Lesson video

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

And here is our learning outcome.

I can understand the relationship between addition and subtraction.

And here are our keywords for today's lesson.

So I'm going to say each keyword and can you repeat it back? So the first keyword is minuend.

The next keyword is subtrahend.

And the next keyword is probably a more familiar word, and that is difference.

And let's look at what those words mean.

So the minuend is the number being subtracted from, a subtrahend is a number subtracted from another, and the difference is the result after subtracting one number from another.

So in the equation, 7 - 3 = 4.

The minuend is 7, the subtrahend is 3, that's the number we're subtracting, and the difference is 4.

And here's our lesson outline.

So the first part of the lesson is using parts and wholes, and the second part of the lesson is writing addition and subtraction equations.

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.

Lucas and Izzy are using bar models.

Here's a bar model with some addend and addend on it.

The sum is the whole in the bar model and the addends are parts.

So addend plus addend equals the sum.

Izzy says, "The minuend is the whole and the subtrahend and difference of both parts." So the minuend subtract the subtrahend equals the difference.

There are two bar models and in one of them, the sum is the whole, and in the other the minuend is the whole.

Izzy and Lucas used base 10 blocks.

"I've represented 105 using base 10 blocks," says Lucas.

There's 105.

"I've represented 102 using base 10 blocks," says Izzy.

And there is 102.

And here we've got a bar model and 105 is going to represent part of that bar model.

105 is one of the parts.

102 is going to represent the other part.

So 102 is the other part.

So to find the sum, we'd have to add those two addends together.

So an addend plus an addend equals the sum.

The sum just means the whole.

So if you combine those together, we get the answer, 207.

105 + 102 = 207.

"The sum of 105 and 102 is 207," says Lucas.

So Izzy and Lucas now write equations using the bar model.

So we've still got the same three numbers.

And Lucas is reminding us of course, that the whole can be the sum.

So an addend plus an addend equals the sum.

So if Lucas was to write addition equations using that bar model, he could write 105 + 102 = 207.

Or he could swap the addends around.

102 + 105 = 207.

Izzy is saying, "The whole can be the minuend." So the whole can be the sum, but the whole can also be the minuend.

And the minuend subtract the subtrahend equals the difference.

So we can have 207, which represents the whole, subtract one of the parts equals the other part.

207 - 105 = 102.

Or we can swap around the subtrahend and the difference, 207 - 102 = 105.

Izzy and Lucas have written four equations.

They've written two addition equations and two subtraction equations.

Izzy and Lucas used base 10 blocks.

Here's our base 10 blocks.

So the base 10 blocks represent 270.

So we've got there two 100s and seven 10s.

So the 270 is going to represent the whole on the bar model.

"We're going to split the whole into two parts," says Izzy.

There are our two parts.

So this is one of the parts, that's 140.

And here's the other part, that's 130.

So 270 has been split into two parts, 140 and 130.

Izzy says the whole subtract one part is equal to the other part.

So we have the minuend, the whole, we subtract the subtrahend, subtract one of the parts, that equals the difference.

Write equations using the bar model.

"What is the whole?" says Lucas.

"The whole can be the sum or the minuend," says Izzy.

So can you write two addition equations and two subtraction equations? So remember, addend plus addend equals the sum, so you can write two addition equations.

And the minuend subtract the subtrahend equals the difference.

So can you write two subtraction equations? Pause the video and see if you can write four different equations using that bar model.

And welcome back.

Did you manage to write four equations? Let's have a look to see if you were right.

Let's start by looking at our addition equations.

So remember, addend plus addend equals the sum.

You could have written 140 + 130 = 270.

You could also have written 130 + 140 = 270.

So all we've done is moved around those addends, put them in a different order.

Let's look at our subtraction equations.

270 - 140 = 130.

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

You could also have changed around those parts.

270 - 130 = 140.

Very well done if you wrote all four of those equations.

Lucas uses the addends to find the sum.

So this time, Lucas has got a bar model and he's got the two addends but he hasn't got the whole.

The sum is missing.

"I have to add 205 and 101 together," says Lucas.

Remember, addend plus addend equals the sum.

So to work out the sum, Lucas could calculate 205 + 101, that equals 306.

Or he could calculate 101 + 205 = 306.

Of course, they have the same sum.

So our missing whole is 306.

Izzy says, "I'm going to use the bar model to write two subtraction equations." So what two subtraction equations could she write using the bar model? But remember, minuend subtract the subtrahend equals the difference.

So Izzy's got to start with the whole.

So 306 - 205 = 101.

How could Izzy change around those parts? She could also have 306 - 101 = 205.

Either of those is correct.

Izzy is trying to find the missing number.

This time Izzy has got a bar model with 20 and 220 on it.

Should Izzy calculate 220 and 20? Remember, she's looking for the missing number.

"Or should I calculate 220 - 20?" says Izzy.

What do you think, should she add? Should she subtract? Now, Izzy knows the two parts and needs to find the whole.

It's the whole that is missing.

She needs to add the parts to find the sum.

So she could use either of these.

She could do 220 + 20 = 240.

Or she can start from 20 and add on 220.

That also equals 240.

Which do you think is easier? I think 220 + 20 is easier.

Remember, it's normally easier to start with the bigger number add on the smaller one.

So our missing number is 240.

It was a missing whole, a missing sum.

Use the addends to find the sum.

As our bar model, we got there 120 and 30.

"First, write two addition equations," says Lucas.

So addend plus addend equals the sum.

"Then write two subtraction equations," says Izzy.

So minuend subtract the subtrahend equals the difference.

So first of all, you need to find the sum, then you need to write two addition equations, and then you need to write two subtraction equations.

Pause the video and see if you can complete that problem.

And welcome back.

Did you manage to find the sum? Did you manage to write those two additional equations? Did you also write two subtraction equations? Let's see if you've got the right answers.

So first of all, let's work out that missing sum by adding together the two addends.

So 120 + 30 = 150 30 + 120 also equals 150.

Remember you can just change those addends around.

Still equals the same sum.

So our missing whole, our missing sum is 150.

We can then use that to help us write the two subtraction equations.

150 - 120 = 30, and 150 - 30 = 120.

Very well done if you've got the right answer, 150.

And very well done also if you manage to write two addition equations and two subtraction equations, too.

Let's move on to task A.

So the first part of task A, you are going to write equations using the bar models.

So that first problem we've got 270, that's the whole, and 160 and 110 are the parts.

Can you write two addition equations and two subtraction equations using those same three numbers? And don't forget to think really carefully about where the sum and the minuend appears in the equations.

And part two of task A, use the addends to find the sum.

Then write equations using the bar models.

So for this problem, you've got to actually work out what the sum is.

You've got to add the numbers together, work out the sum, and then write the equations afterwards.

So pause the video and have a go at task A.

And welcome back.

How did you get on? Did you manage to complete it all? Well done if you did.

Let's have a look to see whether you were right.

So here are the answers for part one of task A.

There are four equations describing that bar model.

So we've got 160 + 110 = 270.

We've also got 110 + 160 = 270.

270 - 160 = 110, and 270 - 160 = 110.

So very well done if you've got those correct.

Let's look at part two of task A.

So this time, you had to work out what the missing sum was and then write the four equations.

So that first bar model are parts were 130 and 30.

So the missing sum, the missing whole was 160.

And then hopefully you've written the four equations correctly, too.

And in the second bar model the parts were 202 and 102.

So the missing whole, the missing sum was 304, which you can then use to help you write the four equations.

So very well done if you got onto part two of task A, and excellent work if you completed it.

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

So the second part of the lesson is writing addition and subtraction equations.

We've done a little bit of that already.

We're gonna take it one step further.

Lucas is looking at this bar model.

Lucas says, "We can write eight different addition and subtraction equations using these numbers." Eight addition and subtraction equations, Lucas, wow.

Yes, Izzy agrees.

"Wow, that is a lot of equations." Do you think Lucas is right? He seems quite confident, doesn't he? Lucas starts with addition equations.

"So I can start by adding the addends," says Lucas.

So we're using those same three numbers, 140 and 40 and 180.

So Lucas says 140 + 40 = 180.

So this equation is balanced, both sides are equal.

"Or I can start the equation with the sum," says Lucas.

So Lucas says we could swap around the sum and the addends and put the equation in a different order.

This equation is also balanced.

Both sides are equal.

It doesn't matter what order the equation comes in as long as both sides have the same value.

So Lucas and Izzy find four addition equations using this bar model.

"So one addend plus the other addend equals the sum," says Izzy.

So we can have addend plus addend equals the sum.

So we could have 140 + 40 = 180.

Or we can swap those addends around.

So 40 + 140 = 180.

Lucas says the sum is equal to one addend plus the other addend.

So the sum equals addend plus addend.

So we can start with 180 = 140 + 40.

And we can also swap those addends around, 180 = 40 + 140.

So all four of those additional equations are correct using just that one bar model.

Lucas looks at the subtraction equations next.

"I can start the equation with the minuend," says Lucas.

So 180 - 40 = 140.

And there is our subtraction equation, 180 - 40 = 140.

Lucas says, "I can start with a difference as well." So he could swap that equation around to start with 140.

140 = 180 - 40, that is also correct.

140 = 180 - 40.

Lucas and Izzy find four subtraction equations still using that same bar model.

"So the minuend subtract the subtrahend equals the difference," says Izzy.

The minuend subtract subtrahend equals difference.

So we could have 180 - 140 = 40, or we could swap around the subtrahend and the difference to get 180 - 40 = 140.

Lucas says, "The difference equals the minuend subtract the subtrahend." So we can start a subtraction equation with the difference.

Difference equals minuend subtract subtrahend.

So Lucas says we could write 140 = 180 - 40.

40 = 180 - 140.

That is also balanced, 40 = 180 - 140.

So find four addition equations using the bar model.

Find two equations starting with the addends.

So addend plus addend equals the sum.

Find two equations starting with a sum.

So the sum equals addend plus addend.

Pause the video, see if you can find the four addition equations.

And welcome back.

Did you manage to find all four equations? Are they all different? Let's see whether you were right.

Let's start off with those two that start with the addends.

So you should have written 120 + 50 = 170.

And you should also have written 50 + 120 = 170.

And now, let's look at the two equations starting with a sum.

So you should also have written 170 = 120 + 50.

And the last one, 170 = 50 + 120.

Very well done if you wrote those four equations.

Now, can you find four subtraction equations using the bar models? So using the same three numbers, can you find four subtraction equations? So Izzy says the minuend subtract the subtrahend equals the difference.

So minuend subtract subtrahend equals difference.

Lucas says, "The difference equals the minuend subtract the subtrahend." So can you also write two subtraction equations starting with a difference? Difference equals minuend subtract subtrahend.

So you need to find two subtraction equations starting with the minuend and two subtraction equations starting with the difference.

Pause the video, see if you can write all four subtraction equations.

And welcome back.

Did you manage to write all four? Let's have a look to see if you were right.

The first equation you might have written down was 170 - 120 = 50.

You should have also have written 170 - 50 = 120.

So two equations started with a minuend.

Then two equations started with a difference.

120 = 170 - 50 and 50 = 170 - 120.

Very well done if you wrote down all four of those subtraction equations.

So Izzy completes the bar model then writes addition and subtraction equations.

So here's the bar model that Izzy's going to complete.

It's only got one number on the bar model so far.

"So I need two numbers with a sum of 350," says Izzy.

There are lots of lots of possible answers here, but Izzy is looking for two numbers that have a sum of 350.

Izzy thinks hard and comes up with the numbers 210 and 140.

210 and 140 equals 350.

"Can you think of eight addition and subtraction equations, Izzy?" says Lucas.

The first one Izzy's going to write down is two addends equaling a sum.

So 210 + 140 = 350.

She can change those two addends around.

So 140 + 210 = 350.

So she's found the two equations starting with the addends.

Now if she can change those equations around and find two more addition equations starting with the sum.

So 350 = 210 + 140 and 350 is also equal to 140 + 210.

So there's our four addition equations.

Izzy now needs to find four subtraction equations.

So she's going to start an equation with a minuend.

So 350, that's the whole remember, subtract 210 equals 140.

Izzy can swap around that difference and the subtrahend.

So 350 - 140 = 210.

Izzy's got two more subtraction equations to find.

How would she start them? She started two of the minuend.

She can start too with the difference.

So 210 = 350 - 140.

And her last one, 140 = 350 - 210.

Very well done, Izzy.

That is all eight additional subtraction equations.

They are all different and they are all correct.

Very well done, Izzy.

Izzy writes some equations using the bar model.

So she writes down 308 = 203 + 105.

She writes down 105 + 308 = 203.

She writes 308 = 203 - 105.

And she also writes 308 - 105 = 203.

"I don't think they're all correct, Izzy," says Lucas.

So Lucas doesn't think all of those calculations are correct.

Actually some of them are not equations because they are not equal.

"Can you help me?" says Izzy.

"Which ones are wrong and can you correct them?" Have a good look and see if you can work out which ones are correct, which ones are not right, and can you actually correct Izzy's equations? Pause the video and have a go at solving that problem.

And welcome back.

Did you manage to find any that were right? Did you manage to find any that were wrong? Did you manage to correct them? Let's have a see if you were right.

So our first equation Izzy's written down is 308 = 203 + 105.

That is correct.

308 is the whole, the sum, and it is equal to the two parts.

Well done, Izzy, first one's correct.

Look at the next one.

105 + 308 = 203.

That is not right.

Sorry, Izzy, that's not right.

You've got there the part and the whole has been equal to the other part.

It's not correct, is it? So if you corrected Izzy's mistake, you may have written down 105 + 203 = 308.

The two parts equals the whole.

Let's look at the next calculation.

So 308 = 203 - 105.

So you've got the whole being equal to one of the parts subtract the other part.

Don't think that's right, Izzy.

So that one's wrong.

And you may have written down, if you corrected that one, you may have written down 203 = 308 - 105.

So one of the parts is equal to the whole subtract the other part.

And Izzy's last equation, 308 - 105 = 203.

We've got there the whole subtract one of the parts is equal to the other part.

That also is correct.

So Izzy got two correct and two wrong.

Very well done if you spotted Izzy's mistakes.

And let's move on to task B.

So for the first part of task B, you are going to write addition and subtraction equations using the bar model.

So can you write eight different addition and subtraction equations using those three numbers? 207 is our whole, 106, 101 are the parts.

That's quite a challenge there.

So eight different equations.

And this is part two.

So first of all, complete the bar model.

So you've got there the sum, the whole, 305.

What are the different parts? Can you think of two numbers with a sum of 305? And then can you write addition and subtraction equations? Can you write eight different addition and subtraction equations using those three numbers? And make sure of course that the two numbers you write down have got a sum of 305.

And here's part three of task B.

So Lucas has written some equations using the bar model, which equations are right and which are incorrect? And if you've got any wrong, can you correct the ones that Jacob got wrong? So can you write them so that they are correct? So pause the video and have a go at task B.

And welcome back.

How did you get on? Did you manage to do all of task B? If you did, that's absolutely brilliant.

Let's have a look to see whether you got them right or not.

So here's the answers for the first part of task B and there are the eight addition and subtraction equations that you should have written using that bar model.

There's eight different ones.

So two starting with the addends, two starting with the sum, two starting with the minuend, two starting with a difference.

So very well done if you wrote down all of those equations.

Let's have a look at part two.

So your answers might have looked like this.

Of course, you may have come up with two different numbers.

So if you had written down the numbers 204 and 101, there are our eight addition subtraction equations using those numbers.

So again, two starting with the addends, two starting with a sum, two starting with a minuend, and two starting with a difference.

Very well done if you manage to complete part two of task B.

And finally, here are the answers for part three of task B.

So Lucas got two of the equations correct.

Two of the equations are right.

Two of the equations are in fact not equations at all because they're not balanced.

They're not correct.

290 + 170 is not equal to 120.

Lucas also made a mistake with 170 - 120 = 290, and also is not an equation because it is not equal.

Very well done if you got onto part three of task B.

So it's quite a lot of work to do in task B.

Very well done if you manage to find Lucas's mistakes and you manage to correct them as well.

That is excellent work.

And hopefully you are feeling much more confident about writing addition and subtraction equations and moving around sums and minuends and subtrahends and differences and still making sure that those equations are correct.

Excellent work today.

Very, very well done indeed.

And finally, let's move on to our summary.

So the sum is the whole in an addition equation.

The minuend is the whole in a subtraction equation.

An equation can start with the parts or with the whole.