Lesson video

Hello there, my name is Mr. Goldie, and welcome to today's math lesson.

I'm sure you're going to enjoy it.

And here is our learning outcome.

I can use the additive relationship to rearrange and solve equations.

And here are our keywords.

So two keywords today.

I'm going to say the keyword, and can you repeat it back? So the first key word is equation.

And the next key word is rearrange.

Excellent stuff.

And let's take a look at what those words mean.

So an equation shows that one number or calculation is equal to another.

So an example of an equation is 10 add 6 equals 16.

And the equals sign shows us that it is an equation.

Rearrange means to change an equation.

It could mean moving the parts or the whole or changing it from an addition into a subtraction equation.

So 10 add 6 equals 16 can be rearranged into 16 subtract 6 equals 10.

And here is our lesson outline.

So the first part of the lesson is rearranging equations with missing numbers.

And the second part of the lesson is problem solving with missing numbers.

And I promise there will be pandas in part 2 of the lesson as well.

So we look forward to.

Let's get started.

In this lesson, you will meet Lucas and Izzy, and they're going to be helping you with your maths today and ask you some difficult questions too.

Lucas is thinking about equations.

"Where is the whole in addition equations?" Lucas asks.

There is a bar model showing sum and the addends.

Where is the whole? "The whole in an addition equation is called the sum," says Izzy.

The sum in an addition equation can appear at the start of the equation.

So 400 equals 300 add 100.

The sum can appear at the end of an addition equation.

So 309 plus 100 equals 409.

Lucas thinks about subtraction equations.

Doing a lot of thinking today, isn't he, Lucas? "Where is the whole?" asks Lucas.

There's something called a bar model with minuend and subtrahend and difference on it.

So they're different parts of a subtraction equation.

Izzy says, "The whole in a subtraction equation is called the minuend." Well, the minuend can appear at the start of the equation.

So in 700, subtract 300 equals 400.

The minuend is 700, and that appears at the start of the equation.

The minuend can appear in the middle of a subtraction equation.

So the sum appears at the end or the beginning of an addition equation.

The minuend can appear at the beginning or the middle of a subtraction equation.

Lucas and Izzy are working out missing numbers in addition and subtraction equations.

"We're going to use bar models to help us complete the equations," says Lucas.

So here, we've got an equation with a missing number.

We've got something, a missing number, equals 65, add 20.

I wonder if one of the parts is missing.

I wonder if the whole is missing.

I wonder what you think.

So there's a bar model with a whole and the two parts.

And a 65 and 20 are the parts.

And it's the whole that is missing.

So the whole is missing.

The sum is missing in that equation.

"When a whole is missing, add the parts together," says Izzy.

So to work out the missing number in something equals 65 add 20, we'd have to add the parts together.

Add 65 and 20 together.

65 add 20 equals 85.

So the missing sum is 85.

Let's try this equation here.

This is a subtraction equation.

A number, a missing number, subtract 100 equals 203.

So what is missing? Is it the whole, or is it one of the parts? So we've got 100 and 203, and they are both the parts.

So we've got the whole, subtract one of the parts, subtract 100, equals, the other part, 203.

And Izzy says, "When a whole is missing, add the parts together." And it doesn't matter if it's a subtraction or an addition equation.

You still add the parts together.

But sometimes you need to rearrange the equation.

It's a bit difficult to add those two parts together like that, isn't it? So we can rearrange that equation into 203 add 100.

That gives us the number 303.

So the missing whole is 303.

303 subtract 100 equals 203.

So any time a whole is missing, add the parts together to find the missing whole.

To find a missing part, subtract the other part from the whole.

So let's look at this equation here.

So 20 adds something equals 105.

20 is one of the parts.

105 is the whole that is made from the two parts.

So to find a missing part, subtract the other part from the whole.

So, "It's often helpful to rearrange the equation to make it easier to calculate," says Izzy.

So we can change that calculation.

We can rearrange that equation into 105, the whole, subtract 20, the part that we know.

105 subtract 20, what would that be? Not too sure.

We could always use something to help us work out the answer.

So we've got 100 and five 1s.

And we can subtract two of those 10s.

Subtract 20 from the hundred, and that leaves us with eight 10s or 80.

105 subtract 20 equals 85.

So 20 add 85 equals 105.

That is our missing part.

Remember, to find a missing part, subtract the other part from the whole.

This time, we've got a subtraction calculation.

270 subtract something equals 100.

And again, we know the whole.

The whole is the minuend, the number at the beginning of the equation, 270.

How could we rearrange the equation to make it easier to calculate? The 270 is the whole, and 100 is one of the parts.

What did Lucas say? Lucas said, "To find a missing part, subtract the other part from the whole." So we can rearrange that equation into 270 subtract 100 to help us work out the missing number.

So 270 subtract 100 is 170.

So 270 subtract 170 equals 100.

Lucas and Izzy sort missing number equations.

And they're going to sort them onto this table.

So we've got there missing part.

You gotta subtract the other part from the whole, or missing whole.

Add the parts together.

And the difficult part is recognising, working out whether it's a missing part or a missing whole.

So let's look at the four equations they've got to solve, four equations they've got to sort.

"Is the part missing?" says Lucas.

Or "Is the whole missing?" Says Izzy.

Let's look at the first one.

So 67 subtract something equals 20.

It's the missing part.

67 is the whole, and we subtracted one of the parts to get the other.

Lets look at the next equation.

So something subtract 100 equals 106.

Is it a part that's missing, or is it a whole? It's missing whole.

Starting with that, the whole, we subtract one of the parts and up with the other part.

Let's look at the next equation.

So 110 adds something equals 180.

So 180 must be the whole, and the two parts add together to make the whole.

So 110 adds something equals 180.

We've got a missing part, haven't we? So that there is sorted into the missing parts, the part that's missing.

And the last one, something equals 104 add 204.

We've got there a missing whole.

Okay, so it will be sorted into there.

So Izzy and Lucas have sorted the missing number equations into the right places, thinking about whether it's a missing part or a missing whole.

Now Lucas and Izzy are gonna work out the missing numbers.

So they're going to try and calculate the answers, work out what the missing numbers actually are.

So "Do you need to rearrange the equation?" asked Lucas, or can you work it out how it is? So for that first calculation, you're gonna subtract the other part from the whole.

So we know that the whole is 67.

If we subtract 20, we'll get our other missing part, our missing number.

So 67 subtract 20, subtract two 10s, would be 47.

So the missing part is 47.

Our next number is 110, add something equals 180.

So remember, you have to subtract the other part from the whole.

So we can rearrange that into a subtraction calculation.

So start with the whole, 180, subtract the part that we know, 110, and that will give us our answer.

What is 180 subtract 110? 180 subtract 110 equals 70.

So our missing number there, our missing part is 70.

Let's look at our missing wholes.

So we've gotta add the parts together to find the missing whole.

So our first one's a subtraction calculation, but we can rearrange that into an addition calculation.

Add the parts together to find the missing whole.

So 106 add 100 equals 206.

So the missing number, the missing whole is 206.

And the last one, something equals 104, add 204.

The answer is 308.

And Izzy says, "I just added 104 and 204 to find the sum." We didn't need to rearrange that pun.

Now it's your turn to have a go at a problem on your own.

So firstly, can you sort the equations? You're gonna sort them into whether it's a missing part or a missing whole.

There are two equations.

So Lucas says, "Is the part missing?" And Izzy says, "Is the whole missing? So have a good look at those two equations.

Is it a part that's missing, or is it a whole that's missing? Pause the video and see if you can sort those equations.

And welcome back.

Let's see whether you sort them into the right places.

So let's look at our first equation.

Something subtract 40 equals 52.

Is it a missing whole, or is it a missing part? It's a subtraction calculation.

And remember, if it's a subtraction calculation, the whole is either at the beginning or in the middle.

And the whole in this one here must be at the start.

Got a number, subtract 40, subtract one part, equals the other part.

So we got there a missing whole.

So you should have sorted that into the missing whole.

70 add something equals 370.

We've got there a missing part.

The two parts go together to make the whole.

That is a missing part problem.

So very well done if you sorted those two into correct places.

And now you're going to calculate the missing number in each equation.

So think carefully.

Do you need to rearrange the equation to work out the missing number? So pause the video and have a go at trying to work out the missing numbers in those two equations.

And again, welcome back.

Did you manage to work out the answers? Did you rearrange the equations to help you work them out? Let's have a look.

So let's look at the missing part problem.

First of all, it says 70 add something equals 370.

We know it's a missing part.

To work out a missing part, subtract the other part from the whole.

So we could rearrange that equation to be 370 subtract 70, then that would give us the missing part.

370 subtract 70 is 300.

So our missing number there is 300.

70 add 300 equals 370.

Let's look at the other problem.

So it's a missing whole problem, isn't it? There's a whole that's missing.

You gotta add the parts together to find the whole.

So 52 add 40, well, 50 add 40 is 90, isn't it? So 52 add 40 must be 92.

So 92 subtract 40 equals 52.

Very well done if you manage to find the missing answers, and very, very well done indeed if you manage to rearrange those equations to help you work out the answers quickly and efficiently.

Excellent work.

And let's move on to task A.

So task A, you're going to be sorting the equations.

Thinking carefully, is the part missing, or is the whole missing? And if you manage to sort them, you might want to do this as you go along, can you answer the equations? Can you work out what the missing number is? And think carefully, do you need to rearrange the equations to help you work out the answers? You might want to write down the rearranged equation you are working out.

And here are the equations that you are going to be sorting.

So there are 12 different equations with missing numbers.

Think very carefully.

Is it the whole's missing? Is it the part's missing? Put it in the right place on the table.

Try and work out the answer and think carefully about whether you need to rearrange the equation to help you work out the answer.

Okay, good luck with that task.

Pause the video and have a go at task A.

And welcome back, and let's look at those answers and see whether you got them right.

So here are the answers for task A.

So we've got there all the different missing part equations and all the different missing whole equations.

We've also got there how you could have rearranged them to help you work out the answer easily.

So for example, the first missing part question on the table is 105 subtract something equals 99.

We could rearrange that equation into 105 subtract 99.

You can subtract 100, add one back on again.

That gets us the answer 6.

Or you could have counted on six to get from 99 to 105.

It doesn't matter how you worked it out as long as you thought carefully about the most official way for you of working out the answer.

And on the other side, we've got the first missing whole problems. We've got something equals 55 add 20.

You have to add the parts together to get the whole.

So 55 add 20 equals 75.

So the missing whole was 75.

Very well done if you managed to sort those missing number equations into the right places, and you thought carefully about how you're going to answer those questions.

And maybe you jotted down some rearranged equations as well to help you work out the answers.

So very, very well done if you manage to complete task A.

And let's move on to part 2 of the lesson.

So problem solving with missing numbers.

And as I said, there'll be pandas involved in these problems too.

There are some cherries in a bowl.

Here's our panda.

So Pedro eats 22 cherries.

There are 33 left.

How many cherries were in the bowl to start with? Now it's a missing number problem.

What's missing? Is it the whole, or is it one of the parts? "What equation should I write?" says Izzy.

It's a missing whole problem.

We're starting off with a number.

We're not sure what the number is.

We subtract 22 'cause Pedro eats 22 cherries, and we're left with 33.

There are 33 cherries left.

So how many cherries were in the bowl to start with? It's the whole that is missing.

How would you work out a missing whole? "How should I rearrange the equation?" says Lucas.

Add the parts together, and that will give you the missing whole.

So we've got to rearrange that equation, that subtraction equation, into an addition equation.

So 33 add 22.

33 add 22 equals 55.

So our missing whole, our missing number, the number of cherries in the bowl to start off with was 55.

So Pedro has 350 millilitres of milkshake.

Pedro, the panda, is quite keen on his milkshakes.

You might not have known that, but he is.

He drinks some.

There is 120 millilitres of milkshake left.

How many millilitres did Pedro drink? How would you work out the answer? "What equation should I write?" asks Izzy.

Well, this time, we've got the whole.

We've got the number we're starting with, 350.

We're subtracting a part.

We're subtracting something, and we're left with 100, or Pedro is left with 120 millilitres of milkshake.

How would you work out the missing number? This time, it's the subtrahend that is missing, is the number that we're subtracting that is missing.

"How should I rearrange the equation?" says Lucas.

So how could we rearrange the equation to make it easier to work out the answer.

When there's a part missing, we can subtract the other part from the whole.

So we can rearrange this and swap around the subtrahend and the difference.

So take the other part away from the whole.

So 350 millilitres subtract 120 millilitres, and that would equal 230 millilitres.

So the missing part is 230.

So remember, when it's a missing part, subtract the other part from the whole, and that would give you the missing part.

Pedro has some party hats.

You might not know this about pandas, but they are quite keen on their party hats too.

He buys another 25 hats.

Now I know the picture shows that he's got five hats.

Ignore that.

That might not be the right number.

He buys another 25 hats.

He now has 40 hats.

How many hats did he start with? "What equation should I write?" asks Izzy.

So think about our problem.

Think about how you change it into an equation.

What would you write? We don't how many hats he started with.

That's what we're trying to find out.

But we know if we add 25 to that number of hats, we're left with 40.

'Cause he buys another 25 hats, and he now has 40 hats.

And we're trying to work out how many hats he started with.

So we've got there a missing part problem, haven't we? A part is missing.

"How should I rearrange the equation?" asks Lucas.

What do you do when there's a part missing? How do you work out the missing part? Well, you subtract the other part from the whole.

So we can rearrange that equation into 40 subtract 25, and that will give us the number that Pedro started with.

So what is 40 subtract 25? Let's use base 10 blocks to help us work out the answer.

There are four 10s.

Let's subtract two 10s.

Let's subtract five, and that leaves us with 15.

So the missing number is 15.

40 subtract 25 equals 15.

So he must have started with 15 hats, not five like it is in the picture.

15 add 25 equals 40.

And here's a problem for you to try on your own.

So a tree is 85 metres away from Pedro.

There's our tree.

Pedro walks towards the tree.

He sits down when he's 30 metres away from the tree.

There's Pedro sitting down 30 metres away from the tree.

Pedro likes milkshake.

He's not quite so keen on exercise.

How far did he walk? How would you work out how far Pedro walked? What equation should you write, and how should you rearrange the equation? So pause the video.

See if you can work out the answer.

And welcome back.

How did you get on? Did you manage to work out the answer? Did you think carefully about how you rearranged that equation? Let's have a look, see if you've got the right answer.

So first of all, the equation you should have written was 85 metres.

That's how far he was away from the tree.

Subtract some things.

We don't know how far he walked, equals 30 metres.

We now know he was 30 metres away from the tree.

So a part is missing.

When there's a part missing, swap around the parts.

Subtract the other part from the whole.

So 85 metres subtract 35 metres.

That will give you your answer.

We could use base 10 blocks to work out the answer.

There's base 10 blocks.

There's 85.

We've gotta subtract three 10s.

10, 20, 30.

And that leaves us with 55.

So Pedro walked 55 metres towards the trees.

So our missing number is 55 metres.

Very well done if you managed to find out the missing number.

That's excellent work.

Let's move on to task B.

So task B, read each problem carefully.

Write equations and rearrange them to help you find the missing number.

To find a missing part, subtract the other part from the whole.

When a whole is missing, add the parts together.

So here are the first three problems. So there are some cherries in a bowl.

Polly eats nine cherries.

There are 26 left.

How many cherries are in the bowl to start with? Okay, so think carefully about the equation.

You'd have to write to work out the answer.

And then think carefully about how you'd rearrange the equation to help you work out the missing number.

And here's part 2.

So part 2 is slightly large numbers involved.

So again, read each problem carefully and write equations, and then rearrange them to help you find the missing number.

Question A is, Polly drinks 120 millilitres of her milkshake.

She has 260 millilitres left.

How much milkshake did she start with? Okay, so there's other problems there involving other pandas.

So have a go at those problems. Don't forget to write those equations.

Don't forget to rearrange them to help you work out the missing number.

So pause the video and have a go at those problems. And welcome back.

Let's look at those answers.

So here are the answers for part 1 of task B.

The question A was, there are some cherries in the bowl.

Polly eat nine cherries.

There are 26 left.

How many cherries were in the bowl to start with? So we know it's number.

Subtract 9 equals 26.

So it's the whole that is missing, is the minuend that's missing.

So to work on a missing whole, we have to add the parts together.

26 add 9 equals 35.

So very well done if you manage to finish part 1 of task B.

There are the other answers up there as well.

And here are the answers for part 2 of task B.

That first problem, Polly drinks 120 millilitres of her milkshake.

She has 260 millilitres left.

How much milkshake did she start with? Again, it's a missing whole problem.

Something, take away 120, equals 260.

So if we add the parts together, we get the missing whole.

260 add 120 equals 380.

And there's the answers for B and for C as well.

So very well done if you got onto part 2 of task B, and you managed to answer those questions, and you thought really carefully about whether it's a missing part and were a missing whole, and you had to go rearrange those calculations to help you work out the answer as well.

Excellent work today, and I hope you're feeling much more confident solving problems with missing numbers.

And here is our lesson summary.

So when a whole is missing, add the parts together.

To find a missing part, subtract the other part from the whole.

And rearrange the equation to make it easier to calculate the missing number.