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 learning all about using column subtraction to subtract from a two or three-digit number.

You may have used column subtraction before, but this is a good chance to remember how to set it out accurately and what column subtraction is all about.

So let's have a look at what's in our lesson.

We've got three keywords today.

We've got minuend, subtrahend and column subtraction.

Let's just practise them.

I'll take my turn, then it'll be your turn.

So my turn, minuend.

Your turn.

My turn, subtrahend.

Your turn.

My turn, column subtraction.

Your turn.

These may well be words you're familiar with, but they're going to be really useful in our lesson today.

So let's just remind ourselves of what they mean.

So the minuend is the number being subtracted from.

It's the whole that we start with.

A subtrahend is a number being subtracted from another and the subtrahend is like one of the parts in a part-part-whole model and column subtraction is a way of subtracting numbers by writing a number below another.

It helps us to organise our thoughts and to keep track of what we've subtracted and what we still need to subtract.

There are two parts to our lesson today.

In the first part, we're going to be looking at column subtraction with two-digit numbers.

And in the second part of our lesson, we're going to look at column subtraction with three-digit numbers.

So let's make a start with two-digit numbers.

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

Alex uses Base 10 blocks to represent 68 subtract 27.

He says, "I start with 68," and there are his Base 10 blocks representing 68, 6 tens and 8 ones.

And Lucas says, "When we use Base 10 blocks for subtraction, we only make the minuend." That's our starting number.

The subtrahend in this case is the number that we're taking away.

It's part of the 68.

Lucas says, "Subtract the number with the smallest place value first." So we're going to think about subtracting our ones.

So we've got 68 and we're subtracting 27.

So Alex says, "First, I subtract 7 ones," and he subtracted those 7 ones.

"Then, I subtract 2 tens," and he subtracted 2 tens.

"68 subtract 27 is equal to 41." We can see that we've got 4 tens and 1 one left where we subtracted our 27 from 68.

Alex and Lucas used Base 10 blocks alongside column subtraction.

We've done all the thinking for column subtraction with the Base 10 blocks.

Now we're just going to represent it in a slightly different way.

I'm going to calculate 68 subtract 27.

So there are 68 represented as Base 10 blocks, 6 tens and 8 ones.

And Lucas reminds us, "The minuend always appears in, first, in a column subtraction.

The subtrahend is written underneath." And our minuend in this case, our whole, the number we're starting with is 68.

So there's our 68.

And we're subtracting 27.

So 27 is our subtrahend.

It's one of our parts.

And Alex says, "First, I subtract the ones, 8 ones subtract 7 ones is equal to 1 one." And there we can see the ones disappearing in the Base 10 blocks and we can see the one being recorded as our difference within those big equal signs.

Alex says, "Then, I subtract 2 tens." There they are.

"6 tens subtract 2 tens is equal to 4 tens," and we record our 4 tens as part of our difference within those equal signs.

Alex and Lucas calculate 77 subtract 45 using column subtraction.

So we're going to picture the Base 10 blocks this time.

Remember that the minuend is written above the subtrahend.

Can you remember which is which in this calculation? The minuend is the number we start from.

It's our whole, so that's 77.

And 45 is our subtrahend.

It's what we're subtracting.

It's what we're taking away from the minuend.

So there's 77 subtract 45 set out as a column subtraction.

"We start with the numbers with the smallest place value." "7 ones subtract 5 ones is equal to 2 ones.

And 7 tens subtract 4 tens is equal to 3 tens." And if you imagine those Base 10 blocks, we'd have represented 77 and then we'd have subtracted 5 ones and then 4 tens.

So our answer, our difference is 32.

77 subtract 45 is equal to 32.

And there's Alex writing it out as an equation.

Time to check your understanding.

Can you use column subtraction to calculate 59 subtract 39.

And the column subtraction has been set out for you.

The minuend is written above the subtrahend.

Our minuend is 59.

That's our whole.

And our subtrahend, the part we're subtracting is 39.

And Alex is reminding you to "start with the numbers with the smallest place value." So pause the video and complete this column subtraction.

How did you get on? Did you remember to start with the digits with the smallest place value? So we're starting with the ones.

"9 ones subtract 9 ones is equal to 0 ones." So we've got no ones in our difference.

5 tens subtract 3 tens is equal to 2 tens.

So 59 subtract 39 is equal to 20.

Alex wants to find the missing ones digit in this column subtraction, hmm.

He says, "To find the missing whole, I can add the parts together." Oh, let's just think about that.

We always write the minuend at the top, we start with the minuend, and the minuend is our whole.

So in this case, our parts or our subtrahend 52, and our difference, which is 33.

So if we add together the parts, we will find our whole.

So this time, two and three are our parts.

So "2 ones add 3 ones is equal to 5 ones.

So the missing digit must be a five." And if we check that using subtraction, 5 ones subtract 2 ones is equal to 3 ones, so that works.

Interesting to think about where the whole is and where the parts are when we're thinking about our subtraction.

Time for you to have a go now.

Can you find the missing tens digit in this column subtraction? Pause the video, have a go, and then we'll get together for some feedback.

How did you get on? This time, we knew our whole number of tens was seven, so we were missing a part.

And Lucas is reminding us, "To find a missing part, we subtract the known part from the whole." So 7 ones subtract the 2 ones that we have in our difference is equal to 5 ones.

So the missing digit is five.

And if we think about our column subtraction, 7 tens subtract 5 tens is equal to 2 tens.

So that's correct.

Alex is using two of these numbers to make his column subtraction and he's got to make it correct with the difference being 23.

He says, "I need to find the minuend and the subtrahend.

So he needs to find the whole, the number he's starting with, and the subtrahend, the number he's subtracted, one of the parts.

And Lucas is saying, "You need to find two numbers with a difference of 23" because we can see there that our difference written between our big equal sign is 23.

He says, "I'll start by looking at the ones numbers.

There's a difference of three between five and two." So if we have a minuend with a ones digit of five and a subtrahend with a ones digit of two, then 5 ones subtract 2 ones will equal 3 ones.

He says, "I'm going to choose 45 and 12." So let's see if he's correct.

He's starting with the ones.

"5 ones subtract 2 ones is equal to 3 ones." Yes, that works.

"4 tens subtract one 10 is equal to 3 tens," or we were looking for 2 tens, weren't we? So that's not going to be correct.

Good trial, Alex, but not quite the right answer.

"45 subtract 12 is equal to 33.

45 and 12 are not the right numbers" for this calculation to be correct.

Over to you.

Can you find the correct numbers? Use two of these numbers to make the column subtraction correct.

So Alex says, "Find the minuend and the subtrahend." And Lucas says, "Find two numbers with a difference of 23." Pause the video and have a go.

Can you find the two correct numbers to make the column subtraction correct? How did you get on? Alex says, "Let's choose 68 and 45.

So he's written them into the column subtraction.

68 is our minuend, it's our largest number, and we're subtracting a number and we've got some left.

So we know that 68 must be our minuend.

It's our largest number.

And so 45 is our subtrahend, the part we are subtracting.

Let's start with the ones.

"8 ones subtract 5 ones is equal to 3 ones." And for the tens, 6 tens subtract 4 tens is equal to 2 tens.

So that's correct, that works.

"68 subtract 45 is equal to 23.

So 68 and 45 are the correct numbers." Well done, Alex.

Time for you to have some practise.

So for part one, you're just going to complete these column subtractions.

And for part two, you're going to find the missing digits in these column subtractions.

And for part three, you're going to make each column subtraction correct using any two of these numbers.

So Alex says, "Find the correct minuend and subtrahend for each column subtraction." So pause the video, have a go at your tasks, and we'll get together for some feedback.

How did you get on? So these were the answers to the three questions in number one.

So you just had to complete the column subtractions.

So Alex is reminding you to "start with the numbers with the smallest place value." So you started with the ones and then worked out the tens.

So I hope you got those correct.

So for question two, you were filling in the missing numbers.

Some of the missing numbers were in our whole, in our minuend, and some of them were in the part, in the subtrahend.

And Alex is reminding us, "To find a missing whole, I can add the parts together." And Lucas says, "To find a missing part, subtract the known part from the whole." So let's think about that as we think about these gaps.

So in A, we were missing the tens digit of the minuend, so the 10 digit of our whole.

So we knew that the two parts were the three that we'd subtracted and the one that was our difference.

So 3 tens out of 1 ten is equal to 4 tens.

So our missing tens digit was four.

So in B, the missing ones digit in our minuend, was our whole number of ones.

And we could see that we'd subtracted two and we had a difference of four.

So 4 ones plus 2 ones plus equals 6 ones.

So we combined the parts to make the whole, so our missing whole number of ones was six.

For the missing tens digit in the subtrahend, we were missing a part.

There were 6 tens in our whole and we'd subtracted some tens and we were left with three.

Well, you might know that if six is the whole and three is a part, then three is the other part.

Or you might have subtracted the known part from the whole six.

Subtract three is equal to three.

So our missing number of tens in our subtrahend was three.

And in C, we had a whole number of tens missing and we had a part missing, the ones digits of our subtrahend.

And that's an interesting one because we had 8 ones in our whole and we had 8 ones in our difference.

So none had been subtracted.

So our missing ones digit was actually a zero.

And then you could use Alex's point finding a missing whole by adding the parts together to add the 3 tens that we'd subtracted and the 4 tens in the difference to give our 7 tens in our whole, in our minuend.

So I hope you use some of that reasoning to work out those missing digits, thinking about what represented the whole and what represented the parts.

And in three, you had to find the missing minuend and subtrahend from the cards that were given to you.

And Alex says, "You could have found ones numbers with a difference of five" for the first one, "of two" for the second example, "and six" for the final example, because we had differences of 25, 32 and 56.

So thinking about those ones digits to begin with would've helped you.

So the missing minuend and subtrahend for the first one were 48 and 23.

48 subtract 23 is equal to 25.

For the middle one, the missing minuend was 75 and the missing subtrahend was 43.

And for the final one, the missing minuend was 89 and the missing subtrahend was 33.

I hope you enjoyed reasoning about subtraction and that you were successful.

Let's move on to the second part of our lesson where we're going to be looking at column subtraction with three-digit numbers.

Alex and Lucas calculate 354 subtract 131 using column subtraction.

And Lucas is reminding us, "The minuend is written above the subtrahend." We're starting with the whole.

So 354 is our whole, our minuend, and we're subtracting 131, our subtrahend, one of our parts.

And Alex has remembered, "We start with the numbers with the smallest place value." So we're going to start with the ones.

"4 ones subtract 1 one is equal to 3 ones 5 tens subtract 3 tens is equal to 2 tens and 3 hundreds subtract 1 hundreds is equal to 2 hundreds." "354 subtract 131 is equal to 223.

So subtracting with three digits is no harder than subtracting with two digits.

We just need to remember to think about our hundreds as well.

Alex and Lucas calculate 493 subtract 63 using column subtraction.

Yep, well remembered, Lucas.

"The minuend is written above the subtrahend," but we need to be careful here, don't we? Did you spot that? We're subtracting a two-digit number, so we need to make sure that our 63 is lined up with our tens and our ones of our three-digit number, but we still start with the numbers with the smallest place value, so we start with our ones.

"3 ones subtract 3 ones is equal to 0 ones," and it's really important to record that zero to show that we have a number with no extra ones.

9 tens subtract 6 tens is equal to 3 tens and we've got no hundreds to subtract, but we need to remember that we do have 4 hundreds in our 493.

So 4 hundreds just stays as 4 hundreds.

We have no hundreds to subtract.

So 493 subtract 63 is equal to 430.

Time for you to have a go.

Write 446 subtract 220 as a column subtraction, and then find the difference.

And Lucas says, "Remember to write the minuend above the subtrahend." We always start with our whole.

And Alex says, "Remember, start with the numbers with the smallest place value." So pause the video and record 446 subtract 220 as a column subtraction and find the difference.

How did you get on? Did you follow Lucas' advice? This time we had two three-digit numbers, so we knew they were going to line up.

There were no gaps, but we do have a zero in our subtrahend, the number we're subtracting, 220.

So we start with the ones.

"6 ones subtract 0 ones is equal to 6 ones.

4 tens subtract 2 tens is equal to 2 tens and 4 hundreds subtract 2 hundreds is equal to 2 hundreds.

So 446 subtract 220 is equal to 226.

Well done if you've got that right.

Alex wants to find the missing digits in this column Subtraction.

So again, he's got to think about, what's our whole and what are our parts? He says, "Let's start with the numbers with the smallest place value." It's always good to start there.

At the moment, it doesn't seem to be important, but it will be important the further we go with column subtraction.

So let's start with the ones.

"9 ones subtract some ones is equal to 4 ones." So what's our whole and what are our parts here? Ah, Alex says, "To find a missing part, we subtract the part that we know from the whole." Our whole in this case is the 9 ones in our minuend and the part we know is the 4 ones in our difference.

So nine subtract four is equal to five.

So our missing ones digit must be a five.

9 ones subtract 5 ones is equal to 4 ones.

What about our tens? What's missing here? We've got some tens and we've subtracted 5 tens and it's equal to 0 tens, hmm.

This time, we're missing the whole number of tens.

And Alex says, "To find a missing whole, add the parts together." Well, one part is five and the other part is zero.

So whatever we subtracted from, we've got zero left.

So it must be the same number.

Five add zero is equal to five.

So our missing tens digit must be a five.

5 tens subtract 5 tens is equal to 0 tens.

And what about our hundreds? Again, we're missing a part this time, aren't we? "7 hundreds subtract some hundreds is equal to 4 hundreds." "To find the missing parts, subtract the known part from the whole." So this time we know that four is one of our parts, and seven subtract four is equal to three.

So our missing number of hundreds from our subtrahend must be three.

"7 hundreds subtract 3 hundreds is equal to 4 hundreds." Lots of thinking there, thinking about which are our wholes and which are our parts.

So can you do some of that thinking? Can you find the missing digits in this column subtraction.

And Alex says, "Start with the numbers with the smallest place value first." So pause the video and think about your parts and wholes and work out the missing digits in this column subtraction.

How did you get on? So Lucas started with the ones, So he said, "Some ones subtract 1 one is equal to 7 ones." So what's missing here? We're missing the whole, aren't we? "To find the missing whole, add the parts together." So 1 one add 7 ones is equal to 8 ones.

So our missing ones digit in our minuend must be eight.

What about the tens? We're missing a whole again, aren't we? "So some tens subtract 3 tens is equal to 5 tens." So we know about the two parts, the part we've subtracted and the part that we're left with.

So this time we can add together the 3 tens and the 5 tens to give us 8 tens.

So our missing tens digit in our minuend must be eight.

Eight subtract three is equal to five.

What about the hundreds? Are we missing a whole or a part? We're missing apart this time, aren't we? We're missing the part that we're subtracting in the subtrahend.

"So 6 hundreds, our whole, subtract some hundreds is equal to 3 hundreds." Can you use some number facts here to help you? Well, Alex says, "To find the missing part, we subtract the known part from the whole." So six is our whole, our known part is three.

Six subtract three is equal to three.

So our missing hundreds digit in our subtrahend must be three.

Six subtract three is equal to three.

Well done if you've got that correct and well done if you use that reasoning about parts and wholes to help you.

We've got some polar bears here.

So Bertha is standing on these scales with her baby, Basil.

We can see them there.

Together, their mass is 444 kilogrammes.

And you can see the arrow on our scale pointing roughly there, but we've got the actual figures in our problem.

So together, their mass is 444 kilogrammes.

Basil clambers off the scales.

Oh, dear.

He's gone.

Bertha's mass is 321 kilogrammes.

So how heavy is Basil? Hmm, that's an interesting one.

We know their mass together was 444 and we know that Bertha's mass is 321 kilogrammes.

So that's a part.

So we know the whole and one part and we know that when we know the whole and one part we can subtract the part to find the other part.

So we can work out Basil's mass by subtracting Bertha's mass from 444 kilogrammes, which was their total mass.

So we could do a column subtraction.

444, which was the total mass of Basil and Bertha, and we're going to subtract 321, which is the mass of Bertha.

Four ones subtract 1 one is equal to 3 ones 4 tens subtract 2 tens is equal to 2 tens and 4 hundreds subtract 3 hundreds is equal to 1 hundred.

So baby Basil has a mass of 123 kilogrammes.

And if we added together the 123 and the 321, we should get a total of 444 to check that our two parts were correct.

Time to check your understanding.

Can you think about the part-part and whole here to solve this problem? So Brody is standing on these scales with her baby, Bella, and together, their mass is 387 kilogrammes.

Brody clambers off the scales this time and just leaves Bella on the scales.

Bella's mass is 75 kilogrammes.

So how heavy is Brody? Alex says, "Work out Brody's mass by subtracting Bella's mass from 387 kilogrammes." 387 was our whole.

75 is a part.

That's the mass of Bella.

The other part is the mass of Brody.

So we can find a part by subtracting one part from the whole.

So complete that column subtraction to find out what Brody's mass is.

Pause the video now.

How did you get on? So we started with the ones.

7 ones subtract 5 ones is equal to 2 ones, 8 tens subtract 7 tens is equal to 1 ten and 3 hundreds subtract 0 hundred is equal to 3 hundreds.

Baby Bella only weighed 75 kilogrammes.

So just a two-digit number.

So what's our answer? What's the difference? It was 312.

So Brody has a mass of 312 kilogrammes.

Time for you to do some more practise.

So for number one, you're going to complete each column subtraction to find the difference.

For two, you're going to find the missing digits in each column subtraction, thinking about what do we know? Is it the whole or is it a part? And for three you're going to work out the mass of each polar bear using column subtraction to calculate each answer.

So again, we have some information about mother and baby bears and their masses and we have to work out the missing information.

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

How did you get on? So these were the answers to these column subtractions.

And Alex is reminding you, "Start with the numbers with the smallest place value." I hope you got those correct.

So the difference in A was 323, the difference in B was 226 and the difference in C was 210.

So for question two, you had to work out the missing values in the calculations.

So did you spot when you were trying to find a missing whole and when you were trying to find a missing part? And Alex is reminding us, "To find a missing part.

you subtract the known part from the whole." And Lucas reminding us, "To find a missing whole.

you add the parts together." So all the values in our minuend, in our whole, our starting number, so the number at the top of our calculation, those were all the wholes.

So to find those, we had to combine the parts that we knew about.

If the missing value was in our subtrahend, the number we were subtracting, it was a missing part.

So we needed to subtract the known part from the whole to find the missing part.

So I hope you used that thinking as you were working.

And here are the answers to question three when we were looking at the mass of the bears.

So in A, Becky and baby Bruno have a total mass of 478 kilogrammes.

If Bruno had a mass of 135 kilogrammes, how heavy is Becky? So we know one part and we know the whole.

So we need to subtract the part we know from the whole to work out the other part.

As Alex is reminding us, "To find a missing part, subtract the known part from the whole." So 478 subtract 135 was equal to 434.

So Becky is 434 kilogrammes.

Billy and baby Brett have a total mass of 377.

If Billy has a mass of 266 kilogrammes, how heavy is Brett? Again, to find a missing part, we subtract the known part from the whole.

377 subtract 266 is 111.

So Brett's mass is 111 kilogrammes.

I hope you were successful in thinking about parts and wholes and using column subtraction to solve those problems. And we've come to the end of our lesson.

So today we've been thinking about looking back over column subtraction and using it to subtract without any regrouping and we'll come on to regrouping in later lessons, I'm sure.

So what have we learned about today? So we start by subtracting the number with the smallest place value when we're using column subtraction.

The minuend appears first in a column subtraction.

That's the number we're subtracting from.

And we can also think of that as the whole.

The subtrahend is written underneath the minuend.

That's the number we're subtracting.

It's one of our parts.

And we can use a zero to show where there are no ones, tens or hundreds represented.

And those zeros are really important.

Thank you for all your hard work today.

I hope you've enjoyed solving problems, finding missing numbers, and finding the mass of bears as well.

I've enjoyed working with you today and I hope we get the chance to work together again soon.

Bye-bye.