Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in our maths lesson today.

We are going to be doing some counting.

We're going to be looking at numbers, we're going to be thinking about numbers, and I hope we're going to have some fun as well.

So let's make a start.

Hello and welcome to this lesson in our unit on composition of numbers 11 to 19.

This lesson is all about solving subtraction problems using knowledge of 10 and a bit in different contexts.

So let's have a look and see what we're going to be learning about today.

We've got some key words.

You might know these words, but they're going to be useful today, so it's worth having a practise.

So I'll say the word and then it'll be your turn.

So my turn, partition.

Your turn.

My turn, whole.

Your turn.

My turn, part.

Your turn.

Well done.

As I say, they might be words that you know, but they're going to be useful today, so watch out for them as we go through our lesson.

We've got two parts to our lesson today.

We're going to be looking at missing number problems, and we're going to be looking at subtraction problems. So let's make a start on missing number problems. And we've got Jacob and Laura helping us in our lesson today.

So we know that teen numbers can be partitioned into 10 and a bit, and this can be shown on a part-part-whole model.

So you can see our part-part-whole model, and we can see we've got number 11 here partitioned into 1 ten and 1 one.

So our whole is 11, and this time we're thinking about it as a subtraction.

So our whole is 11, we can subtract one part and we are left with the other part.

So 11 subtract one is equal to 10.

The whole subtract one part is equal to the other part.

We may not always be able to see the parts, but if we know the whole and one part, we can work out the missing part.

And we can use subtraction to work out the missing part.

So Jacob and Laura have collected 18 sticks at the park.

Jacob has dropped his sticks.

How many did he drop? Jacob says, "We had 18 sticks in total, but I dropped mine." 18 is the whole.

We started with 18 sticks.

So he's put 18 as the whole in the part-part-whole model.

Laura says, "I have eight sticks." Then Jacob says, "One part is eight.

I don't know how many I had." So Laura's recorded her part of eight, but what they don't know is the missing part, the part that Jacob had but dropped.

Laura says, "We can subtract eight from 18 to work out how many you dropped." 18 subtract eight is equal to.

And Jacob says, "I think I can partition 18 to work it out.

18 is 1 ten and 8 ones." So Laura says, "Well, the missing part must be 10," because we know she's got 8 ones.

"So you dropped 10 sticks, Jacob," she says.

18 subtract eight is equal to 10.

And there are the 10 sticks that Jacob dropped.

So we're going to read the story, and we're going to put the numbers into the right places in the part-part-whole model, and you are going to have a go at this one.

So the story says: Jacob and Laura have collected 12 sticks at the park.

Jacob has 10 sticks.

Laura has dropped her sticks.

How many did she drop? So see if you can read the story and put the numbers into the right places in the part-part-whole model.

Pause the video and then we'll have a look at it together.

How did you get on? So did you manage to see that 12 was the whole? Those were the sticks that they collected together.

And Jacob has 10 sticks, so that's one part, but Laura's dropped sticks of the part we don't know.

So well done if you put those in the right places.

So Jacob and Laura counted 15 birds at the park, but five birds flew away.

How many birds were left? Jacob says, "We saw 15 birds in total.

The whole is 15." So he's filled that in in the part-part-whole model.

Laura says, "One part is five because five flew away." "Five is one part.

How can we find the missing part," says Jacob? Well, Laura says, "We can subtract five from 15 to work out how many are left." Do you remember, we said if we know the whole and one part, we can subtract that part to find the missing part.

So 15 subtract five is equal to.

And Jacob says, "I think I know! 15 can be partitioned into 10 and five." Teens numbers can be partitioned into 10 and a bit.

Well, we know the bit.

We know the five.

Five is the 5 ones in 15.

So the missing part must be 10.

15 subtract five is equal to 10.

15 is the whole.

10 is a part and five is a part.

Jacob says, "We used what we know about a teen number," to work out that there were 10 birds left.

Jacob and Laura collected 17 stones.

Seven are brown and the rest are grey.

How many are grey? "What's the whole this time? Seven or 17," says Jacob.

Laura says, "Well, 17 is the whole.

We have 17 stones in total." So 17 is the whole.

There are 17 stones and seven are brown.

So there must be seven brown stones.

The other part is the grey stones.

Laura says, "We can subtract again." 17 subtract seven is equal to.

And Jacob says, "I can use partitions of 17 to help me." He says, "10 stones are grey," because he knows that 17 can be partitioned into 1 ten and 7 ones.

17 subtract seven is equal to 10.

17 can be partitioned into 7 ones and 1 ten.

"Of course!" says Laura.

"17 is 1 ten and 7 ones." And there are the grey stones, all 10 of them.

So again, read the story and tell a friend what you know about the whole to help you to solve the problem.

Jacob and Laura have collected 18 leaves at the park.

Eight leaves are green and the rest are brown.

How many leaves are brown? So read the story and think about what's the whole in this story and how will that help you solve the problem? Pause the video and then we'll have a look at it together.

How did you get on? Did you spot that the whole is 18, which is 1 ten and 8 ones.

So 18 can be partitioned into 10 and eight and that would help us to solve the problem.

Another check for you.

Jacob has 15 conkers and he gives 10 to Laura.

Which part-part-whole model shows how many he has left? So which is the correct part-part-whole model to work out how many conkers Jacob has left? He had 15 and he gives 10 to Laura.

Pause the video, and then we'll have a think about it together.

How did you get on? Which part-part-whole model shows how many he has left? Did you spot that it was this one? 15 is the whole; he knew about the 10 he gave to Laura.

And then the remaining bit is how many he has left.

In the other part-part-whole models, we've not found the whole correctly.

The whole was 15.

That was the number of conkers that Jacob starts with.

In the other two, we've got 10 and five as our whole.

So that's not gonna help us to solve this problem.

Time for you to do some practise now.

Use the pictures to show the group of 10 and fill in the missing parts in the part-part-whole model and equation.

So Jacob collected some stones.

He collected 14, but he lost four.

How many of them did he have left? And Jacob and Laura collected 18 leaves in total.

Laura had eight leaves.

How many leaves did Jacob have? So can you fill in the part-part-whole model and complete the equation? This time you're going to draw a picture to represent each problem and find the missing part.

Jacob found 13 stones.

Three of them were grey.

How many were not grey? Laura collected 19 leaves, but nine leaves blew away.

How many does she have now? Pause the video, have a go, and then we'll look at the answers together.

How did you get on? Did you show the group of 10 and fill in the missing part? So Jacob collected 14 stones, but then he lost four of them.

So we know he had 14 to begin with, and he had one of his parts was four that he lost.

So the other part must be 10 because we know that 14 can be partitioned into 4 ones and 1 ten.

They were collecting some leaves.

They had 18 leaves in total.

And we know that Laura had eight leaves.

How many leaves did Jacob have? Well, 18 subtract eight is equal to 10.

And we know that's correct because 18 can be partitioned into 1 ten and 8 ones.

And this time Jacob found 13 stones.

Three of them were grey.

How many were not grey? So 13 stones and three of them were grey.

What was our missing part? Well, our missing part was 10 because 13 can be partitioned into 3 ones and 1 ten.

And Laura collected 19 leaves, but 10 of them blew away.

So she lost 10 of her leaves.

But we know that 19 is made from a 10 and 9 ones.

So 19 subtract 10 must be equal to nine.

I hope you got on well with those and used your knowledge of 10 and a bit and partitioning teen numbers to help you.

Onto the second part of our lesson, thinking about subtraction problems. So part-part-whole models and bar models can be used to show a whole and its parts.

The parts can be combined to make the whole.

So a part and a part together equal the whole.

The whole can be partitioned into the parts, and one part can be taken away from the whole to find the other part.

So if we think about our equation, 15 subtract five is equal to 10.

15 is the whole, five is a part and 10 is a part.

So we take away one part to find the other part, and we're going to be using this to help us to solve our problems. So Jacob has 17 sticks.

He lost some and he has 10 left.

How many did he lose? So 17 subtract, hmm, is equal to 10.

Jacob says, "This equation looks different." Laura says, "We can still use partitioning to help." 17 is the whole and 10 is a part.

What is the other part? Oh, Jacob says, "I must have lost seven sticks." The missing part is seven.

We know that 17 can be partitioned into 1 ten and 7 ones.

So those 7 ones are the seven sticks that Jacob lost.

Let's fill in our stem sentence.

17 is a whole.

10 is a part and seven is a part.

So our missing part is seven.

That's how many sticks he lost.

Jacob has 17 cubes this time.

10 of them are red and the rest of them are blue.

How many are blue? So we can say, 17 subtract 10, that's the 10 red ones, which is one part.

We'll leave us with the other part, which is the blue ones.

And Jacob says, "This equation looks different." Again, do you remember the missing part was after the subtraction sign before? We've just sort of swapped the parts over, haven't we? Laura says, "We can still use partitioning to help." 17 is the whole and 10 is a part.

What is the other part? And Jacob says, "10 cubes are red.

So seven cubes are blue." The missing part is seven.

Let's think about our stem sentence.

17 is the whole.

10 is a part and seven is a part.

We know that 17 can be partitioned into 1 ten and 7 ones.

So if there are 10 red cubes, there must be seven blue cubes.

And we know that 17 subtract 10 is equal to seven.

So let's have a look at this one.

Jacob had some cubes.

Laura took 10 and he has seven left.

How many cubes did he have at the start? Hmm.

What's missing this time? So the equation they've written is, hmm, subtract 10 is equal to seven.

Let's think about the problem again.

Jacob had some cubes.

Laura took 10 and he has seven left.

So 10 were taken away, seven are left.

We dunno what number he had at the start, do we? We are missing a whole this time.

Jacob says, "This equation looks different." That missing number is walking around, is wandering around our equation, isn't it? Laura says, "We can still use partitioning to help." 10 is a part and seven is a part.

So what are we going to do this time? What is the whole? "10 and seven make 17.

I had 17 at the start," says Jacob.

So this time our whole is missing.

So we need to combine our parts to equal the whole.

So the whole is 17.

Let's fill in our stem sentence.

17 is the whole.

10 is a part and seven is a part.

So our whole this time is 17.

Another check for you.

What's the missing part each time? Something equals 17, subtract 10.

17 subtract something is equal to 10.

And 17 subtract 10 is equal to something.

What's the missing part? Is it seven? Is it 10, or is it 17? Pause the video and have a think, and then we'll talk about it together.

How did you get on? Did you spot that, each time, the missing part is seven? That's right.

So, each time, the whole is 17 and one of the parts is 10.

So we know that if 17 is the whole and one part is 10, then the other part must be seven.

Time to check your understanding again.

This time you're gonna have a look at these equations and find out which of them have the same answer.

So work out the answers and spot the ones that have the same answer.

Pause the video and then we'll talk about it together.

How did you get on? Did you spot that these first ones here are all equal to 10? 14 subtract four, 15 subtract five, and 16 subtract six, they all equal 10 because each time we've taken away the ones digit, haven't we? And we've left the 10 behind.

What about the other ones? Did you spot this time the answers were seven, eight, and nine? 'Cause this time from our teens number, we've subtracted the 10.

So we are left with the ones value, which is seven in 17, eight in 18, and nine in 19.

So it was the first set that all had the same answer.

So we've got some marbles here.

Laura has red, blue, and yellow marbles.

There are 17 marbles in total.

Five marbles are red and five marbles are blue.

How many are yellow? Hmm.

Lots of information there.

We know though that whole is 17.

There are 17 marbles in total, and we know that five marbles are red and five marbles are blue.

So we know two of the parts.

So something special about those parts.

What we don't know is the missing part of the yellow marbles.

Jacob says, "17 is 1 ten and 7 ones." Laura says, "I can see a group of 10." Have you spotted the group of 10? That's right.

Five and five combined to make 10.

Five plus five is equal to 10.

We can subtract the part we know from the whole to find the missing part.

So we know we've got 17, subtract five and subtract five, but we know that that's subtracting 10.

And Jacob says, "This is the same as 17 subtract 10." The other part must be seven because 17 can be partitioned into 10 and seven.

So our missing part, our missing yellow marbles is equal to seven.

There are seven yellow marbles.

We've got another problem with the marbles here.

Laura again has red, blue, and yellow marbles and there are 18 marbles in total.

This time we know that six marbles are red and four marbles are blue.

How many marbles are yellow? Jacob's reminding us 18 is 1 ten and 8 ones.

I can see a group of 10.

She spotted that the six marbles and four marbles will make a total of 10 marbles.

So now Jacob's 18 is 1 ten and 8 ones can help us.

She says, "We can subtract the parts we know from the whole to find the missing part." So now we've got 18, subtract six, subtract four.

And this is the same as 18 subtract 10.

And we can use our partitioning, can't we? We know if 18 is the whole and 10 is a part, then other part must be eight.

So we must have eight yellow marbles.

18 subtract six, subtract four is equal to eight.

Eight are yellow.

And we can complete our part-part-whole model this time.

Time for you to check your understanding.

Which equation matches the part-part-whole model? We've got three parts this time.

So which one matches? Pause the video, have a think, and then we'll look at it together.

How did you get on? Did you spot that it was the middle one? Our whole is 16, and we've got three parts, five, five, and six.

So 16, subtract five, subtract five is equal to six.

And we can see that those two fives would combine to make 10.

So if 16 is a part and 10 is a part, six must be the other part.

Another one to have a look at, which equations have the same answer? Can you solve those equations and work out which ones are going to have the same answer? Pause the video, have a go and then we'll talk about it.

How did you get on? Did you see that 13 subtract 10 is the same as 13 subtract three, subtract seven because three plus seven is equal to 10.

And 15 subtract 10 is equal to five, which is the same as 15 subtract five, subtract five because if we subtract two fives, we've subtracted 10.

And 17 subtract 10 is the same as 17 subtract seven, subtract three because seven and three are equal to 10 as well.

So those were our equations giving us the same answer.

And can you picture those as part-part-whole models with two parts and three parts? Time for you to have some practise.

You're going to use bar model and equations to work out these answers.

So A says Laura had some cubes and she gave three to Jacob.

She had 10 left.

How many did she have at the start? B says Jacob has 13 cubes.

10 are red and the rest are blue.

How many are blue? And C says Laura had 13 cubes and gave some to Jacob.

She has three left.

How many did she give to Jacob? So you're going to use a bar model.

You could use a part-part-whole as well, but have a think about it with a bar model, and C, if you can, use the bar model and the equations to work out these answers.

So we've got some equations there.

So see if you can match the right equation to the problem that you're solving and use the bar model to help you.

And then you are going to fill in the missing numbers on the bar models and in the equations to make these correct.

And for the final part, you're going to fill in the missing parts for these equations and match the ones with the same answer.

So pause the video, have a go at your tasks, and then we'll have a look at the answers together.

How did you get on? Did you solve the problems? Did you find out which equations are going to help you? So Laura had some cubes and she gave three to Jacob.

She had 10 left.

How many did she have at the start? So we were missing a whole, but we can see from our bar model that we've got a whole of 13.

One part is 10 and one part is three.

So three plus 10 is equal to 13.

Jacob has 13 cubes, 10 are red and the rest are blue.

How many are blue? So 13 cubes.

13 is the whole, 10 is a part.

The other part must be three.

And Laura had 13 cubes and she gave some to Jacob and she has three left.

How many did she give to Jacob? Well, she must have given 10 to Jacob because if 13 is the whole and three is a part, the other part must be 10.

So the bar model can really help us to see what we know, what we don't know and whether the missing information is one of the parts or whether it's the whole.

So how did you get in filling in these missing numbers? So for this first bar model, we had 16 as the whole, 10 is a part, and six is a part.

And those are the subtraction equations.

We can write that link to our bar model.

For the second bar model we had 15 is the whole, 10 is a part.

So the other part must be five and those subtraction equations we can write.

And the last one, 14 was the whole, 10 is a part and four is a part.

And again, we can write our subtraction equations to match our bar model.

And what about these, did you manage to work these out and match them? So let's put in some answers.

17 subtract 10 is equal to seven.

15 subtract 10 is equal to five.

Can you see what's happening here? We are taking away the 1 ten each time.

So we are left with our ones digit.

So 16 subtract 10, we are left with our six ones.

18 subtract 10, we're left with our eight ones.

So can you then see that 15 subtract five, subtract five is equal to five 'cause we've subtracted a five and a five, which is, like, 10.

16 subtract six, subtract four, well, six plus four is equal to 10.

So we've subtracted 10 again.

17 subtract seven, subtract three, seven plus three is equal to 10.

We've subtracted 10 again, and 18 subtract eight, subtract two, again, we've subtracted 10 again.

Eight plus two is equal to 10.

So you can see that our 17 subtract 10 matches with 17 subtract seven, subtract three.

15 subtract 10 matches with 15 subtract five, subtract five.

16 subtract 10 matches with 16 subtract six, subtract four.

And 18 subtract 10 matches with 18 subtract eight, subtract two.

Fantastic thinking.

I hope you used your part-part-whole knowledge a lot to help you work out those questions.

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

What have we learned about today? We've learned that those teens numbers can be partitioned into 10 and a bit, and that can really help us when we're solving problems. We can solve addition and subtraction problems with ones parts or tens parts missing and knowing about our partitioning really helps us.

And a part-part-whole model or a bar model can help to represent the missing whole or the missing parts and help us to see what it is we are trying to work out to solve a problem.

Thank you for all your hard work and your mathematical thinking today.

I hope you've enjoyed solving problems, and I hope I get to see you again soon.

Bye-bye.