Lesson video

Hello, my name's Mrs. Cornwell, and I'm going to be helping you with your learning today.

I'm really looking forward to today's lesson.

I know you're going to work really hard, and we'll do really well.

So let's get started.

Okay, so welcome to today's lesson, which is called "Find Pairs of Numbers That Sum to 10," and it comes from the unit, "Addition and Subtraction Facts Within 10." Okay? And so that's what we're going to be doing in today's lesson.

We're going to be partitioning 10 into pairs of numbers that sum to 10, and identifying those pairs, and spotting them quickly 'cause it's really important to be able to spot those pairs quickly and partition 10 quickly because it can help us with our work and help us to solve equations really quickly.

Okay, so let's get started with that then.

So our keywords for today are sum.

My turn, sum.

Your turn And pair.

My turn, pair.

Your turn.

And odd.

My turn, odd.

Your turn.

And even.

My turn, even.

Your turn.

Well done.

Excellent.

So in the first part of our lesson today we are going to partition 10 into two parts.

Okay? In this lesson you'll meet Sam, and you'll also meet Jacob.

Okay, so what is 10 then? It can be 10 fingers on your two hands, can't it? It can be 10 beads on a bead string.

It can be 10 counters on a full tens frame.

It can be two dice with a five on, or a Hungarian tens frame that's called when you see the dice pattern side by side like that.

What do you notice about all of these representations of 10? That's right.

They all show two fives within the 10, don't they? Okay, let's look at some more representations.

So we've got a number line there, haven't we? That goes up to 10.

And we've got a 100 square there, and it's got 10, the first 10, shaded on there, hasn't it? It is important to know how to partition and recombine the parts of 10 because it can help us when working with much larger numbers.

We are going to play some games to help us find the number pairs that sum to 10.

So let's play 10 Fingers.

Work with a partner.

I will clap three times, then say show me 10.

Then, you and your partner will each hold up some fingers that sum to 10.

Okay? So let's practise together first.

One, two, three, show me 10.

Okay, so you could show a five and a five, couldn't you? You show five and your partner show five.

10 is equal to five plus five.

Fantastic.

10 is made up of the number pair five and five.

Okay, are you ready again? One, two, three, show me 10.

Oh that's right.

This time you could have one person showing three and the other person would need to show seven, wouldn't they? So 10 is equal to three plus seven.

Excellent.

10 is made of three and seven.

Okay, are you ready? Again, one, two, three, show me 10.

Oh this time we've shown a four and a six aren't we? 10 is equal to four plus six.

So, well done.

10 is made of four and six.

Perhaps you could continue this game with your partner.

It will help you to really remember those number pairs that sum to 10, won't it? Okay, so let's play a different game that's going to help us remember our number pairs to 10.

Okay? So I have a whole group of 10 counters, and I will hide some in my hand and leave the other part of the group on the table.

Can you work out how many are in my hand? Oh, so we've got five on the table, haven't we? So how many do you think are in the hand? That's right, it was another five.

Five are missing.

I know because 10 is made of five and five.

10 is equal to five plus five.

Okay, let's try another one.

So this time we can see seven, can't we? That's right.

So three must be missing.

We know because 10 is made of seven and three.

10 is equal to seven plus three.

Okay, let's try another one.

So, oh, this time there are eight on the table, aren't there? So that's right.

Two must be missing because I know 10 is made of eight and two.

Okay, so well done with that.

Okay, so now we're going to play a different game.

Now, we're going to use this number frame to play guess my number.

Okay, so can you see the fives inside the 10? You may use these to help you subitize the amounts.

Find the missing number and explain how you know.

Okay? So how many are missing? So I'll hide some and then you've got to say how many are hidden.

So we can see two, can't we? So eight are missing.

I know because 10 is made of two and eight.

Okay, now I'm going to hide some more.

So a different number.

How many are missing this time? So we can see seven, can't we? So three are missing.

I know because 10 is made of seven and three.

Okay, so perhaps you could continue that game.

You could play it with 10 objects couldn't you? And hide some for your partner to guess.

So now it's time to check your understanding again.

There are 10 beads on this bead string.

Can you see the fives within the 10? They may help you to recognise the numbers quickly and to subatize.

Okay, so when I hide some of the beads, you've got to say how many are missing and explain how you know.

Are you ready? Okay, so pause the video now and say how many are missing and how you know.

And that's right.

Did you get that? Nine beads were missing.

I know because 10 is made of one and nine.

Okay, are you ready? We'll hide some more.

Okay, so pause the video again while you say how many are missing and how you know.

Okay, did you get it? Five beads were missing.

I know because 10 is made of five and five.

Excellent.

Perhaps you could play that game with a partner and a bead string, and you could hide some for your partner to guess.

Okay, so here we've got a part-part-whole model, okay? And we can see the whole amount is 10.

We know 10 can be partitioned into two smaller numbers.

We call these number pairs that sum to 10.

If we want to remember our number pairs to 10 more quickly, we can work systematically through them, exploring how they change each time to help us.

Okay, so there's 10 counters there.

We can see them, can't we? And we know if we have zero in one part, the whole 10 will move to the other part won't it? 10 is equal to zero plus 10.

Okay, how about if we move one counter over? How many will be in the other part now? That's right, it will be nine won't it? Okay, so 10 is equal to one plus nine.

How about if we move another counter over? So that would be two.

That's right.

And on the other side it would be eight.

That's right.

10 is equal to two plus eight.

And how about if we moved another counter over? So what would it become there? What would our number pair be? So if we move another counter over, how will that pair change? That's right.

So that part will become three.

Okay.

And the other addend will become seven, won't it? Are you starting to notice a pattern here? So 10 is equal to three plus seven.

I wonder what the next number pair would be if we move another counter.

So let's have a look.

That's right.

So that addend will become four, and the other addend will become six, wouldn't it? That's right.

Okay, so 10 is equal to four plus six.

Okay, and then let's see how the pair will change if we move another counter over.

That's right.

So that part will become five.

10 is equal to five plus five.

That's right.

Excellent.

Then it's equal to six plus four.

Well done.

And then it would be seven plus three.

That's right.

And then it would become eight plus two.

And then it would be nine plus one.

And then it would be 10 plus zero, wouldn't it? Well done.

So we can use one number pair to help us find another pair, and that can be really useful.

Imagining one counter, for example, moving over to help you find a new number pair.

If the sum is the same when the first addend increases by one, the other addend decreases by one.

That was what was happening wasn't it? So we can see there, can't we, that the first addend there was increasing by one, becoming one more? And so the second addend there was decreasing by one.

That was becoming one less.

So that can be a really useful strategy.

So you can use one number pair to help you find another number pair.

Okay, so here's Jacob, and he buys two toys and spends exactly 10 pounds in the toy shop.

But we are not sure which two toys he bought.

So let's see which ones he could have bought.

Remember, the two toys have to sum to exactly 10 pounds.

The number on each toy tells you how many pounds it cost.

So let's use our number pair to 10 to help us find out which toys he could have bought.

So he could have bought the robot there, couldn't he? That's one.

And what would he have bought to go with the robot? That's right.

He would've bought the cowboy there.

So one and nine because they sum to 10.

Okay.

Or he could have bought that toy there, which cost three pounds.

Okay, and what would he have bought? That's right, it would've been the knight because three and seven sum to 10.

Okay.

And if he bought the toy there that was six pounds, what would he have bought with that? That's right, it would've been the dinosaur because that's four pounds.

Six and four sum to 10.

And how about if he'd bought the unicorn? That's right.

So eight and two pair to 10.

Now, what about the toy that's left there that costs five pounds? That's right.

This toy costs five pounds.

So to spend 10 pounds, he wouldn't have needed to buy two of them, wouldn't he? Five and five is equal to 10.

So well done with that.

Okay, so here's your task for the first part of today's lesson.

You will need a partner.

So here's Sam telling us what to do.

"I will write 10 to represent the whole in my part-part-whole model.

Then I will roll a dice and write the number rolled on my part-part-whole model, as well." So there's 10 and she rolled six.

So she wrote six in her part-part-whole model.

Okay, then I will draw that number of counters on a tens frame, and see how many are missing to find the missing part of the part-part-whole model, the missing addend.

Okay, so we can see that she rolled six, and drew those on and she could see that there are space for four more counters.

So 10 must partition into six and four.

Okay? And then you will write the missing addend in the part-part-whole model like that.

So pause the video now while you do that.

Okay, so let's see how you got on with this.

So you may have done this.

Okay, so Sam's telling us she wrote 10 in her part-part-whole model and then rolled a three on her dice.

So she wrote three in one part of the part-part-whole model and drew three counters on her tens frame.

Okay, and then she can clearly see now, can't she, that there are seven spaces left on her tens frame for seven counters? So 10 was partition into three and seven.

There are seven empty spaces on the tens frame, and so you can clearly see that missing addend there, can't you? So well done, if you did that.

Excellent.

Okay, so now it's time to move on to the next part of our lesson, okay? Where we will use strategies to quickly identify pairs that sum to 10.

So Jacob sorts the numbers one to 10 into two groups, okay? And you can see them there can't you? What do you notice about the shapes that the numbers made in each group? The ones within each number are arranged in pairs, aren't they? Each one has a partner.

These are the even numbers.

The ones within each number in this group are not arranged in pairs.

There is an extra one without a partner.

These are the odd numbers.

10 is an even number.

What do you notice about the shape of the addends when it is partitioned? So we can see it partitions into two and eight, doesn't it? Or eight and two.

It partitions into four and six or six and four.

When part 10 was partitioned, the ones within each addend were arranged in pairs.

They were even weren't they? 10 is an even number.

Even numbers can be partitioned into two even parts can't they? That's right, well spotted.

Now, let's partition 10 in a different way.

So there's 10, and let's think about what we notice about the shape of the numbers this time.

So 10 can be partitioned into one and nine or nine and one.

10 can be partitioned into three and seven or seven and three.

That's right.

Or it can be partitioned into five and five, can't it? This time when 10 was partitioned, the ones within each addend were not arranged in pairs.

Even numbers can also be partitioned into two odd parts, can't they? Okay, so knowledge of odd and even numbers can help us decide if a number pair will sum to 10.

Let's think about the even numbers.

They have no extra one.

A tens frame has space for 10 counters.

So our 10 number shape fits onto it exactly.

We can fit our number shapes onto a tens frame to explore how they fit together, can't we? So let's have a look.

We can fit the four shape and the six shape together, and they sum to 10.

There we can see they fill up the full tens frame, don't they? Or the full 10 number shape.

Okay, we can fit the two shape and the eight shape together, and they also sum to 10.

The ones within even numbers are arranged in pairs.

So when combined there are never any extra ones.

They will always sum to an even number.

Now, let's think about the odd numbers.

Not all of the ones within the number shape are in pairs.

They have an extra one that is not arranged in a pair.

Can you see it and the shape's there? Each one has an extra one sticking up doesn't it? What happens to that extra one within each number shape when two odd numbers are added, I wonder? Let's see.

We can fit the one shape and the nine shape together, and they sum to 10.

There we can see.

We can fit the three shape and the seven shape together, and they sum to 10.

We can fit the five shape and another five shape together, and they sum to 10.

Odd numbers have an extra one within their number shape.

So when two odd numbers combine, they form a new pair.

They always sum to an even number.

Jacob has partitioned 10 into two numbers, and he has hidden one.

"I think the missing number is six," says Sam.

Let's explain why Sam can't be right.

Three is an odd number.

Six is an even number.

Even numbers can only be partitioned into two odd parts or two even parts.

10 cannot be partitioned into six and three.

And we can see that it was actually a seven that was needed to fit together with the three and sum to 10.

There we go.

And we can see how they fit together there.

So now it is time to check your understanding.

Here are some pairs at sum to 10.

Which one is incorrect? Explain how you know.

So pause the video now while you look at that.

Okay, and let's see what you thought.

Did you spot it? That's right.

B, four and five cannot sum to 10, can they? Because it shows an odd and an even number.

Four is an even number, and five is an odd number.

And we know that 10 can only be partitioned into two odd numbers or two even numbers.

So well done if you noticed that.

Okay, so we must learn to spot which number pairs do not sum to 10.

So we can quickly recognise and use the pairs that do sum to 10 because we know that's really important for our learning and for helping us with our number work, isn't it? So Sam is sorting some expressions into those that sum to 10 and those that don't.

Let's help her, okay? And then we can explain how we know that we are right.

Okay and then Sam is giving us a bit of a clue, a reminder here, isn't she? She's saying "10 is an even number.

Even numbers can be partitioned into two odd parts or two even parts." Can't they? So here's our first expression, seven plus three.

Do we think that can sum to 10 or not? That's right, it can.

I know seven and three are both odd numbers, so they can sum to 10.

I imagine the number shapes on my tens frame to help me see the numbers.

What about four plus six? What do we think about that? That's right, that can sum to 10 as well, can't it? I know that both four and six are even numbers, so they can sum to 10.

I imagine the number shapes on the tens frame to help me.

Four plus five.

What do we think about that? Yes that's right.

It can't sum to 10 can it? I know that four is an even number, and five is an odd number, and 10 can only be partitioned into two odd numbers or two even numbers.

Three plus six.

What do we think about that? That's right, all that also counts sum to 10.

Can it? I know that three is an odd number, and six is an even number, and 10 can only be partitioned into two odd or two even numbers.

So that can't be right either.

So well done, if you spotted the odds and evens and used those to help you.

Look at each equation and flash your 10 fingers, if it is a number pair that sums to 10.

Okay, five plus five.

What do you think? That's right, it does sum to 10, doesn't it? We know two odd numbers there, and we know five and five is a number pair to 10.

Five and six.

What do we think about that? That's right, that can't be a number pair to 10 'cause we've got an odd number and an even number, and also we know that it's one more than five plus five, which was a number pair to 10.

Five plus four.

What do we think about that? That's right, that can't be a number pair to 10, can it? Because we've got an odd number and an even number again, and also we know that it's one less than five plus five, which is a number pair to 10.

Eight plus two.

What do we think about that? That's right, we know eight and two is a number pair to 10, and they're both even numbers.

So we know that we're definitely right.

What about two plus eight? What do we think about that? That's right, it's just the addends were just added in a different order from the last expression.

So two plus eight are both even.

So they can sum to 10.

Eight plus one.

What do we think? That's right.

So if eight plus two sum to 10, then eight plus one can't sum to 10 because it's one less.

And also we can see there's an even number and an odd number there.

So they can't sum to 10 can they? Okay, so Jacob is sorting these expressions.

Let's help him decide if they sum to greater than 10 or less than 10.

Remember, we can use our pairs that sum to 10 to help us.

We can use the number facts that we already know to help us to think about new facts, can't we? So seven plus four, what do we think about that? That's right, it's greater than 10, and we know because seven plus three sums to 10.

Four is greater than three.

So seven plus four must be greater than 10.

Five plus six.

What do we think about that one? That's right, that's also greater than 10.

I know that five plus five sums to 10.

Six is greater than five.

So five plus six must sum to greater than 10.

Four plus five.

What about that one? That's right, I know that five plus five sums to 10.

Four is less than five.

So four plus five must sum to less than 10.

And three plus six.

What about this one then? That's right.

That's also less than 10, isn't it? I know four plus six sums to 10.

Three is less than four.

So three plus six must sum to less than 10.

So well done, if you used your number pairs to 10 to help you with that.

Okay, so now it's time to check your understanding again.

Match the following expressions to show whether they sum to 10, greater than 10, or less than 10.

Okay, so pause a video now while you do that.

Okay, and let's see how you got on.

So three plus eight, what do you think about that? That's right, that's greater than 10.

Okay.

And you may have thought three plus seven is equal to 10.

Therefore, eight is greater than seven, isn't it? So three plus eight must be greater than 10.

Okay, what about six plus four? That's right, that's exactly 10.

We recognise that as a number pair to 10, don't we? And what about three plus six? That's right, that's less than 10.

You may have thought three plus seven is equal to 10.

So three plus six must be less than 10.

Or you may have used the six plus four that we've just used.

Both of those expressions have a six, don't they? And we know three is less than four.

So if six plus four is equal to 10, then three plus six must be less than 10.

So well done if you spotted that.

Excellent.

So here's the task for the second part of our lesson today.

Work with a partner, and you will need a set of zero to 10 digit cards.

Okay? And then there Sam's telling us, "We will deal the cards equally between us, then take it in turns to place a card face up next to our partner's card." "When a number is placed that makes a pair that sums to 10, we shout 'snap.

' The first person to do so wins the pair." The winner is the person who wins the most pairs.

Okay? So pause the video now while you try that.

Okay, so here's your task for the second part of our lesson today.

Sort the cards into the table below to show whether their sum is greater than, equal to, or less than 10.

And explain how you know.

So remember you can use your number pairs to 10 to help you decide whether other number pairs are greater than or less than 10.

Okay? So pause the video now while you try that.

Okay, and let's see how you got on.

So you may have done this.

So we're playing Snap, aren't we? So Sam puts a one and Jacob puts an eight.

That's not a number pair to 10, is it? Then Sam puts a two and Jacob puts a six.

That's not a number pair to 10.

Three and seven.

Snap.

That is a number pair to 10.

Okay? And so Sam spotted those, so she gets to keep that pair.

And then zero plus five.

That's not a number pair to 10.

Six and four.

Snap.

So Jacob spotted that.

So he gets to keep that pair.

So well done with that.

Okay, so here's the second part of our task then.

You may have done this.

So four plus six, what did we think about that? Is it less than 10? Does it sum to less than 10, equal to 10, or greater than 10? That's right, I know that's four plus six sums to 10.

A number pair to 10 isn't it? What about four plus five? That's right.

That will sum to less than 10 because if four plus six sums to 10, four plus five must be less than 10.

Five is less than six, isn't it? That's right.

Seven plus three is a number pair to 10, isn't it? So what about seven plus four then? That's right.

If seven and three sums to 10, seven plus four must sum to greater than 10 because four's greater than three.

Okay, what about eight plus three? That's right, that's greater than 10.

We know eight plus two sums to 10.

So eight plus three must sum to greater than 10.

Okay.

And you may have also used the seven plus three to help you with that one as well.

Okay.

And then three plus six.

That's right, that's less than 10.

I know it was three plus seven sums to 10.

So three plus six will sum to less than 10.

So well done.

You worked really hard, and hopefully you'll be able to keep practising those number pairs to 10 because they are really important, aren't they? And they will help you with so much work later on.

So well done.

Okay, so let's think about what we've learned in today's lesson.

10 can be partitioned into pairs of numbers that sum to 10.

Quickly remembering these number pairs is important for later work.

Knowledge of odd and even numbers can help you recognise if a pair of numbers sum to 10.

And we can use the patterns in numbers to predict new number pairs.

And this can help us remember our number pairs to 10 more quickly, which is really important, isn't it? So well done.

You've worked really hard now.

I've really enjoyed our lesson today.