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I can solve problems finding the missing part when the other part and the whole is known.

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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

Each of the numbers one to five can be partitioned into two parts.
Use the sentence, the whole is ___ and one part is ___ so the other part must be ___
Notice the smaller the number being partitioned, the fewer the number of combinations.

Common misconception

Children may confuse the part and the whole, or add the whole and one part to find the missing part.

Encourage the use of the stem sentence ___ is the whole, ___ is a part and ___ is a part, to reinforce what the numbers represent.

Keywords

Partition - Partition means to split up a whole into parts.
Part-part-whole model - A part-part-whole model is a pictorial representation that shows the whole and its parts.
Missing part - A missing part is one of the parts that cannot be seen.

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Hello, I'm Mrs. Kaley, and I'm going to help you with your learning today.

So in today's lesson, we will solve problems finding a missing part when one part and the whole is known.

So let's have a look at today's lesson outcome.

Here's the outcome of today's lesson.

\"I can solve problems finding the missing part when the other part and the whole is known.\" Let's have a look at today's keywords.

Here are the keywords for today's lesson.

Can you repeat them after me? We've got partition.

My turn, partition.

Your turn.

Then we've got part-part-whole model.

So repeat that after me.

My turn, part-part-whole model.

Your turn.

Then we've got missing part.

Can you say that after me? Missing part.

Your turn.

Well done.

Now, partition means that we are going to split a whole into parts.

A part-part-whole model is a representation showing the whole and the parts that it's been split into.

And a missing part means that we know the whole and we know one of the parts, but one of the parts is missing so we need to work it out.

Here's the outline of today's lesson.

We are going to solve problems finding a missing part when one part and the whole is known.

We'll start off by representing missing number problems and then we'll move on to solving missing number problems. Let's start on the learning.

Here are some children that are going to help us today.

We've got Aisha and Lucas.

Objects can be partitioned into two or more parts.

This can be shown on a part-part-whole model.

Here's a part-part-whole model.

Can you see the whole at the top? And it's been split into two parts.

We may not always be able to see the parts.

One of the parts is missing now.

If we know the whole and one part, we can work out the missing part.

Aisha said, \"The whole is something and one part is something, so the other part must be something.\" That's a stem sentence that we can use in today's lesson.

We can tell a story represented by a part-part-whole model.

You can see the part-part-whole model here with the whole at the top and the two parts it's been partitioned into.

You can see the stem sentence as well.

Can you practise saying it? The whole is (hums), and one part is (hums), so the other part must be (hums).

And we're going to find out the numbers that go in the gaps.

Here's a problem for us to look at.

\"The ladybird is climbing up the flower.

The flower is four centimetres tall, and the ladybird is one centimetre up.

How much further does it need to go?\" Can you see the flower with the ladybird on it? It's already moved one centimetre up the flower.

Now it's got to try to get to the top of the flower.

We know that the whole is four because that's how tall the flower is, four centimetres.

We know that one of the parts is one centimetre because he's already travelled one centimetre up the flower.

So here's the part-part-whole model that represents what we know so far.

We know four is the whole and one is one of the parts.

I wonder what the other part might be.

Here's our stem sentence.

\"The whole is four and one part is one so the other part must be.

.\" I wonder how much more he needs to travel up the flower to get to the top.

It's three.

Three centimetres to get to the top of the flower so the missing part is three.

Now he's going to move to the top of the flower.

One centimetre, two centimetres, three centimetres to get to the top of the flower.

Here's another problem.

\"The spider is climbing up the spout.

The spout is five metres tall, and the spider is two metres up.

How much further does it need to go?\" Can you see the spout there? And the spider has already travelled two metres up the spout.

So we know that the whole is five because the spout is five metres tall, and we know that one of the parts is two metres because he's already moved two metres up the spout.

Here's our stem sentence.

Let's see if we can say it together.

\"The whole is five and one part is two.\" That's the part that we already know.

\"So the other part must be.

.\" I wonder how much more he needs to travel to get to the top of the spout.

It's three.

Three metres more.

Let's see him move up to the top of the spout.

One metre, two metres, three metres.

So the missing part was three metres.

Here's another problem for us to solve.

\"Aisha is going to clap four times.\" So we know that the whole is going to be four.

\"She has clapped once.

How many more claps will she do?\" Can you see? She's already done one clap.

(claps) One.

How many more does she need to do to make four claps in total? Here's our part-whole model.

We know that four is the whole and one is one of the parts.

So I wonder what the missing part is.

Here's our stem sentence.

Can you say it with me? \"The whole is four, and one part is one, so the other part must be.

.\" Lucas thinks that she will clap three more times.

Do you think he's right? Yes, she's going to clap three more times.

So four was the whole, one is a part, so the other part must be three because four can be partitioned into one and three.

Here's another problem for us.

\"Lucas is going to nod his head three times.\" So we know that the whole is going to be three.

\"He has nodded two times.

How many more nods will he do?\" So you can see he's already done one, two nods.

How many more to make three in total? Here's our part-whole model.

Can you see we got three as the whole.

Two is one of the parts, and we need to work out the missing part.

Here's our stem sentence to help us.

Can you say it with me? \"The whole is three and one part is two, so the other part must be.

.\" What do you think it's going to be? Aisha said, \"You will nod one more time.\" Do you agree with her? Yes, the missing part was one, so I can see three was the whole, and two is a part and one is a part.

Three has been partitioned into two and one.

We can draw a part-part-whole model to match a story.

So Lucas and Aisha are going to tell a story.

Lucas said, \"I will nod four times.\" So that's going to be the whole.

Nod, nod, nod.

He's already done three nods, hasn't he? Here's the part-part-whole model to go with this story.

We know that four is the whole and three is one of the parts.

What do you think the other part's going to be? Let's say our stem sentence together.

\"The whole is four and one part is three, so the other part must be.

.\" Aisha thinks the other part is one.

She said, \"You will nod one more time.\" Do you agree? So the other part must be one.

The missing part was one.

I can see four has been partitioned into three and one.

Let's check your understanding.

Which part-part-whole model matches the story? So Lucas and Aisha are going to tell another story.

Lucas said, \"I will nod four times.\" So that's going to be the whole.

Nod, nod.

That's one of the parts.

How many times has he already nodded? Aisha thinks you will nod two more times.

Which part-part-whole model represents the story? Pause the video and think about this one.

That's right, it's the second part-part-whole model.

I can see four is the whole.

Two is a part and two is a part.

Let's say the stem sentence together.

\"The whole is four and one part is two, so the other part must be two.\" The missing part was two.

Four can be partitioned into two and two.

Let's check your understanding again.

Which story matches the part-part-whole model? Can you see, five is the whole, and two is a part, and three is a part.

Here are some stories that might match the part-part-whole model.

Lucas said, \"I will nod five times.\" Nod, nod.

Aisha said \"You will nod one more time.\" Does that make five altogether? Here's another story.

Aisha said, \"I will clap five times.\" Clap, clap.

(claps) Lucas said, \"You will clap three more times.\" Which story matches the part-part-whole model? Is it the top one or the bottom one? That's right, it was the bottom story.

The top story didn't make five for the whole.

The bottom story did.

Let's say the stem sentence together.

\"The whole is five and one part is two.\" Can you see Aisha has already clapped twice.

And Lucas said, \"You will clap three more times.\" \"So the other part must be.

.\" Three.

That's right.

I can see five was the whole, two is a part and three is a part.

So five has been partitioned into two and three.

Let's check your understanding again.

Can you do an action to work out the missing parts? So can you see, we've got four as the whole for both of these part-part-whole models.

The first one, one is a part, and the second one, two is part.

Can you pause the video and think of an action to work out the missing parts? You might clap your hands or you might nod your head or tap your feet so pause the video and have a go.

How did you get on with this one? Let's look at the first part-part-whole model.

We've got four as the whole and one as one of the parts.

Aisha is going to clap once.

Can you do it with me? (claps) One.

Lucas thinks you will clap three more times.

Can you try it? One (claps), two (claps), three (claps).

Does that make four for the whole? Yes, it does.

So the missing part was three.

Let's look at the bottom part-part-whole model.

We've got four as the whole again.

This time we've got two as one of the parts.

Lucas is going to nod twice.

Can you try it? Nod, nod.

Aisha said, \"You will nod two more times.\" Do you think that will make four altogether? Yes, let's try it.

Nod, nod.

So two is the missing part.

Four has been partitioned into two and two.

Aisha and Lucas found four ways to clap three times.

We can see the whole on these part-part-whole models, and we can see one of the parts, but one of the parts is missing.

Let's see if we can work them out.

Let's look at the first part-part-whole model.

We've got three as the whole, and Aisha and Lucas are going to clap the parts.

Aisha is going to clap three times.

That's one of the parts.

And Lucas is going to clap zero times.

That makes three altogether.

Shall we try that? One (claps), two (claps), three (claps).

Let's look at the second part-part-whole model.

Again, we've got three as the whole, and one of the parts is two so Aisha is going to clap two times.

Can you try that? One (claps), two (claps).

How many more claps do we need to make three as the whole? That's it.

One more clap.

One (claps).

That makes three altogether.

Let's look at the next part-part-whole model.

Again, we've got three as the whole, and we've got one as one of the parts.

So Aisha is going to clap once.

Are you ready? (claps) One.

How many more claps do we need to make three altogether? That's right.

Two more claps.

One (claps), two (claps).

And on the last part-part-whole model, we've got three as the whole and zero as one of the parts so Aisha is going to clap zero times.

So Lucas will clap three times.

The missing part was three.

One (claps), two (claps), three (claps).

Lucas found four ways to partition the number three.

He has spilled ink on some of the numbers.

What are the missing numbers? Lucas said, \"I will use counters to check.\" So let's look at the first one.

Three was the whole and three was one of the parts and the other part is zero.

So I can see with his counters, he's got three on one side and zero on the other.

Let's look at the second one.

Three is the whole and two is one of the parts.

So what's the other part? Can you see, he split his counters into two parts.

That's right.

One was the missing part.

Let's look at the next one.

Three is the whole and one is one of the parts.

So the missing part is.

Two.

That's correct.

I can see Lucas has got one counter in one part and two in the other part.

And the final one, we had three as the whole and he's got zero in one part so the other part must be.

Three counters.

Three has been partitioned into zero and three.

Let's check your understanding.

What could the missing part be here, and what do you notice about the missing parts? So have a look at the part-part-whole models and see if you can work out what the missing parts are.

And there's a stem sentence to help you as well.

You could use counters to check your answers, so pause the video while you have a go.

How did you get on with this one? So the first part-part-whole model, two was the whole, and one is one of the parts.

So the whole is two and one part is one.

So the other part must be.

It's one.

Well done.

Let's look at the second one.

Can you say the stem sentence with me? \"The whole is three and one part is two, so the other part must be.

.\" One.

That's right.

Let's look at the third one.

Can you say the stem sentence with me? \"The whole is four and one part is three, so the other part must be.

.\" It's one again.

Well done.

Let's look at the last one.

Can you say the stem sentence with me? \"The whole is five and one part is four, so the other part must be.

.\" It's one again.

What did you notice about the missing parts? They were all one, weren't they? One part, the one that we could see, is one less than the whole, so the other part is one.

Here's a task for you to have a go at.

Can you complete the stem sentences to partition the number four? Look at the part-part-whole models.

We can see the whole, and we can see one of the parts, but one of the parts is missing.

Can you try to work out the missing part and then fill in the numbers on the part-part-whole models? You could use counters to help you.

Here's the second part of your task.

Can you complete the stem sentences to partition other numbers? So think of some small numbers up to six that you could partition, and you could use counters to help you.

So put the whole at the top of the part-part-whole models, then split your counters into two parts and write down what one of the parts is and then work out the missing part.

Then see if you can fill out the stem sentences.

So pause the video while you have a go at your tasks.

How did you get on with your tasks? Did you complete the stem sentences to partition the number four? So we had the part-part-whole models.

I can see that four is the whole, and three is one of the parts.

Let's say the stem sentence together.

\"The whole is four and one part is three, so the other part must be.

.\" It was one.

Well done.

Let's look at the last one.

Can you say the stem sentence with me? \"The whole is four and one part is two.

So the other part must be.

.\" That's two as well because four can be partitioned into two and two.

How did you get on with the second task? Did you partition some other numbers? Here are some examples.

I tried to partition the number five.

So five is the whole and I had three as one of the parts.

Can you say the stem sentence with me? \"The whole is five and one part is three, so the other part must be.

.\" It's two.

So five can be partitioned into three and two.

Let's look at the other example.

I had three as the whole and two as one of the parts.

Can you say the stem sentence with me? \"The whole is three and one part is two, so the other part must be.

.\" It's one.

So three can be partitioned into two and one.

Which examples did you try? Let's move on to the second part of the lesson.

We will solve missing number problems. \"A whole can be partitioned into two or more parts.

The parts might look the same or different.

Sometimes we might know the whole but not the parts.\" Lucas is saying, \"I wonder what the parts could be?\" Let's look at another problem.

The ladybird is climbing up the flower again.

The flower is four centimetres tall, and the ladybird is two centimetres up.

How much further does it need to go? So we know that four is the whole, and we know that two is one of the parts, and we've got to work out the missing part.

Here's our stem sentence to help us.

Can you say it with me? \"The whole is four and one part is two, so the other part must be.

.\" How much further does he need to move up the flower? It's two centimetres.

Let's see him going up two centimetres.

Are you ready? One centimetre, two centimetres.

Now he's at the top of the flower.

Here's another problem for us to look at.

The ladybird is climbing up the flower.

The flower is five centimetres tall, and the ladybird is one centimetre up.

How much further does it need to go? So we know that the whole is five and one of the parts is one, and we've got to work out the missing part.

Let's say our stem sentence together.

\"The whole is five and one part is one, so the other part must be.

.\" How much further does he need to go up the flower? That's right, it's four centimetres.

So let's see him going up the flower four more centimetres.

One centimetre, two centimetres, three centimetres, four centimetres.

Now he's at the top of the flower.

Here's the spider again.

\"The spider is climbing up the spout.

The spout is five metres tall, and the spider is three metres up.

How much further does it need to go?\" So we know that the whole is five and one of the parts is three so now we've got to work out the missing part.

Let's say our stem sentence together.

\"The whole is five and one part is three, so the other part must be.

.\" How many more metres does he need to travel up the spout? It's two more metres.

Let's see him going up the spout two more metres.

One metre, two metres.

Now he's at the top of the spout.

So five can be partitioned into three and two.

Here's another problem for us.

\"There are two pots and five seeds.

Aisha puts more seeds in pot A than pot B.

How many seeds might be in each pot?\" Remember, pot A needs to have more seeds than pot B.

Aisha is asking a question, \"How many seeds cannot be in pot A?\" Aisha and Lucas are going to have a go at putting the seeds in the pots.

Aisha thinks pot A could have three seeds.

There's three seeds for pot A.

Lucas thinks pot B could have two seeds.

Does that make five altogether? Yes, it does, doesn't it? And are there more seeds in pot A than pot B? Yes, three is more than two.

They're going to try it in a different way.

Aisha said, \"Pot A could have four seeds.\" So let's put four seeds in pot A.

I wonder how many are going to be in pot B.

Lucas said \"Pot B could have one seed.\" Does that make five altogether? Yes, it does.

And has pot A got more than pot B? Yes, four is more than one.

They're going to try it a different way.

Aisha said, \"Pot A could have five seeds.\" So let's put five seeds in pot A.

I wonder how many are going to be in pot B.

Lucas said, \"Pot B could have zero seeds.\" Do you agree? And has pot A got more than pot B? Yes, it has.

Five is more than zero.

Aisha is asking a question.

\"Are there any other ways?\" Lucas thinks, \"No, we have found them all.\" Aisha is asking \"How many seeds cannot be in pot A?\" Lucas said, \"Pot A cannot have fewer than pot B.\" And Aisha said, \"Pot A must have more than pot B.\" So Lucas said, \"Pot A cannot have zero, one, or two seeds.\" It's got to have more than that to be more than pot B.

\"Aisha and Lucas have represented their ideas as part-part-whole models.

They have spilt ink on some of the numbers.

What are the missing numbers?\" So I can see that the first part-part-whole model has got the whole missing.

Do you remember what the whole was? The whole is five.

One of the parts is three and one of the parts is two.

The second part-part-whole model, I can see one of the parts is missing.

The whole is five.

One of the parts is one.

So the other part is.

It's four.

And the last one, I can see five is the whole five is one of the parts, so the missing part is zero.

Let's check your understanding.

What could the missing parts be? I can see we've got five counters and two hands.

You could try this if you've got five counters or five cubes or five small objects to put in your hands.

Lucas said, \"I have more counters in my left hand.\" So see if you can try it with some counters.

Remember, there have got to be more counters in your left hand than your right hand.

I wonder how many different ways it can be done.

So pause the video while you try different ways and you could represent it on a part-part-whole model.

Here's some ways that Lucas has tried.

He's got three counters in one hand, so three is one of the parts.

In the other hand he's got two counters, so the missing part is two.

So five has been partitioned into three and two.

Is there a different way that you tried? Here's a different way that Lucas did it.

He's got four counters in one hand, so four is one of the parts, and he's got one counter in the other hand.

So five has been partitioned into four and one.

Could he have done it a different way? This time, he's got five counters in one hand, so that's one of the parts.

And in the other hand he's got zero counters.

So five can be partitioned into five and zero.

Are there any other ways that he could have done it? He's found all the ways because remember, he needs to have more counters in his left hand than in his right hand.

Here are some part-part-whole models.

What could the missing parts be and what could the missing parts not be? So I can see that three is the whole.

So we could have, the missing parts could be zero and three, or they could be one and two, or two and one, or they could be three and zero.

So we could use any of the numbers from zero up to three, but we can't use the numbers four, five, or six as the missing part.

Here's a task for you to have a go at.

Can you write the missing parts to go over the pictures? So we've got some spiders climbing up the spout.

The spout is five metres tall, so the whole is five each time.

Can you see that the spider has started to move up the spout? So we can see one of the parts, and you need to work out the missing part.

Here's the second part of your task.

Aisha has found four ways to partition the number three.

Can you write the missing part and do an action to go with the part-part-whole models? So you might try clapping or nodding or tapping your feet to work out the missing parts.

And Aisha is saying a stem sentence to help you.

\"The whole is (hums) and one part is (hums), so the other part must be (hums).\" So pause the video while you have a go at your tasks.

How did you get on with the first part of your task? So did you write the missing numbers to go with the pictures? I can see that the whole is five.

And for the first picture, one of the parts is one, so the missing part is four because five can be partitioned into one and four.

The second picture, I can see five is the whole, and two is one of the parts, so the missing part is three because five can be partitioned into two and three.

And on the last picture, I can see five is the whole and three is one of the parts, so the missing part is two because five can be partitioned into three and two.

How did you get on with that one? Here's the second part of your task, and here are the missing parts.

Can you see three has been partitioned into three and zero, and two and one, and one and two, and zero and three.

And the stem sentence can help us.

Can you say the stem sentence with me? So let's look at the first part-part-whole model.

\"The whole is three.

One part is three, so the other part must be zero.\" Let's look at the second one.

\"The whole is three and one part is two, so the other part must be one.\" Let's look at the third one.

\"The whole is three, one part is one, so the other part must be two.\" And the last one, \"The whole is three, one part is zero, so the other part must be three.\" How did you get on with that one? Did you do some actions to go with the part-part-whole models? So here, Lucas and Aisha are trying some actions.

For the first one, Lucas is going to nod three times.

One, two, three.

And Aisha said, \"You will nod zero more times.\" So the missing part is zero.

The second part-part-whole model, the whole was three.

One of the parts is one, so Aisha is going to clap once.

(claps) And Lucas said, \"You will clap two more times.\" (claps) And that makes three altogether.

The next part-part-whole model, we've got three as the whole and two is one of the parts, so Lucas is going to nod twice.

One, two.

Aisha said, \"You will nod one more time.\" So that makes three altogether.

The last one, the whole was three, and one of the parts is zero.

Aisha said, \"I have three seeds in the whole and zero seeds in pot A.\" And Lucas said, \"You will have three seeds in pot B.\" How did you get on with those ones? We've come to the end of our lesson.

Today, we've been solving problems, finding a missing part when one part and the whole is known.

This is what we've learned today.

Objects can be partitioned into two or more parts in different ways.

This can be shown on a part-part-whole model.

The smaller the number to partition, the fewer the number of combinations.

We may not always be able to see the parts.

If we know the whole and one part, we can work out the missing part.

Remember, you can always use cubes or counters or an action to check.

Well done, everyone.

See you next time.

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