits total 10.

One of my ones digits is six, and I know that six plus four makes 10, so therefore, the missing ones digits in my two digit number must be four, because six plus four totals 10.

When two, two digit numbers total 100, the tens digits total 90.

I wonder if you can see what the missing tens digit must be.

Well, I know that three plus six totals nine, so therefore the plus 60 must total 90.

So my missing tens digits is 60 or six tens.

If I recombine those parts, my missing complement to 100 is 64.

Because 36 plus 64 is equal to 100.

We can see that our tens digits sum to 90, and our ones digits total 10.

And we can see that 90 plus 10 is equal to 100.

Therefore, 36 and 64 are compliments to 100.

Time to check your understanding.

True or false, 44 and 66 are compliments to 100.

Do you think this is true or false? And I would like you to justify your answer.

So one of these options is a correct justification for your answer.

Is this A, 44 and 66 are compliments to 100 because four plus six equals 10, and 40 plus 60 equals 100? Or, 44 and 66 are not compliments to 100 because four plus six equals 10 and 40 plus 60 equals 100, so that makes 110 in total.

Have a think, pause the video here.

And welcome back.

So, are 44 and 66 compliments to 100? When you add them together, do they total 100? Well done if you said this was false, they do not total 100.

And the reason being, is that when you add the ones digits four and six, you do get 10.

But when you add 40 and 60 together you get 100 and we know that when you add the tens digits together in compliments to 100, they total 90, not 100.

Well done if you recognise that 44 and 66 are not compliments to 100.

Time for your first practise task.

For question one, we'd like you to complete the models to find the compliments to 100.

So if we look at the first example, we have 72 plus something is equal to 100, what is the missing compliments to 100? We have partitioned the first number 72 into 70 and two to help you.

For question two, you need to find the missing compliments to 100.

So we have 45 plus something equals 100, 35 plus something equals 100, 25 plus something equals 100, 15 plus something equals 100, and 5 plus something equals 100.

Hmm, I think I can see a pattern there.

Once you've filled in the missing compliments to 100 and remember, you can partition to help you do that, think about what do you notice about our sequence, and can you write your own similar sequence? And then for question three you have some expressions or pairs of numbers that you need to sort into the correct place in the table.

So the table says compliments to 100 or not compliments to 100.

So the first pair is 28 and 72.

If you think they are a compliments 100, they go in the first column.

If they are not a compliments 100, put them in the second column.

When you've done that, what do you notice about the compliments to 100? Good luck with those tasks.

Pause the video here, and I'll see you shortly for some feedback.

And welcome back.

How did you get on with those tasks? Let's have a look at some of the answers.

So, for question one, we asked you to complete the models to find the compliments to 100.

The first one is 72 plus 28 is equal to 100.

Well done if you've got 28.

The second one is 49 plus 51 is equal to 100.

Well done if you've got that.

Let's have a quick look at that second example.

Remember, our ones digits and our two digit numbers must total 10 in order for it to be a compliments 100.

I have nine, I know that nine plus one totals 10, so my missing ones digits had to be one.

We also know that in two two digit numbers that compliments to 100, the tens digits have to total 90.

My first tens digit was four or 40, so I know that four plus five is equal to nine, so 40 plus 50 totals 90.

So my missing tens number, was 50.

If I recombined those partition parts 50 and one, the missing number was 51.

Well done if you got those correct.

For question two, we had to find the compliments to 100.

So you can see the answers there.

We have 55, 65, 75, 85, 95.

Now well done if you got those, but I'm more interested in what you noticed about those numbers.

So Izzy noticed that the ones total 10 and the tens total 90, and that 90 plus 10 totals 100.

So if we look at 45 plus 55 totals 100, we can see that the ones digits are fives and that five plus five is equal to 10.

We can see that we have four tens and five tens, which makes nine tens or 90.

Well done if you spotted that.

Izzy also noticed that the ones digits in the add-ins, the parts we're adding together, is always the same.

It's always a five.

Well done if you spotted that.

She also noticed that in the number she wrote, so 55, 65, 75, 85 and 95, the tens digit increases by one each time.

So we have five tens, six tens, seven tens and so on.

Well done if you spotted any of those things, or you spotted some things that Izzy didn't notice.

We also asked you to write your own sequence.

Jacob made up his own sequence here.

Now you might not have written this sequence, there are lots of different sequences that you could have written.

But Jacob noticed that in his case the ones digits total 10 and the tens digits totaled 90 in each case.

So well done if you notice that with your pattern.

For question three, we asked you to sort the number pairs into the correct place in the table.

So have a quick check to make sure that your number pairs are in the same place as mine.

What did you notice about the compliments to 100? Well hopefully you notice that repeating idea, that the one digits in the two digit numbers total 10 and the 10 digits always total 90.

Well done if you spotted that.

Let's move on to the second part of our lesson where we're solving problems using numbers that total 100.

Year three need to earn 100 points for a treat.

They have 62 points already.

How many more points do they need to earn to get their treat? Hmm? What do we know? What don't we know? Can we use a bar model to represent the problem? Well here's the bar model that represents the problem.

We know that year three need to earn 100 points for their treats.

So our whole is 100.

They already have 62 points, so one of our parts is 62.

But we don't yet know how many more points they need to get to 100 so that they can earn their special treats.

What could we do to find out? Well, we know that this is a compliments to 100 problem.

We know that 62 plus something totals 100 and hopefully by now you are realising that in these examples the ones digits needs to total 10, and the tens digits needs to total 90.

So, we've partitioned 62 into 60 and two, and I know that two plus eight makes 10.

So our ones digits must be 62.

So two and something that ends in an eight.

Izzy is reminding us that in this case when two two digit numbers total 100, the tens digits total 90.

I have six tens, or 60, I know that 60 plus 30 makes 90.

So we now have our missing number 30 and eight or 38 because our tens total 90 are ones total 10, and we know that 90 plus 10 totals 100.

So year three need to earn 38 more points in order to get their special treats.

Let's look at another example.

During the class treat, so they've earned their class treat, well done year three.

Izzy pours some squash, there was 100 millilitres of squash in this jug.

How much did Izzy pour? So again, think about what do we know, what don't we know? And can we use a bar model to represent this problem? Well, here is my bar model.

So, imagine the situation there was 100 millilitres in this jug.

Izzy comes along to make some squash and pours out an unknown amount, but now there is 75 millilitres of squash left in the jug.

So we know that the hole is 100 or 100 millilitres, and we know that one part is 75, but we don't know the missing part how much Izzy poured out.

But, we can use our compliments to 100 to work out the answer.

So they need to work out this compliments 100, 75 plus something equals 100.

Well we know that the one digits have to total 10, and Jacob thinks he can do this without partitioning, which is great.

So we know that five plus five is equal to 10.

So the one digit in our missing number is a five.

We know that five plus five makes 10, and we need nine more tens to make 100.

So we know that the tens digits need to make 90.

So I know or Jacob knows that 70 plus 20 is 90.

So the missing digit, the missing tens digits has to be two.

75 plus 25 equals 100.

That means Izzy must have poured out 25 millilitres of squash from the jug.

And we can see that here.

We can see, that we started off on 100, if we take out 25, we are left with 75, or if we add 75 and 25, that totals 100.

Let's look at another example.

Izzy bought an orange and a banana, the orange cost 54 pence.

Izzy paid one pound, which you should know is 100 pence.

So she paid 100 pence for an orange and a banana.

How much was the banana? Again, have a think.

What do we know? What don't we know? And can we use a bar model to represent the problem? Well we know that Izzy spent or paid 100 pence, and we know that the orange cost 54 pence, so one of the parts is 54, but we don't know how much the banana cost.

So we have 54 pence plus something is equal to or totals 100 pence.

Aha, we have another compliments to 100 problem.

So, let's think about the answer here.

Izzy knows that the ones need to total 10.

So we have 54, so four ones, and she knows that six plus four totals 10.

We know that the tens needs to total 90.

So we have 50, so five tens, so 50 plus 40 makes 90.

Now we have 90 plus 10, which makes 100.

So what is our missing number? Well our missing number is 40 and six, or 46.

So the banana costs 46 pence.

Time to check your understanding.

Jacob bought an apple and a pair.

The apple and a pair together cost 100 pence in total.

The pair cost 63 pence.

How much was the apple? Use your partitioning if you need to.

Pause the video here, and see how you get on.

And welcome back.

So, we could have made a bar model here.

We know that the total is 100 pence, we know one of the parts is 63 pence, and we don't know the other part, but we know that it is a compliment to 100.

So we know that 63 pence plus something totals 100.

We can use the idea that our one digits total 10, and our tens digit total 90 to know that the missing compliments 100 is 37.

So well done if you said that the apple costs 37 pence.

Let's look at a different problem.

Izzy blows up 34 balloons for her party.

Well done Izzy, that must take a long time.

But Izzy's mom blows up a further 66 balloons, goodness me, that's a lot of balloons.

Izzy says, \"We have blown up 100 balloons in total.\" Hmm, how can we check whether Izzy is correct? Well, we can think about adding together 34 and 66.

We know that 30 plus something must make 90, and four plus something must make 10 in order for them to be a compliment to 100.

So, the tens have to total 90.

Let's check.

30 plus 60 totals 90.

Three plus six is nine, so 30 plus 60 is 90.

Now, we've got a six here, so let's have a look.

Four plus six makes 10.

So we have the correct compliments for 100.

34 plus 66 totals 100.

Therefore, Izzy was correct.

They did blow up 100 balloons all together for the party.

Time for you to check your understanding.

There are 100 cakes to sell at the school fair.

Izzy and Jacob sell 24 cakes.

Izzy says that they need to sell 86 more cakes in order to sell all of the cakes.

Jacob thinks that they need to sell 76 more cakes to sell all of the cakes.

Who is correct? Use the pothole models to help you, pause the video here, and have a think.

And welcome back.

What did you think? Well, we can see here that if we add together 24 and 86, 20 plus 80 is 100.

Now we know that with compliments to 100, the tens digits total 90.

So Izzy cannot be correct.

But is Jacob correct? Well in his case, 20 plus 70 makes 90, which is the total of tens that we're looking for.

Let's just check the ones.

We know that in compliments to 100, the ones must total 10.

So we have four plus six.

Yep, that totals 10.

So therefore, Jacob is correct because 24 and 76 are compliments to 100.

Well done if you've got that correct.

Time for your next practise task.

First of all, I'd like you to use compliments to 100 to solve these problems. So, Jacob has 100 pence and spends 37 pence on an apple.

How much money does he have left? Izzy scored 100 points in a game, she scored 62 points collecting coins and the rest of the points she got from solving a puzzle.

How many points did she get for solving the puzzle? Two pieces of ribbon have a length of 100 centimetres.

If one piece of ribbon is 91 centimetres long, how long is the other piece of ribbon? Then, I would like you to think about the bar model that we have here.

And I'd like you to write your own story, or your own word problem that fits this bar model.

And finally, this equation has two missing digits.

Can you make it correct? Can you find more than one way? So just to explain that equation, we have 100 equals something six.

So this is a two digit number where the one's digit is a six plus something four.

So a two digit number where the one's digit is a four.

Can you put a digit in each box to make that correct? Good luck.

Pause the video here and I'll see you shortly for some feedback.

How did you get on? Let's have a look at some of the answers.

So for question one, Jacob had 100 pence, he spent 37 pence, so we needed to find the compliments 100 for 37.

37 plus 63 totals 100.

So he must have 63 pence left.

The second question, Izzy scored a hundred points in total.

62 of them were from collecting coins and the rest we didn't know how many points she had, but we know that 62 plus 38 are compliments to 100.

So the missing number was 38.

And finally, if we have two pieces of ribbon that are 100 centimetres altogether, if one of them is 91 centimetres, the other one must be nine centimetres because 91 plus nine totals 100.

Well done if you got those.

Question two, there are lots of different stories that you could have said, and I can't possibly guess the stories you came up with.

But we know that the missing number here was 54.

54 and 46 are compliments to 100.

So Jacob decided to say, I'm collecting stickers.

I have 46, I want to have 100 stickers.

How many more do I need that would fit the bar model? Well done Jacob.

Izzy says Jacob has 100 stickers, 46 of them are gold and the rest are silver.

How many are silver? Well done if you wrote a problem like that.

Then, for question three, we have the missing digits.

So Izzy is reminding us that the missing tens digits have to total 90, which means there are more than one way of doing this.

So you might have said 100 equals 16 plus 84.

So the missing digits were one and eight.

You might have said 100 equals 26 and 74, where the missing digits were two and seven.

Well done if you got those answers or some other answers were the missing tens digits total 90.

We have come to the end of the lesson and I know how hard you have worked to think about compliments to 100.

Let's summarise our learning.

We've explored compliments to 100 by showing pairs of numbers, which total 100.

And we know that when the ones digits of two numbers total 10, and the tens digits total 90, the numbers are a compliments to 100.

Thank you so much for learning with me today.

I hope you've had as much fun as I've had and I look forward to seeing you again soon.

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