Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you on this lesson from our unit on reviewing column addition and subtraction.

Are you ready to work hard? Are you ready to remember perhaps some things that you've learned before? Well, if so, let's make a start.

So in this lesson, we're going to be identifying the minuend and subtrahend in column subtraction.

I wonder if you've come across those words before.

Let's have a look.

So our key words are minuend, subtrahend, difference, and column subtraction.

So I'll have a go at saying them and then it'll be your turn.

So my turn, minuend.

Your turn.

My turn, subtrahend.

Your turn.

My turn, difference.

Your turn.

My turn, column subtraction.

Your turn.

Well done.

Quite a few words.

I'm sure you've come across them before, but let's remind ourselves what they mean because they're going to be really useful as we go through our lesson today.

So the minuend is the number being subtracted from.

We're thinking a lot about subtraction today, and the number we start with is called the minuend.

A subtrahend is a number being subtracted from another one, perhaps the number we're taking away.

And the difference is the result after subtracting one number from another.

So we might think of it as the answer to our subtraction.

So here, you can see a simple subtraction all labelled up.

So we've got seven subtract three is equal to four.

So in this case, our minuend is seven.

That's the number being subtracted from.

The subtrahend is three, the number being subtracted, seven subtract three.

And four is our difference.

The results, the answer, the number we are left with after we've subtracted one from another.

So look out for those words as we go through the lesson today.

Column subtraction is a way of subtracting numbers by writing a number below another.

It's just a way of laying out the numbers so we can keep track of what we've subtracted and what we still need to subtract.

It's really useful with larger numbers 'cause it allows us to think about the columns and the place value of the numbers as we're subtracting.

You may well have come across this before.

So this is a chance to remind ourselves what column subtraction is all about.

So our lesson is in two parts today.

In the first part, we're going to be identifying the minuend and the subtrahend.

And in the second part, we're going to be reordering subtraction calculations.

So let's make a start.

And we've got Alex and Lucas helping us in our lesson today.

Oh dear, Alex has forgotten how to use column subtraction.

Well, he's had a bit of a break from it, I think.

So let's see if we can remind him and help him.

He says, "I remember practising column subtraction in Year 3, but I've forgotten how it works." Luckily, he has Lucas to help him.

Lucas says, "It's not a problem, Alex.

I can remember." Excellent.

I hope you can remember as well.

Maybe we can all help Alex together.

They start by representing the calculation using Base 10 blocks.

So Alex says, "I start with a number of Base 10 blocks." So there we go.

He started with, let's have a look, 77.

I think he's got there seven 10s and seven ones.

And Lucas says, "This is called the minuend." Remember, the number we are subtracting from.

He says, "I subtract a number of blocks." He subtracted a number of blocks.

They've gone faint on our screen, haven't they? And Lucas says, "This is called the subtrahend," the number we are subtracting.

"I have some blocks left," says Alex.

And there are the blocks that are left.

And Lucas says, "This is called the difference." So this is the result when we've subtracted one number from another.

Alex writes an equation.

He says, "I start with 77." There are our 77 blocks.

And it's called the minuend.

I subtract 46.

And Lucas says, "This is called the subtrahend." So he's written down 77, subtract 46.

The minuend subtract the subtrahend.

He says, "I'm left with 31." And Lucas says, "This is called the difference," the result when we've subtracted one number from another.

So 77 subtract 46 is equal to 31.

Alex uses a bar model to represent his calculation.

Can you picture how it's going to look? Lucas says, "The minuend subtract the subtrahend is equal to the difference." 77 subtract 46 is equal to 31.

And here's the bar model that represents that.

Alex says, "77 is the minuend.

46 is the subtrahend.

And 31 is the difference." Can you think of another way to talk about those? Have you used the words part, part and whole? Let's see if we hear those being used as well.

Alex changes around the subtrahend and the difference.

And Lucas says, "The minuend subtract the subtrahend is equal to the difference." Aha, he's changed it 'round.

Does that still work? 77 is the minuend.

31 is the subtrahend.

And this time, 46 is the difference.

Alex identifies the minuend in each representation.

And he's reminding us the minuend is the number being subtracted from.

So our sort of starting number in our subtraction.

The minuend is the whole.

Ah, that's interesting, Lucas.

Thank you.

So the minuend is like our whole.

So there is our whole, all the blocks that we started with.

We have subtracted some, and we have some left, but the whole that we started with is our minuend.

So what about in the equation? That's right, 92 is our minuend.

That is the whole.

We're subtracting 52, and we will have some left.

What about in the bar model? Where is the minuend? That's right.

As Lucas said, the minuend is the whole.

So it's our whole bar.

So in this bar model, 42 is the minuend.

It's also the whole.

What about this last equation? Where is the number that we're subtracting from? The order that the equation's been written down is slightly different, isn't it? That's right, there's our minuend.

That's the number being subtracted from.

10 is equal to 36, subtract 26.

We've started with 36.

We've subtracted 26.

And our difference is 10.

The minuend does not always appear first in an equation.

And that's something to watch out for as we go through this lesson and many other lessons.

Over to you.

Can you find the subtrahend in each representation? We were looking for the minuend before.

Alex is reminding us, "A subtrahend is a number subtracted from another." So the number that we are taking away.

Pause the video and have a look and see if you can find the subtrahend in each of these representations.

How did you get on? Did you spot that these slightly fainter Base 10 blocks are the number that's been subtracted? So they are our subtrahend.

What about in the equation? 50 is equal to 61 subtract 11.

That's right.

11 is our subtrahend.

That's the number being subtracted.

What about in the bar model? Well, 44 could be the subtrahend, but 43 could be the subtrahend.

They're both parts, and the subtrahend is one of our parts.

So either part in the bar model could be the subtrahend.

And what about in our final equation? That's right, 24 is the number being subtracted.

So 24 is the subtrahend.

Alex wants to represent an equation as a column subtraction.

He says, "How would I represent 77 subtract 46 is equal to 31?" Lucas says, "Let's take a look." So there's our 77.

And that was our minuend, and we start with the minuend.

And we're subtracting 46.

So can you remember what 46 will be called? That's right.

The subtrahend is written beneath with the digits in the correct columns.

So 46 is our subtrahend, the number we're subtracting.

Then we write that big equal sign.

This equal sign shows that it is a different way to write an equation.

We're not writing it in a line anymore.

We're writing it as a column.

But that shows us that this is an equation.

And we already know that the answer is 31, and the answer is called the difference, and the difference appears within the equal sign.

Alex writes another equation as a column subtraction.

He says, "I'm going to set this out as a column subtraction.

89 subtract 65 is equal to 24." So he says we start with the minuend, which is 89.

And then underneath it, we record the subtrahend, which is 65.

And then the difference, which we know is 24, appears in the equal sign.

So 89 subtract 65 is equal to 24.

Alex is going to set this equation out as a column subtraction.

22 is equal to 78 subtract 56.

What do you notice this time? The equation's written down in a different order, isn't it? So we've got to be careful.

Where is the minuend? Where is the number that we are subtracting from, our whole? So there's our column subtraction.

He says, "I've got to write the minuend first, but where is it?" Can you help Alex out? Where is the minuend in that equation? This time, the minuend is in the middle of the equation, but it is the number being subtracted from.

22 is equal to 78, subtract 56.

So 78 is still our minuend.

So we start with the minuend.

The subtrahend is written beneath it.

56 is the number we're subtracting.

And then our difference actually appears at the beginning in this.

Our difference is 22, and that is written within the equal sign.

Over to you to check your understanding.

Which column subtraction shows 33 is equal to 54 subtract 21? And Alex says, "Think carefully about where the minuend appears in the equation." Remember, the minuend is the number we're subtracting from.

It's our whole in a bar model.

Pause the video, have a go, and then we'll talk through the answers together.

How did you get on? Well, this one is not correct, is it? This shows a minuend of 33 subtracting 54, and the answer to that is not going to be 21.

So that's not been written out correctly.

What about the column subtraction on the far right of the screen on the other side? 54 subtract 23 is equal to 31.

Well, this doesn't show the equation that we have at the top of this page.

It is correct.

54 subtract 23 is equal to 31, but it doesn't represent our equation.

So it's not correct.

But this middle one does show that 33, this, the difference, is equal to 54 subtract 21.

So 54 is our minuend, and 21 is our subtrahend.

And 33 there is our difference.

We just had to remember that it was written slightly differently as the equation.

Well done if you've got that right.

Alex writes this column subtraction as an equation.

So he's going the other way around this time.

So there's his column subtraction, and he's going to write it as an equation.

He starts with the minuend.

Can you see which the minuend is? That's right, the minuend is 59, the number we're subtracting from.

The subtrahend is written next.

The subtrahend is the number we are subtracting.

So in this case, that's 20.

And then the difference appears on its own next to the equal sign in this occasion.

We've just got the difference after the equal sign, and the difference is 39.

So 59 subtract 20 is equal to 39.

Time for you to have a go.

Can you write this column subtraction as an equation? So here's the column subtraction, and you're going to write it as a subtraction equation.

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

How did you get on? Did you start with the minuend? And did you see that the minuend this time was 74? The number that we are subtracting from.

And then we had to write the subtrahend, the number being subtracted, and that was 13.

And then after the equal sign on its own on this occasion, because we had our minuend first, is the difference.

And the difference in this case is 61.

So well done if you manage to write that column subtraction as a subtraction equation.

Time for you to do some practise now.

So for the first part, you're going to write these column subtractions as equations.

And then for the second part, you're going to write these equations as column subtractions.

And then finally, Alex has jumbled up the numbers for these column subtractions.

Can you use each number once to make each column subtraction correct? Pause the video, have a go, and then we'll look at the answers together.

How did you get on? So these were the answers to the first one.

You had to write equations based on the column subtractions.

So 47 subtract 32 is equal to 15.

65 subtract 21 is equal to 44.

And 89 subtract 57 is equal to 32.

So we had our minuend first in all of those, subtracting our subtrahend, and then equal to our difference.

And Alex says, "The difference appears on its own next to the equal sign," in these examples.

Now what about these ones? The first two were quite straightforward 'cause we had the minuend first, but the last one, we had to think a bit, didn't we? So in this case, the minuend was 49, which is the number recorded at the top of the column subtraction.

Subtract 26, which is the subtrahend.

And in the equal sign is the difference, 23.

And then for the second one, that 56 was our minuend, written first.

13 was our subtrahend, and 43 was our difference, written in the equal sign.

And then for the last one, we swapped the order of the equation around.

So we had the difference first.

43 is equal to 63 subtract 20.

So we needed to see that 63 was our minuend.

So that was recorded at the top.

Subtract 20, our subtrahend, and that our difference was 43 in the equal signs.

And Alex is reminding you, you need to start with the minuend when you're recording your column subtractions.

So here are some possible solutions for three.

So you could have had 54 subtract 14 is equal to 40, 43 subtract 22 is equal to 21, and 64 subtract 44 is equal to 20.

You may have found some other ways to complete those calculations as well.

Alex says again, "Each minuend is the largest number and is written first in each column subtraction." Okay, and onto the second part of our lesson, reordering subtraction calculations.

Alex represents column subtraction as a part-part-whole model.

Oh, that's interesting, isn't it? Do you remember we talked a little bit about which was the whole and which were the parts when we were thinking about subtraction? So there's a part-part-whole model.

He says, "The minuend is the whole.

59 is the number we start with." So 59 is our whole.

22 is the subtrahend.

It's also a part.

And 37 is the difference.

And that is also one of our parts.

And Lucas says, "The parts can also be swapped around." So our whole is always going to be our whole, but we could record our parts, our subtrahend and our difference, in a different order.

So let's have a look at that.

So there is our part-part-whole model, but we can swap our parts around.

And if we record it as a column subtraction, we could say that 59 subtract 37 is equal to 22.

Because if we know one part, we can subtract it from the whole to find the other part.

And we know that our two parts are 37 and 22.

And Lucas is reminding us, with the language we've learned today in this lesson, the subtrahend and the difference can be moved.

They are the same as our two parts.

So can you represent the column subtraction as a part-part-whole model? Where would you write the minuend, subtrahend and difference? And can you find two different answers? Pause the video, have a go, and we'll get together for some feedback.

How did you get on? So here are the two solutions.

44 is our whole, is our minuend, and our two parts are 13 and 31, the subtrahend and the difference.

But we could also record those the other way around.

44 is our whole.

31 could be our subtrahend, and 13 could be our difference.

Alex writes this part-part-whole model as a column subtraction.

Ah, he's gonna go the other way this time.

Okay.

So he's going to write this as column subtraction.

The minuend is the whole.

So 265 is the number we start with.

And Lucas says, "265 and 210 are both three-digit numbers." But 55 could be the subtrahend.

So we could have 265 subtract 55, and 210 would be the difference.

But he's got a different way to write this part-part-whole model as a column subtraction.

The minuend is the whole.

The whole is always going to be 265 in this case.

But this time, we could have a different subtrahend.

210 could be the subtrahend.

And what would our difference be? That's our other part, isn't it? The difference would be 55.

Time for you to have a go and check your understanding.

Can you find two ways to write this part-part-whole model as a column subtraction? Pause the video, have a go, and then we'll get together for some feedback.

How did you get on? Did you find the two column subtractions you could write using this part-part-whole model? So 113 could be the subtrahend, and 140 could be the difference.

253's got to be our minuend.

It's our whole, isn't it? But 140 could be the subtrahend, and 113 could be the difference.

So two different ways that we could record that part-part-whole model as a column subtraction because we know that the parts can swap around.

The whole will always be the minuend, but the parts could be the subtrahend or the difference.

Time for you to do some practise.

Can you represent each column subtraction as a part-part-whole model and find two different answers? And question two, can you find two different ways of completing the column subtraction for each part-part-whole model? And in part three, use three-digit numbers to complete each part-part-whole model.

Use the same numbers to complete each column subtraction.

So you're going to create a part-part-whole model with three-digit numbers, and then you're going to rewrite that as two different column subtractions.

So pause the video, have a go at your tasks, and we'll get together for some answers and some feedback.

How did you get on? Here was question one where you had to create part-part-whole models from the column subtractions.

So for the first one, 67 was our whole.

Our minuend is the same as our whole.

24 and 43 are our parts, either the subtrahend or the difference.

So we get those two part-part-whole models written from the same column subtraction.

And then we've done the same for the second one.

88 is always the whole.

But 53 and 35 could be either the subtrahend or the difference.

The parts could swap over.

And there's Lucas saying, "The subtrahend and the difference can be swapped around." So here, we had the part-part-whole models, and you were creating the column subtractions from them.

So our whole, our minuend was 293, but our subtrahend could be 53 or 240.

And our difference could be either of those as well.

And in the second example, 368 had to be our minuend.

It is our whole.

But the subtrahend and the difference, 255 and 113, either could go in either place.

So the minuend is written first in each column subtraction.

We start with the whole, and we subtract from the whole.

And for part three, lots of different ways you could have done this.

So you were finding three three-digit numbers to make sense in a part-part-whole model and then rewriting them as two different column subtractions, remembering that the minuend will always stay the same.

It is our whole, but the subtrahend and the difference are our two parts, and we can swap those around.

And just remembering, you should have used the same three numbers in each column subtraction pair as you can see here.

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

I hope you've been reminded about column subtraction and about identifying the minuend and the subtrahend, and the difference as well, when we are writing our column subtractions.

And we've also looked at how they link to part-part-whole models and bar models with the minuend being the whole and the subtrahend and the difference being our parts.

So let's summarise our learning for the day.

The minuend and the subtrahend are written in columns with the same value digits in the same column.

That's when we're using our column subtraction.

The subtrahend, the number we're subtracting, is written beneath the minuend.

So the minuend is our top number.

And the difference is recorded beneath the subtrahend inside the big equal sign.

Thank you for your hard work today.

I've enjoyed working with you, investigating column subtraction and minuends and subtrahends, and I hope we get to work together again soon.

Bye-bye.