Lesson video

Hi, my name is Ms. Combe.

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.

The outcome of today's lesson is that by the end of the lesson, you'll be able to use known facts to find pairs of numbers that total 100.

We have two keywords for this lesson, total, and two-digit number.

I'm going to say them, and I would like you to say them after me.

My turn, total.

Your turn.

Well done.

My turn, two-digit number, your turn.

Let's take a look at what those words mean.

A total is the result of adding.

So in 25 plus 75 is equal to 100, the total is 100.

A two-digit number refers to a value between 10 and 99, including 10 and 99.

The number is made up of two digits, which represent tens and ones.

So, our lesson today has two parts.

In the first part of the lesson, we'll be using number pairs to make 100, and in the second part of the lesson, we'll be looking at other two-digit numbers that total 100.

Let's get started in the first part of our lesson.

Izzy is letting us know that number pairs for 10 are going to be really important in today's lesson.

Jacob's asking, hmm, "Do you know all the number pairs that total 10?" Hopefully, you should have those facts at your fingertips.

Number pairs that total 10, such as knowing that three plus seven is equal to 10, are really, really important.

They're a really good skill to have automatically, and they're going to be really important in this lesson.

Number facts to 10 can help us find pairs of numbers that total 10.

So here, we have seven plus three is equal to 10.

We can see that seven plus three is equal to 10, because I've represented it on the number line.

And we also have some cubes, we have seven cubes and three cubes, and altogether we have 10 cubes.

So, Jacob knows that seven plus three is equal to 10.

How can that help him calculate 97 plus three? Shall we have a look? So we know that seven plus three is equal to 10.

And if we show 97 plus three on a number line, we can see that 97 plus three is equal to 100.

We've still got seven and we're adding three.

Seven plus three is equal to 10.

So 97 plus three.

Well, we know that 97 plus three would make 10 tens, which is equal to 100.

So we can see the relationship there.

And we can use a stem sentence to describe this.

I know that seven plus three is equal to 10, so I know that 97 plus three is equal to 100.

And we're going to be using that a lot in this lesson.

Let's look at a different example.

We know that eight plus two is equal to 10, and we can use that to say mm plus mm is equal to 100.

Let's have a look at our number line.

If we know that eight plus two is equal to 10, we can use that to say that 98 plus two is equal to 100.

Let's have a look at another example.

Which number facts to 10 are helping here? Well, I can see, in the top number line, that six plus four is equal to 10.

So therefore, we must know that 96 plus four is equal to 100.

We also know that we can say subtraction facts with our pairs to 10.

So I know that seven plus three is equal to 10, therefore I know that 10 subtract three is equal to seven.

And I can show that on my number line, I have counted back three from 10 to get to seven.

And we can use those number facts to think about our larger numbers as well.

So, let's think about this example.

If I know that 10 subtract three is equal to seven, well, I can use that to do 100 subtract three.

100 subtract three is equal to 97.

We can use a stem sentence to describe this relationship as well.

I know that 10 minus three is equal to seven, so I know that 100 minus three is equal to 97.

I know that 10 minus two is equal to eight, and I know this because I know that two plus eight or eight plus two is equal to 10.

So 10 minus two is equal to eight.

If I know that, then I know that 100 minus something is equal to something.

Well, I know that 10 minus two is equal to eight, and I can show that on my number line.

So therefore, I know that 100 minus two is equal to 98.

Let's say that sentence together.

I know that 10 minus two is equal to eight, so I know that 100 minus two is equal to 98, well done.

We can show this relationship in different ways.

So we know that 10 minus two is equal to eight, and we can use that to say that 100 minus two is equal to 98.

And we can show that using a parts-whole model, or we can show that using a bar model.

And we know that the parts can be represented in either order.

So 100 is the whole in both of these representations, 98 is a part of the whole, and two is a part of the whole.

We know that 98 plus two is equal to 100, so we know that 100 minus two is equal to 98.

They are all different representations for the same idea.

Time to check your understanding.

Jacob is saying 100 minus six is 40.

Andeep is asking, hmm, "Do you agree with Jacob?" What do you think? Pause the video here and have a go.

How did you get on? Now, you may have shown this on the number line and you may have used your known facts.

I know that 10 minus six is equal to four, because I know that six plus four is equal to 10.

So therefore, I know that 100 minus six is equal to 94, as you can see on the number line.

So 100 minus six ones is equal to 94.

So Jacob might have been thinking of 100 minus six tens.

So we don't agree with Jacob, Jacob is incorrect.

Well done if you said that.

Another chance for you to check your understanding, I would like you to lose the number line to complete the equations.

So we have 100 minus one equals, 100 minus two, and so on.

Remember to think about your number pairs to make 10.

If I know that 10 minus one is equal to nine, how does that help me? Pause the video here and have a go.

How did you get on? Hopefully you got the answers that you can see on the screen.

So 100 minus one is equal to 99, 100 minus two is equal to 98, and so on.

Well done if you said those.

I'm going to get you to think again now.

So we have the same equations that we've just looked at.

And my question to you is what do you notice about the subtrahend and difference in these equations? So just as a reminder, the subtrahend is the number that we are subtracting.

So I've highlighted them there.

So in 100 minus one is equal to 99, the subtrahend, the number we're subtracting is one.

In 100 minus five is equal to 95, the subtrahend, the number we're subtracting is five.

The difference is the answer to our equations.

So in 100 minus one equals 99, the difference is 99.

So, pause the video and either have a discussion or have a think about, what do you notice about the subtrahend and the difference in this set of equations? Welcome back.

So, what did you notice? Now, you may have said things such as one, two, three, four, and five, the subtrahends, are all single-digit numbers.

You might have said the differences are all two-digit numbers, well done if you spotted that.

But we can also think about a really nice pattern here.

As the subtrahend increases by one, the difference decreases by one.

Let's have a look at what we mean.

100 minus one is equal to 99, the subtrahend is one, the difference is 99.

If we look at the next one, 100 minus two is equal to 98.

Well, the subtrahend is now two, so it's gone from one to two, which is an increase of one.

The difference has gone from 99 to 98.

Hmm, that's a difference of one as well, that is decreasing by one.

And if you look down the column of equations, you will see that the pattern holds.

Well done if you spotted that, 'cause that's quite a tricky thing to spot, but it's a really important thing.

And it's really important as mathematicians that we're always looking for patterns.

Time for your first practise task.

The first thing I'd like you to do is use the number line and number pairs to 10 to fill in the missing numbers in the equations.

So for example, you have 99 plus mm is equal to 100.

Now, be aware that some of them, we have the 100 in different places.

So the next one along, we have 100 equals 96 plus mm, but don't let that put you off.

Remember, use your number pairs to 10.

For question two, I'd like you to take a look at these expressions.

So we have things like 93 plus six, 94 plus six, 92 plus eight, and so on.

I would like you to sort them into those that are equal to 100, and those that are not equal to 100.

So have a good think about them, and sort them into ones that are and are not equal to 100.

And then once you've done that, question three asks you to change the expressions that are not equal to 100 so they are equal to 100.

So, for example, if you think 93 plus six is not equal to 100, could you change one of the addends, one of the parts, so that it is equal to 100? Pause the video now and have a go at those three tasks, and I'll see you some feedback shortly.

How did you get on? For question one, you can see the answers to the missing equations on the screen now.

Pause the video, have a look through, and give yourself a tick if you got all of those correct.

So what did you notice about the ones digits in the equations? We've got one, two, three, four, five, six, oh, they're all going up in ones.

So, well done if you kept spotting those patterns.

For question two, the expressions that are equal to 100 are as follows, 94 plus six, 99 plus one, 92 plus eight, 91 plus nine, 96 plus four, and 20 plus 80.

Well done if you found all of those.

For those that are not equal to 100 then, let's have a look at how you could have changed them so that they are equal to 100.

So, for example, 96 plus three is not equal to 100.

I know that six plus three is equal to nine, so 96 plus three must be 99, which is not 100.

So there are two different ways you could change that.

If we made it 96 plus four, that would make 100, because six plus four is equal to 10.

So 96 plus four makes 100.

We could also change the larger addend.

So instead of it being 96, we could make it 97, because I know that seven plus three is equal to 10.

So 97 plus three is equal to 100.

For 93 plus six, you could have had 93 plus seven, or 94 plus six.

13 plus 97, well, oh, that's a bit complicated.

There are too many tens.

So I could have had 13 plus 87, or three plus 97, because I know that three plus seven makes 10.

And similarly, for 93 plus 17, I could have had 93 plus seven or 83 plus 17.

Well done if you got all of those correct, and found ways to make those expressions equal to 100.

Let's move on to the second part of our learning today.

Izzy is asking, well, "I wonder now how we else we can apply our understanding of pairs to 10?" And Andeep is saying, well, "I wonder if other two-digit numbers total 100?" So we've been looking at a two-digit number and a one-digit number.

so I wonder if other two-digit numbers total 100.

So this is a slightly different representation, but let's talk through it.

This shows 98 plus two is equal to 100.

I can see that I have 90, or nine tens.

And then in the very top row of my 100 square, I have an eight and I have a two.

And I know that eight plus two is equal to 10, so I know that that whole bar would be filled up with eight and two.

The ones digits, eight and two, total 10.

We already have 90, so we have 90 plus 10, which we know makes 100.

Hmm, what's changed this time? What do we notice? Well, we knew that 98 plus two was equal to 100.

We knew that, we've just looked at that.

This time, we have 88 plus 12 is equal to 100.

Let's look at how the model shows 88 plus 12.

We now have two two-digit numbers which total 100.

So this time, we have 80, eight tens, and then 12, we have a 10 and a two.

And we've got an eight from the 88.

We know that eight plus two is 10.

And we also can say that because 12 is 10 more than two, 88 has to be 10 less than 98.

Let's look at another way of explaining this idea.

88 plus 12 is equal to 100.

We can partition 88 and 12, so we can partition 88 into 80 and eight, and we can partition 12 into two and 10.

We know that eight plus two, so the eight from the 88 and the two ones from 12, we know that eight plus two makes 10.

So we can now think of this as 80 plus 10 plus 10, and we know that 80 plus 10 plus 10 is equal to 100.

The ones digits total 10 in this case.

What's changed this time? Well, this time, we have 78 plus 22 equals 100.

And we can partition 78 into 70 and eight, and we can partition 22 into 20 and two, or two and 20.

We know that eight plus two is equal to 10, that is a known fact that we know.

So now we have 70 plus 10 plus 20.

Well, I know that 10 plus 20 is 30, and I know that 70 plus 30 is equal to 100.

The ones digits still total 10.

It's time for you to check your understanding.

Which pair of two-digit numbers total 100 in this representation? So we've looked at very similar representations, so think of what was the same and what's different.

Pause the video now and think about what this representation is showing you.

How did you get on? Hopefully you saw this representation as 68 plus 32 is equal to 100.

So we can partition 68 into 60 and eight, and we can partition 32 into two and 30.

We know that eight plus two is equal to 10.

And so, therefore we have 60 plus 10 plus 30 is equal to 100.

We have 68 and 32 which make 100.

Well done if you saw that.

Andeep has noticed something, he says that "When two two-digit numbers total 100, the ones digit total 10 and the tens digits total 90." Now, you might have spotted that already.

Let's have a look at this example.

We have 32 plus 68 is equal to 100.

In 32, the tens digit is three, so we have three tens.

In 68, the tens digit is six, so six tens.

We know that three plus six is equal to nine.

So three tens plus six tens is equal to nine tens, or 90.

Andeep's right so far.

The ones digits are two and eight, and we know that two plus eight or eight plus two is equal to 10.

And we therefore have 90 and 10, which we know makes 100.

Andeep has spotted another brilliant pattern to help us find two-digit numbers that total 100.

Time for you to check your understanding.

We have three bar models here, which of those represent two two-digit numbers that total 100? So A says 24 plus 84, does that make 100? Think about what Andeep said.

We have 75 plus 25 is equal to 100, or 48 plus 62 is equal to 100.

Remember, Andeep's helping us out here, when two two-digit numbers total 100, the ones digits total 10 and the tens digits total 90.

Pause the video here, have a think.

How did you get on? Well, let's have a look using Andeep's rule.

For A, we have 24 and 84.

So I have two tens in 24 and eight tens in 84.

Hmm, two plus eight makes 10 tens or 100.

The tens digits do not total 90.

So therefore, those two numbers cannot add together to make 100.

Let's look at the second example, 75 and 25.

So you have seven tens and two tens.

Seven plus two is nine, so 70 plus 20 is 90.

So far, so good.

Let's check the ones.

Five ones in 75, five ones in 25.

I know that five plus five makes 10, so the ones digits total 10.

So yes, that one is a correct bar model.

Let's have a look at the last one.

We have four tens and six tens.

Four plus six is 10.

Hmm, so that's 10 tens.

That's not 90, that's 100.

So therefore, those numbers do not total 100.

So the bar model is incorrect.

Well done if you've got all of those correct.

Time for your second practise task.

For your first task, I would like you to tick the pairs of two-digit numbers which total 100.

So if you think that 23 plus 77 make 100, you can give it a tick.

If you don't think it does that, give it a cross.

For the second part of the question, change the pairs that do not total 100 so that they do total 100.

Can you do this in more than one way? Pause the video here, have a go at this task, and then come back when you're ready for some feedback.

How did you get on? Did you remember Andeep's special rule about finding two-digit numbers that total 100? Remember, when two two-digit numbers total 100, the ones digits total 10 and the tens digits total 90.

So if we apply that understanding to our lists in the first column, 55 plus 55 does not total 100 because five tens plus five tens makes 10 tens, which is not 90.

In the second column, we have two examples there which do not total 100.

36 plus 74 does not total 100, because three tens plus seven tens makes 10 tens, which is not 90, it doesn't fit Andeep's rule.

So we asked you to change the pairs that do not total 100 so they do total 100, and to see if you could find more than one way.

Let's look at the first example.

55 plus 55, well, we know that 55 plus 55 is five tens plus five tens, which makes 10 tens, that's not 90.

So we could have had 55 plus 45, or 45 plus 55, because in those examples, the 10 digits total 90 and the one digits total 10.

36 plus 74 does not make 100, but 36 plus 64, or 26 plus 74, would make 100.

And finally, 71 plus 26 does not make 100.

You could have had some different things here, but 71 plus 29, or 74 plus 26, would work and would make 100.

Well done if you found more than one way to correct those totals that did not make 100.

We have come to the end of our lesson, and I'm really pleased with how hard you have worked in this lesson.

Let's summarise our learning.

Number facts to 10 can be applied to multiples of 10.

Number facts to 10 can help us work out pairs of two-digit numbers that total 100.

And remember our very special rule, when a pair of two-digit numbers totals 100, the ones digits will total 10, and the tens digits will total 90.

Thank you so much for learning with me today, and I look forward to learning with you again soon.