Lesson video

Hello there.

My name is Ms. Coe.

I am really excited to be part of your learning journey today.

In this lesson, we're going to be looking at solving problems, which is one of my favourite things to do in maths.

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

Welcome to this lesson in the unit of composition of numbers six to ten.

In this lesson today, we'll be looking at problem solving using holes and parts.

And by the end of this lesson, you'll be able to say that you can identify a missing part when a hole is partitioned into two parts.

Let's look at our key words for today.

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

Are you ready? My turn.

Partition.

Your turn.

My turn.

Hole.

Your turn.

My turn.

Part.

Your turn.

Excellent job.

I want you to listen really carefully for those words today, and see if you can use them when you're talking about the learning.

In this lesson today, we're going to be identifying missing parts when a hole is partitioned into two parts.

Our learning today has two cycles.

In the first part, we're going to be focusing on finding a missing part.

And in the second part of our learning today, we're going to be looking at partitioning problems. Let's get going with the first part of our lesson.

In this lesson today, you're going to meet two friends, Jacob and Laura.

They're going to be helping us with our maths, so keep an eye out for what they have to say.

Objects can be partitioned into two or more parts, and we can use a part-part-hole model to show this.

Here's our part-part-hole model.

You can see that the hole is positioned at the top and the two parts are at the bottom.

We might not be able to always see the parts, so sometimes one or even both of the parts might be hidden.

But if we know the hole and one of those parts, we can work out the missing part, and that's what we're going to look at now.

We can use some stem sentences to help us, and I wonder if you can spot these when we're doing our learning today.

The hole is_______, and one part is______, so the other part must be_________.

Laura and Jacob are playing a hiding game.

Laura has eight counters, and she's going to show one hand to Jacob.

So, she has her counters in two hands.

She has eight counters altogether, and she's showing one of her hands to Jacob with some counters in.

Jacob has to guess how many are hiding in the other hand.

So, Laura asks, how many am I hiding in my right hand? Let's see if we can help Jacob out.

How many counters can you see in Laura's left hand? That's right, she's got seven counters in her left hand.

So, we need to see how many counters are hiding in her right hand.

Jacob is going to say, I think the missing part is________.

Well, can you see what the missing part will be? If Laura has eight counters altogether, and she has seven in her left hand, then absolutely the missing part is one.

And Jacob can say, I think the missing part is one.

Let's think about why.

Well, if we know that the hole is eight counters, Laura had seven counters in her left hand, and we know that seven and one make eight.

Seven is one part, one is another part, and eight is the hole.

So, the missing part had to be one.

Laura and Jacob continue to play the game.

Laura still has eight counters altogether, and she has shown one hand to Jacob.

How many am I hiding in my right hand? She asks Jacob.

So, let's see if Jacob can guess how many are hiding in the other hand.

Jacob is going to say, I think the missing part is_________.

Can you see what the missing part is? Well, Jacob says the missing part is zero.

Let's check.

Absolutely.

Laura's right hand is empty.

That is because the hole is eight.

One part is eight, so the other part has to be zero.

If Laura had all of the counters in her right hand, all eight counters, then she couldn't have had any in her left hand.

Laura and Jacob go on to play a different game.

So, this time Laura has drawn a bar model, and Jacob has drawn a part-part-hole model, and they're going to try and guess each other's missing part.

Let's see what they got up to.

So here is Laura's bar model.

Can you think about what the hole is, what the part is, and can you see where the missing part is going to go? And this is Jacob's part-part-hole model.

So, we have a hole, we have one part, and we're missing a part.

And Laura is going to say, I think your missing part is_______.

Now let's take a closer look at that part-part-hole model.

We can see that the hole is eight.

One part is two.

Can you guess what the missing part is? That's right.

The missing part is six.

We know that eight can be partitioned into two and six.

So, if eight is the hole and one part is two, the missing part had to be six.

Let's look at the bar model.

Now remember the bar model is just a different way to show parts and holes.

The hole is at the top.

So, in this case, the hole is still eight.

One part is six.

What is the missing part? Well, Jacob says, I think your missing part is two.

And Jacob would be correct.

The hole is eight.

One part is six.

And so, the missing part is two, because six and two make eight.

Well done, Jacob.

We can use our knowledge of odd and even numbers to explain our thinking about a missing part.

So, if we look at the part-part-hole model here, we know that six and eight are both even numbers.

Here's six, and here's eight.

And we can see that they're both even because they're made up of pairs, and they don't have an odd block on the top of their number shape.

Jacob knows that two even numbers make an even number.

So, if one of the parts is six, the missing part has to be an even number as well.

So, the missing part needs to be even.

And we can see from our number shapes that the missing part is two.

And we know that two is an even number because it is made up of one pair.

The missing part has to be two.

Six and two make eight.

Now it's time to check your understanding.

What is the missing part? And how do you know? Pause the video here, have a think, and see if you can reason why, you know what the missing part is.

Welcome back.

How did you get on? Laura said that she thinks the missing part will be odd.

I wonder if you said that.

And that's because two odd numbers can add together to make an even number.

We know that six is an even number because we know that it can be made up of pairs with no odd block.

We know that three is an odd number because it cannot be made of pairs.

Jacob says that two odd numbers make an even number.

So, we can see that three and three make six.

The missing part is three.

Three and three make six.

Six is the whole, three is a part, and three is a part.

Well done if you got that.

Time to check your understanding again.

What is the missing part this time? How do you know? Can you talk about odds and evens in your answer? Pause the video here and have a go.

Welcome back.

How did you get on? This time, Laura says that the missing part will be odd.

And that's because an odd number and an even number make an odd number.

Seven is an odd number.

We can see from its number shape that it cannot be made from pairs.

Four is an even number.

It can be made from pairs.

So, if we know that an odd number can be made up of an even number and an odd number, the missing part will be odd.

What is the missing part? Well, Laura says, I think the missing part is three.

And that's because four and three make seven.

Seven is the whole, four is a part, and three is a part.

Well done if that's what you got.

Laura and Jacob are playing a different game.

This time, Laura has drawn a number line, and Jacob has drawn a part-part-whole model.

They're still working out their missing parts, though.

Here is Laura's number line.

I wonder what you can see on the number line.

Can you see the whole? Can you see one part and the missing part? And here is Jacob's part-part-whole model.

The whole is at the top, and we can see that one part is four.

Laura says, I think your missing part is_______.

Can you see what the missing part is in the part-part-whole model? The missing part is five.

Nine is the whole, four is a part, and five is a part.

Four and five make nine.

What about on the number line? What can we see here? Well, Jacob says, I think the missing part is four.

And he'd be right.

Nine is the whole, five is a part, and four is a part.

Remember, it doesn't matter which order those parts come in.

They are still the same.

So, Nine is four and five, or nine is five and four.

They mean the same thing.

What do you notice about these representations? What is the same and what is different? Well, Jacob noticed that they all have ten as the whole.

On the top of the part-part-whole model and the bar model, you can see the number ten, showing us that ten is the whole.

And in the number line representation, ten has been circled, showing us that that's the whole.

That's one thing that's the same.

Laura has noticed that they all have six as a part.

So, in the part-part-whole model, the known part is six, the same in the bar model.

And in the number line, you can see that one of the jumps has been labelled with six.

They are all showing the same partition, but in a different way.

So that means that the missing parts from all of these have to be the same, because, as Jacob said, they're all showing the same relationship, the same partition.

That must mean that four is the missing part in all of these models.

Well done if you noticed that.

Time for you to have a go at a task.

For your first task, I would like you to find six small objects.

You could use cubes or counters.

Hold them in your hands.

Show one of your hands to your partner.

Ask a friend to guess how many you're hiding in the other hand.

Get them to explain to you how they know.

So, you might say to your partner, how many am I hiding in my right hand? And your partner might say, I think the missing part is ____.

Use part-part-whole models to represent the objects that you have a go with.

For question two, I'd like you to play this missing number game with a partner.

Player one is going to pick a card from pile A.

This is going to be your whole.

Player two is going to pick a card from pile B, and that's going to be one part.

Player two is then going to work out the missing part.

You win the cards if you can work out the missing part.

Let's see what that game looks like.

Jacob and Laura are going to play the game.

Laura has gone first.

She's player one.

She has selected the whole, which is seven.

Jacob has selected one of the parts five.

So, he has said five is a part.

Laura would then say that the missing part is two.

Now remember, it's really important that she explains how she knows.

So, she might say five and two make seven.

Jacob is reminding us that we can use our odds and evens.

So, two is even and five is odd.

And we know that an even and an odd part make an odd whole.

Great explanation.

Laura would then win the cards and then swap roles for the next turn.

Here are some cards that you might want to use for your game.

Pause the video here and have a go at these tasks.

Welcome back.

How did you get on with those two games? Now, your game might have looked very different to this, but here's an example.

Did your friend guess how many counters you were hiding? Laura asks Jacob, how many is she hiding in her right hand? We know she has six counters altogether.

One part is three.

So, Jacob says, I think the missing part is three.

And we can check, we can show our hands.

Let's have another go.

This time, Laura has got six counters altogether, and she's showing Jacob two.

So how many are hiding in Laura's right hand? Jacob says, I think the missing part is four.

And he is absolutely correct.

Well done if you had fun playing this game with your partner.

Did you play the missing number game? Your missing number game might have looked different to this one.

But let's see what Laura and Jacob did.

He might have tried something like this.

Eight is the whole.

Five is a part.

So, the missing part is three.

Three is an odd number, says Jacob.

So, Laura knows that two odd parts make an even whole.

That's a great explanation for why she thinks the missing part is three.

This time, ten is the whole.

Six is one of the parts.

So, what is the missing part? The missing part this time is four.

Four is an even number, says Jacob.

And Laura knows that two even parts make an even whole.

She also knows that six and four make ten.

So, the missing part had to be four.

Let's move on to our second learning cycle, which is all about partitioning problems. We can tell a story represented by a part-part-whole model.

And we can also think about missing parts when telling these stories.

Let's look at this problem.

The ladybird is climbing up the flower.

The flower is six centimetres tall.

And the ladybird is one centimetre up.

How much further does it need to go? So, this is a part-part-whole problem.

We can use the stem sentence to say what the answer is going to be.

We can say the whole is_________, and one part is________, so the other part must be________.

What is the whole in this sentence? Well, the whole is six, because the flower is six centimetres tall.

That's the total length of the flower.

And we know one of the parts.

We know one part is one.

The ladybird has climbed one centimetre.

We don't know the missing part at the moment.

We don't know how much farther it needs to go.

But we can use what we know about the number six to work it out.

The whole is six.

One part is one.

The missing part must be five, because one and five make six.

We can say the whole is six, and one part is one, so the other part must be five.

And we can show it in different ways.

We need to answer the question now.

How much further does it need to go? The ladybird needs to go five more centimetres to get to the top of the flower.

Let's look at another example.

The spider is climbing up the spout.

The spout is eight metres tall, and the spider is six metres up.

How much farther does it need to go? Again, we can think about this as wholes and parts.

What is the whole in this question? Well, in this time, the whole is eight metres.

The spout is eight metres tall.

One part is six, because the spider is six metres up, so he's climbed six metres of that eight metres.

We have a missing part.

We can use what we know about the number eight to find the missing part.

If the whole is eight, one part is six, then the other part must be two, because six and two make eight.

So, we can say the whole sentence.

The whole is eight, and one part is six, so the other part must be two.

Can you say that with me? Are you ready? The whole is eight, and one part is six, so the other part must be two.

Well done.

So, we can say that the spider needs to go two more metres to reach the top of the spout.

Well done.

Let's look at a different problem.

Laura is going to clap seven times.

She has clapped once.

How many more claps will she do? So, this time, the whole is seven, and Laura has clapped once.

She has clapped one time.

Once means just one.

So, how many more claps will she do? Well, we can use our sentence.

I wonder if you can say it with me.

The whole is seven, and one part is one, so the other part must be six.

Jacob says that you need to clap six more times.

So, let's see if we can say that whole sentence.

The whole is seven, and one part is one, so the other part must be six.

Well done if you said that with me.

Time to check your understanding.

Jacob and Laura have partitioned a number in different ways, so the whole is the same.

What are the missing numbers? How do you know? Pause the video and have a go at this task.

Welcome back.

How did you get on? Well, in the first one, we know that the whole is the same each time, so the whole in this part-part-whole model is going to be six.

We could also work that out by saying we know that three and three make six.

Let's look at the middle one.

The whole is six, and one part is two, so what is the missing part? Well, we know that six can be partitioned into two and four, so the missing part is four.

Well done if you said that.

And the last one, the whole is six, one part is five, so the missing part must be one, because five and one make six.

Well done if you got all three of those.

Let's move on to look at a slightly different problem.

Jacob and Laura are both counting cars.

What is the whole this time? So, Jacob counted four cars.

One part is four.

Laura counted six cars, so the other part is six.

Can we say the start of that sentence together? Are you ready? One part is four, and one part is six.

Great job.

So, what is the whole? How many cars did they count all together? The whole must be ten, because ten can be partitioned into four and six, or four and six make ten.

Let's say that sentence together.

Are you ready? One part is four, and one part is six, so the whole must be ten.

Great job.

Let's look at another example like that.

This time, Jacob counted three cars.

One of the parts is three.

Laura counted five cars.

One of the parts is five.

One part is three, and one part is five, so the whole must be eight cars in total, because three and five make eight.

So, you can solve problems if you know both parts, if you don't know the whole, by thinking about how would you partition the number.

Time to check your understanding.

Here are four part-part-whole models.

The whole is seven each time, but as you can see, there are all missing parts.

You have the numbers below, zero to nine.

I would like you to think about what the missing parts could be.

So out of all of those numbers, what could those missing parts be? Pause the video here and have a go.

Welcome back.

Well, the missing parts could be zero, one, two, three, four, five, six, or seven.

So, lots of possibilities there.

The missing parts have to be seven or less, because seven could be partitioned into seven and zero, or lots of other combinations.

The part cannot be bigger than the whole, which is seven.

So, the part could not be eight or nine.

Well done if you said that.

So, let's look at the parts we decided to put in.

Seven could be zero and seven, could be one and six, two and five, or three and four.

So, the parts could not be eight or nine.

Time for your second task.

For question one, we'd like to find the missing parts in the part-part-whole models and then match them to the stories.

So, you have four part-part-whole models there, and you have a missing part in each one.

Once you've found the missing parts, read the stories carefully and match the correct part-part-whole model to the correct story.

Here are the stories.

I am going to clap seven times in total.

I have clapped two times.

How many more claps will I do? I have nine counters in total.

I have three counters in one hand.

How many are in the other hand? I am going to nod eight times in total.

I have nodded three times.

How many more nods will I do? And finally, I have seven counters in total.

I have one counter in one hand.

How many are in the other hand? For question two, I'd like you to fill in the missing parts on the part-part-whole models again.

You have three there with a whole and a missing part.

Once you've done that, I'd like you to tell a story or do an action to go with those part-part-whole models.

The last part-part-whole model is completely blank.

So, I'd like you to make your own missing part problem.

Remember, you can use the sentence to help you.

The whole is ____ and one part is ____, so the other part must be ____.

Good luck with those two tasks.

I know you're going to work really, really hard.

Welcome back.

How did you get on? Did you find the missing parts and match them to the story? So, the first part-part-whole model, seven is the whole, one is a part.

So, the missing part was six.

And that linked to this story.

I have seven counters in total.

I have one counter in one hand.

How many are in the other hand? So, in that story, I had seven as my whole.

One counter was in one hand, so I had six counters hiding in my other hand.

The second part-part-whole model, the whole was seven, one part was two, so the missing part was five.

And that linked to this story.

I am going to clap seven times in total.

I have clapped five times.

How many more claps will I do? So, in this case, we had seven as the whole, and our parts were two and five.

For the next one, the missing part was five.

And the story was, I am going to nod eight times in total.

I've nodded three times.

How many more nods will I do? And I knew that three and five make eight.

And finally, the whole is nine, one part is three, and so the missing part was six.

And that linked to this story.

I have nine counters in total.

I have three counters in one hand.

How many are in the other hand? Well done if you answered all of those correctly.

Now for question two, you might have done lots of different things to go with the part-part-whole models.

Let's see what Laura and Jacob got up to.

The whole is nine, one part is five, and one part is four.

So, Jacob was going to nod five times, and then Laura was going to nod four times.

And that would make nine times in total.

For the second one, the whole was seven, one part was five, and one part was two.

So, Jacob decided to clap this time.

He clapped five times, so Laura clapped two times to make the whole of seven.

For the next one, the whole was eight, and the parts were five and three.

So, Jacob decided to hide some counters.

He had five counters in one hand, so he must have had three counters in the other hand.

And then finally, we asked you to make your own missing part problem.

Now you could have done lots of things, but Jacob and Laura decided to use the whole of nine, and parts of five and four.

So, Jacob said, I have five counters in one hand.

So, Laura said, you must have four counters in the other hand.

Well done if you made up your own problems. We've come to the end of our lesson, and I know you've worked really hard on solving those tricky problems. Let's see what we've learned today.

Numbers can be partitioned into two or more parts in different ways, and we've seen lots of ways that we can partition the numbers six, seven, eight, nine, and ten today.

If we know one of the parts and we know the whole, we can find the other part.

We can use part-part-whole models or bar models to represent a whole number and a missing part.

And knowing about odd and even parts means that we can work out if the missing part is odd or even, which is a great way to explain.

Thank you so much for your hard work today, and I look forward to seeing you again soon.

Bye.