Lesson video

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

And here is the learning outcome.

I can identify the minuend and subtrahend in column subtraction.

Let's take a look at the keywords.

I'm going to say each keyword.

Can you repeat it back? So the first keyword is minuend.

The next keyword is subtrahend.

The next keyword is difference.

And the last keywords are column subtraction.

Let's take a 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 calculation 7 - 3 = 4, 7 is the minuend, 3 is the subtrahend, and 4 is the difference.

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

And here is our lesson outline.

So the first part of the lesson is identify the minuend and the subtrahend.

And the second part of the lesson is reordering subtraction calculations.

Let's get started.

In this lesson, you will meet Sam and Aisha and Sam and Aisha are going to be asking you questions and helping you with your learning today.

Sam is using base 10 blocks to represent a subtraction calculation.

"I start with a number of base 10 blocks", says Sam, here are some base 10 blocks.

This is called the minuend, so this is the starting number.

"I subtract a number of blocks", says Sam.

"This is called the subtrahend", says Aisha.

So a number of blocks has been subtracted.

"I have some blocks left", says Sam.

"This is called the difference", says Aisha.

Sam wants to represent his subtraction using a written calculation.

"I started with 75", says Sam.

There's 75.

This is called the minuend, remember? Then I subtracted 32, this is the subtrahend.

So 32 has been subtracted.

I have 43 left.

So 75 - 32 = 43, and this is the difference.

Sam uses a bar model to represent his calculation.

So here is Sam's calculation represented with base 10 blocks.

And remember, the minuend subtract the subtrahend is equal to the difference.

So here is our calculation 75 - 32 = 43, and we can represent it as a bar model like this.

So 75 is the minuend.

So 75 is the number that we start with.

32 is the subtrahend.

So 32 is the number being subtracted, and 43 is the difference.

So 43 is the result after the subtrahend is subtracted from the minuend.

So in the bar model 75 represents the whole and 32 and 43 are the parts.

Sam changes around the subtrahend and the difference.

It's still with the same calculation, 75 - 32 = 43, but he's going to change around the subtrahend and the difference.

Remember the minuend subtract the subtrahend is equal to the difference.

So let's change around that subtrahend and that difference.

Here's our bar model.

So 75 is still the minuend, so 75 is still our whole.

43 is now the subtrahend.

So we're now subtracting 43 from 75, so 43 is the subtrahend.

32 is the difference.

To represent a bar model as a subtraction equation, there are at least two different ways of doing that, swapping around the subtrahend and the difference.

Sam finds the minuend in each of these representations.

So remember the minuend is the number being subtracted from.

It's the whole.

So with our base 10 blocks, it's all of the base 10 blocks, including the ones that have been subtracted with our equation.

It's our starting number 46 - 22 = 24.

So 46 is the minuend.

For our bar model, it's the whole 45.

And for the last subtraction calculation, the minuend actually appears in the middle.

15 = 38 - 23.

15 is the difference.

And the subtrahend 23 appears at the end of the equation.

Now here's Aisha, just reminding us that the minuend is the whole.

Now here is some to try on your own.

Find the subtrahend in each of these representations.

So what is the subtrahend? Remember a subtrahend is a number subtracted from another.

Pause the video and see if you can work out for each representation where the subtrahend is.

And welcome back.

Did you find the subtrahend for each of them? Let's take a look, see if you were right.

So for the base 10 blocks, the subtrahend is the number being subtracted.

So it's those faded blocks.

The blocks have almost disappeared.

For our first equation, the subtrahend is 20.

33 - 20 = 13.

For our bar model, it could be 15 or 14.

Either part could be a subtrahend, depends on the way the equation was written.

And for our last equation, subtrahend is 24.

38 - 24 = 14.

24 is the part being subtracted.

Very well done if you've got all those correct.

Sam wonders how the minuend and subtrahend are represented in a column subtraction.

"How would I represent 75 - 32 = 43?", asks Sam.

"Let's take a look", says Aisha.

Here's 75, so we start with the minuend.

The minuend is written first.

Subtract 32, the subtrahend is written beneath with the digits in the correct columns.

The one's digit has to be underneath the one's digit of the minuend and the tens digit of the subtrahend has to be beneath the tens digit of the minuend.

The equals sign shows it is a different way to write an equation.

So those two lines actually look like a giant equal sign, but it's just a reminder that this also is an equation and the difference appears within the equal sign.

So this is where we write our difference between the two numbers.

Sam represents 54 - 21 = 33 as a column subtraction.

"What would I start with?", asks Sam.

Do you remember? We have to start with the minuend.

So the minuend is always written first.

So 54 is the minuend.

That's our starting number.

That's the whole.

The subtrahend is written beneath.

Remember we've gotta line up those ones and those 10s to make sure they're in the correct columns.

The difference appears within the equal sign.

That is how you would represent 54 - 21 = 33 as a column subtraction.

Sam represents 14 = 55 - 41 as a column subtraction.

What would I start with this time? Gotta start with the minuend.

Where is the minuend in that equation? So this time the minuend is in the middle of the calculation.

Thank you Aisha.

So 55 is the minuend.

"I've still got to write the minuend first", says Sam.

Yes, very good point there, Sam.

We always start with the minuend.

So we start with the minuend, minuend is 55.

The subtrahend is written beneath with the digits in the correct columns and the difference appears within the equal signs.

The difference is written within the equal sign.

14 is written there.

That is how you would write 14 = 55 - 41 as a column subtraction.

Which column subtraction shows 37 - 14 = 23? There are three different column subtractions there.

Which one matches that equation? "Look carefully at each minuend and subtrahend", says Sam.

So a bit of useful advice there.

Pause the video and see if you can work out which column subtraction shows 37 - 14 = 23.

And welcome back.

Did you manage to answer it? Did you manage to get it right? Let's find out.

The column subtraction that matches that equation is this first one that is 37 - 14 = 23.

The one in the middle shows 37 - 23 = 14.

There's still the same numbers but that difference and the subtrahend have been swapped around.

And that last equation shows two slightly different numbers.

37 - 13 = 24.

So very well done if you got that correct.

Sam wants to write this column subtraction as an equation.

He starts with the minuend.

So the minuend is 88, that's our starting number.

The subtrahend is written next.

The 30 is our subtrahend and the difference appears on its own next to the equal sign.

So the difference appears here.

Write this column subtraction as an equation.

So here's the column subtraction that you are going to write as an equation.

So see if you can work out how you would write that as an equation.

So you might need to use pencil and paper or a whiteboard and whiteboard pen, but see if you can write that column subtraction as an equation.

Pause the video and have a go.

And welcome back.

Let's take a look, see if you got it right.

So start with the minuend.

Minuend is 39.

That is our starting number, that is the whole.

The subtrahend is written next, the subtrahend is 22.

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

The difference appears here.

So the correct equation should have been 39 - 22 = 17.

Very well done if that's what you wrote down.

And let's take a look at task A.

Write these column subtractions as calculations.

So for each of them you're going to write the equation.

So that first one, where is the minuend? Where is the subtrahend? Where is the difference? Can you write the numbers in the correct places? Here's part two of task A.

So write these calculations as column subtractions.

So this time you are given the equation, you've got to write it as a column subtraction.

And again, think very carefully about where the minuend, the subtrahend and the difference go.

And lastly, here is part three of task A.

So write these calculations as column subtractions, but this time you're going to work out the difference in each calculation as well.

So for that first one, we've got 43 - 20 = what number.

And you've got to write down that difference in the equation and in the column subtraction as well.

Pause the video and have a go at task A.

And welcome back.

Let's take a look, see how you got on, see whether you got them right.

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

For the equation you should have written, for that first one, is 49 - 33 = 16.

Let's take a look at the second part of task A.

So this time you had to write them as column subtractions.

So you should have written 56 as the minuend, 22 as the subtrahend, and 34 is the difference that goes in that big equal sign.

Very well done if you've got those correct.

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

So you had to write them as column subtractions, but also you had to work out the difference.

So for that first calculation, the difference is 23.

43 - 20 = 23.

So you should have written that in the equation and in the column subtraction as well.

And that last one was a little bit tricky, wasn't it? 'Cause we got there, the minuend in the middle.

So 43 = 56 - 13.

You should have written the minuend first, 56.

Underneath that you should have written the subtrahend, 13.

And underneath that you should have written the difference, 43.

Very well done if you got those correct.

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

So the second part of the lesson is reordering subtraction calculations.

Aisha represents this column subtraction as a bar model.

"The minuend is the whole.

"It's the number we start with", says Aisha.

So here is our bar model.

Where would 96 go on our bar model when 96 is the whole.

So 96 will appear on that big bar on its own.

51 is the subtrahend.

If you look carefully at the bar model, there are two parts.

One part is slightly bigger than the other.

51 is greater than 45, so 51 has got to appear in a slightly bigger part of the bar model.

So 51 appears here.

And 45 is the difference.

So 45 is the other part of the bar model.

"The parts can also be swapped around", says Sam.

So we can write 96 and 51 and 45 this way around, or we can swap it around.

The two parts can be swapped over.

So this bar model here also represents that column subtraction.

All that's happened is those two parts have been swapped around.

"The subtrahend and difference can be moved", says Sam.

So here's one to try on your own.

Represent the column subtraction as a bar model.

Where would you put the minuend, subtrahend, and the difference? "Can you find two different answers?", asks Sam.

So can you find two different ways of representing that column subtraction as a bar model? Think very carefully about where the whole will go and the parts will go.

Think very carefully about where the larger part will be written.

And the smaller part would be written on the bar model.

Though again, you might need some paper and a pencil or you might want to use a whiteboard and a whiteboard pen.

But see if you can represent that column subtraction as two different bar models.

Pause the video and have a go.

Welcome back, and let's take a look at how you got on.

"Here are the two solutions", says Aisha.

So for the first bar model, 59 is the whole and 21 and 38 are the parts.

Or you could have written this way around.

59 is still the minuend, is still the whole, but the parts are swapped around.

We've now got 38 and 21 the other way around.

Very well done if you managed to draw both bar models correctly.

Aisha wants to represent this bar model as a column subtraction.

"The minuend is the whole.

It's the number we start with", says Aisha.

So we start with 45.

24 could be the subtrahend.

So we could subtract 24 and 21 could be the difference.

21 would be written here.

Aisha thinks of another way to represent this bar model as a column subtraction.

Sam says, "There are two ways to complete the column subtraction using the bar model." So the minuend is the whole, it's the number we start with.

So we still start with 45.

21 could be the subtrahend.

So this time we could subtract 21 instead.

It's one of the parts.

That could be the subtrahend.

24 could be the difference.

So those two parts can be swapped around.

Either one could be the subtrahend or the difference.

Find two ways to represent this bar model as a column subtraction.

And again, use pencil and paper or a whiteboard and whiteboard pen.

Can you find two different ways of representing that bar model as a column subtraction? Think very carefully about those parts.

Pause the video and see if you can work out the answers.

And welcome back.

How did you get on? Did you manage to write two different column subtractions? Let's take a look and see whether you wrote them correctly.

So 21 could be the subtrahend and 15 could be the difference.

The column subtraction you could have written down is 36 - 21 = 15.

15 could be the subtrahend and 21 could be the difference.

Those two parts can be swapped around.

So you could have written down 36 - 15 = 21.

Very well done If you managed to write down both of those columns subtractions.

That is excellent work.

Let's take a look at task B.

The first part of task B, set out each column subtraction as a bar model.

So look carefully at each of them.

How would you write that as a bar model? And look carefully at the size of the parts.

That's going to be crucial here.

So which part is bigger and where would you write those on the bar model? So for that first one, 35 - 24 = 11, which part is larger? Where would it go on the bar model? Let's take a look at part two of task B.

So write two different column subtractions for each bar model.

So for that first bar model, 67 is the whole, 36 and 31 are the parts.

How could you write that as a column subtraction? And think carefully about where you write the minuend in a column subtraction.

Where does that go? And finally, part three of task B.

So use two digit numbers to complete each bar model and then write two different column subtractions to describe each of them.

So the numbers you write this time are up to you.

They've gotta be two digit numbers and try to choose two digit numbers that are a little bit tricky to calculate the answers to.

It's up to you what the numbers are.

Don't make them too easy, don't make them too hard.

So once you filled in the bar model, can you then write two different column subtractions describing that bar model.

So there is task B.

Pause the video and have a go and see how you get on.

And welcome back.

Let's take a look at those answers, see whether you got them right.

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

So set out each column subtraction as a bar model.

That first one, the whole is 35.

That's where 35 should appear on the bar model.

And 24 and 11 were the parts.

24 is the larger part, so it should appear in the larger part of the bar model.

And it doesn't matter whether the subtrahend and the difference have been swapped around that second calculation, that second column subtraction, 43 - 31 = 12, 43 is still the minuend.

But 12 and 31 have been moved around on the bar model.

So 12 actually appears first, even though it's a difference, 31 appears second, even though it's a subtrahend.

It doesn't matter.

It still represents that column subtraction.

What's important is thinking about the size of those numbers and making sure the 31 is the larger part.

So 31 should be written as the larger part on the bar model.

Here are the answers for part two of task B.

So for that first bar model, we've got 67, 36, and 31.

You should have written 67 - 36 = 31.

And you should also have written 67 - 31 = 36.

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

This is completely dependent on which numbers you have chosen.

So you could have chosen the biggest two digit number you may have been able to think of, which is 99.

And the parts may have been 66 and 33.

So you could have written, as the column subtractions, 99 - 66 = 33, and you could have written 99 - 33 = 66.

But hopefully you've remembered to write that larger part as the larger part on the bar model.

And excellent work today, very well done indeed.

And hopefully you are feeling much more confident and recognising where the minuend and the subtrahend appears in a column subtraction.

Excellent work today, very well done.

And finally, let's take a look at the lesson summary.

So the minuend is written first in a column subtraction, the subtrahend is written beneath the minuend and the difference is recorded beneath the subtrahend.