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 edition 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 making efficient use of subtraction strategies, including column subtraction.

So we're going to be looking at calculations and deciding whether the best way to solve it is using column subtraction, or whether there's a more efficient strategy.

So our keywords are efficient, mental strategy and regroup.

So let's practise those words together.

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

So my turn, efficient.

Your turn.

My turn, mental strategy.

Your turn.

My turn, regroup.

Your turn.

I'm sure a lot of those words are familiar to you, but as they're going to be important today, let's have a look and just remind us ourselves of what they mean.

Being efficient means finding a way to solve a problem quickly, whilst also maintaining accuracy.

A mental strategy is a chosen method to find something out which can be done in your head or with some jottings.

And the process of unitizing and exchanging between place value is known as regrouping.

For example, 10 10s can be regrouped for 100, and 100 can be regrouped for 10 10s.

So look out for those words and ideas as we go through our lesson.

There are two parts to our lesson.

In the first part, we're going to be choosing a strategy, and in the second part, we're going to be solving problems efficiently by choosing the correct strategy.

So let's make a start.

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

Alex and Lucas are talking about subtraction.

Alex says, "I really like column subtraction, but is it always the most efficient strategy?" Lucas says, "It really depends on the numbers.

Let's have a look at some calculations." So here are three calculations to look at.

How would you answer each of these? Hmm, what do you think? Alex starts with the first calculation.

He says, "I could use column subtraction to work out the difference." We've got 474, subtract 299.

And Lucas says, "You could, but is it the most efficient strategy?" What do you notice about the subtrahend? Remember, the subtrahend is the number being subtracted.

So 299, what do you notice? Ah, Alex has spotted.

"The subtrahend is 299, which is very close to 300." Hmm, does that make you think of another strategy you could use? Alex says, "I know, I could subtract 300 and then add one." Because if he subtracts 300, he subtracted too many, so he needs to add one back on.

474 subtract 300 is equal to 174, and then 174 add 1 is equal to 175.

So the difference between 474 and 299 is 175.

Alex looks at the next calculation.

What do you think about this one? He says, "I could use column subtraction to work out the difference." Yep, you could, Alex.

Lucas agrees.

"You could, but is it the most efficient strategy? What do you notice about the subtrahend and the minuend?" So the subtrahend is the number we're subtracting and the minuend is our whole, the number we start with.

Alex says, "The subtrahend and minuend are very close together," 501 and 493.

If you picture them on a number line, they're really not that far apart.

"I know," he says, "I could count on to find the difference." Maybe he'll draw a number line as a jotting.

Ah, he has.

So he's put 493 and 501 on, and he knows that there's a sort of landmark number in the way.

There's 500, isn't there? He says, "I would start at 493 and count on 7 to 500 and count on 1 more to 501." So how much has he counted on altogether? He says, "The difference between 493 and 501 is 8." So 401 subtract 493 is equal to 8.

That's a good strategy.

When the numbers are closed together, finding the difference is often the most efficient strategy.

Alex looks at the last calculation.

He says, "I could use column subtraction to work out the difference." Lucas says, "You could, but is it the most efficient strategy?" Well, Alex says, "The subtrahend and the minuend are not close together." So 654 and 378 are quite far apart if you imagine them on number line.

"The subtrahend, the number we're subtracting, is not close to a multiple of 100, so it'll be difficult to subtract mentally." He's right.

378 is not close enough to a multiple of 100 to make it easy to adjust.

Lucas agrees.

"Then column subtraction is the most efficient strategy because regrouping is needed in the ones and the 10s." But we haven't got a nice neat strategy of using a near 100 or counting on to find the difference to help us.

So Alex is going to do column subtraction for the last one.

"I regroup one 10 as 10 ones, so now there are four tens and 14 ones.

14 ones subtract 8 ones is equal to 6 ones.

I regroup 100 as 10 tens.

Now there are 5 hundreds and 14 tens.

14 tens subtract 7 tens is equal to 7 tens, and 5 hundreds subtract 3 hundreds is equal to 2 hundreds." So 654 subtract 378 is equal to 276.

Alex is sorting the calculations into the table.

So the table has one column for using column subtraction and the other column for using mental strategies, including jottings.

He starts off by looking at 832 subtract 365.

He says.

"I'd use column subtraction because I have to regroup in the ones and the tens." He spotted that the six tens and five ones in the number we're subtracting are subtrahend, are greater in value than the three tens and the two ones in our minuend, the number we start with.

He's going to put that in the use column subtraction column.

What's about 541 subtract 538? Alex says, "I'd count on using a mental strategy because the numbers are close together." So he is going to put that calculation into the other column of the table.

Over to you now to sort the last two calculations onto the table.

Would you use column subtraction or would you use another strategy? Pause the video, have a think, and we'll come back and discuss our answers.

How did you get on? Well, for 564 subtract 399, you could adjust 399 to 400, couldn't you? So that we could do as a mental strategy.

We could subtract 400, and then remember that we've subtracted one too many and add the one back on.

What about 531 subtract 288? There's lots of regrouping needed there and the numbers are not close together, so I think that would be one to do as a column subtraction.

Did you agree with those two? Time for you to do some practise.

So on the next slide, you'll see some equations and you're going to sort each equation into the table.

Would you use column subtraction or would you use another strategy? And then you're going to work out those differences.

So you're going to first sort the equations, and then you're going to calculate the differences using the strategy that you've decided is the most efficient.

And here are your equations for sorting.

So pause the video, have a go at sorting and then solving those equations, and then we'll get together for some feedback.

How did you get on? This is how I sorted the equations.

I've got some that I'd use column subtraction for and some that I'd use a mental strategy including jottings.

And I've worked out the answers.

So you might want to pause here and just compare your answers and your sorting with the ones on the screen.

Let's have a closer look at a couple of them.

So here were our column subtraction examples.

And Alex says, "I'd use column subtraction for these.

They'd be difficult to work out using mental strategies." And as an example, he's done the first one, 539 subtract 186.

So nine one, subtract six ones.

We didn't need to do any regrouping, but there were 3 tens subtract 8 tens, so we had to regroup 100 for 10 tens.

So our 5 hundreds became 4 hundreds and we had 13 in our tens.

So 13 tens subtract 8 tens is equal to 5 tens.

And 400 subtract 100 is equal to 3 hundreds.

So our difference was 353.

And these are the equations that we sorted into solving using mental strategies, including jotting.

So let's have a careful look at one of those.

Again, Alex has picked the top one, 444 subtract 99.

Well, the numbers aren't very close together and we would need to use a lot of regrouping if we used a column method, but 99 is very close to 100.

So Alex says, "99 is one less than 100.

444 subtract 100 is 344, so 444 subtract 99 will be 345." It's one more, we'd have subtracted one too many.

Lucas has focused in on 811 subtract 809 and he spotted that those numbers were very close together.

809 add 2 is equal to 811.

So the difference between 811 and 809 is 2.

And on into the second part of our lesson, this time we're going to be solving problems efficiently.

Baby elephants often hold the tails of adult elephants.

I wonder if you've come across any elephants in your maths recently.

So there is a baby elephant holding onto the tail of an adult elephant.

And Alex says, "I'm going to work out the length of each of the elephants." And we've got Erin and Emily and we've got Edmund and Eva.

"Think carefully about the most efficient strategy to use," says Lucas.

So Emily and baby Erin have a total length of 577 centimetres.

There's their total length.

"Baby Erin has a length of 198 centimetres.

I need to work out Emily's length," says Alex.

So Lucas says, "You need to calculate 577 subtract 198, but what's the most efficient strategy?" So Alex calculates.

He says, "198 is very close to 200.

I think the most efficient strategy is to subtract 200 and then add 2." So 577 subtract 200 is 377, but that's 2 centimetres too many that we've subtracted, so we need to add them back on 377 add 2 is equal to 379.

So 577 centimetres subtract 198 centimetres is equal to 379 centimetres.

So that gives us the length of our adult elephant.

Emily and baby Edmond have a total length of 515 centimetres.

Emily's length is 379 centimetres.

Alex says, "I can work out Edmond's length by subtracting 379 from 515." We know that 515 is the whole and 379 is a part, and Edmond's length is the missing part.

So we subtract the part we know from the whole.

Alex says, "I think the column subtraction is the most efficient strategy here." I think he's right, isn't he? There's no number that's very close to 100.

The numbers aren't very close to each other to find the difference, and there's a bit of regrouping to do.

So let's use a column subtraction.

He says, "I regroup one 10 as 10 ones.

Oh, now there are 0 tens and 15 ones." But we needed the 15 ones because we've got to subtract 9 ones.

"15 ones subtract 9 ones is equal to 6 ones.

I regroup 100 as 10 tens.

Now there are 4 hundreds and 10 tens.

10 tens subtract 7 tens is equal to 3 tens.

And 4 hundreds subtract 3 hundreds is equal to 100.

So baby Edmond must be 136 centimetres long." Time for you to have a go.

Baby Edmond and Eva have a total length of 536 centimetres.

Baby Edmond is 136 centimetres long.

How long is Eva? And Lucas says, "What's the most efficient strategy you could use to calculate the difference?" So have a look at the numbers carefully, pause the video, and see if you can work out how long Eva is.

How did you get on? Did you spot that the ones and tens digits of both numbers are the same? We've got 536 and 136.

So Alex says, "It's probably most efficient to add on to find the difference because we're only thinking about hundreds." So what do we need to add to 136 to equal 536.

400.

There's a gap of 400.

136 add 400 is equal to 536.

So Eva is exactly 400 centimetres long.

And Lucas says, "You may have completed a quick subtraction calculation instead." 536 subtract 400 is equal to 136.

You may have spotted that there was a gap of 400.

Time for you to do some practise.

You need to work out the length of each elephant.

The only elephant we know is Enzo, who is 156 centimetres long.

Other than that, we know about some adult and baby elephants together.

So we know that baby Enzo and Eloise have a total length of 555 centimetres.

And then we also have information about Evan and baby Ella and Eloise and Baby Emmett.

We also know about Ezra and Amelia, Ella and Amelia, and Emmett and Evan.

Ooh, so we've got lots of information, but the one elephant we know about is Enzo, who is 156 centimetres.

So you're going to work out the length of each elephant.

And Alex says, "Use the most efficient strategy each time." And Lucas says, "Think about the order in which you'll need to answer the questions." So where will you start? Which pairing will you start thinking about in order that you can find the length of all the elephants? Pause the video, have a go, and we'll come back and discuss the answers.

And here are the answers.

Remember, we only gave you the length of Enzo to start off with, so you had to work through the information in the right order so that you could work out how long the other elephants were.

So by knowing that Enzo was 156 centimetres, we could work out that Eloise's length was 399 centimetres.

There was an interesting strategy for this, 156 and 555.

We can see that there's a 55 and a 56 there, can't we? So 555 minus 400 would equal 155, but that's one centimetre too short.

So we need to add that centimetre on to make 156, which means we've only subtracted 399 centimetres.

So Eloise's length had to be 399 centimetres.

Now we know Eloise's length, we can work out baby Emmett's length.

Their total length was 567 centimetres and we had to subtract 399, so that was very close to 400.

So we could subtract 400 centimetres to get 167.

But then we've subtracted one centimetre too many, so we had to add one centimetre back on, so 168.

Emmett's length is 168 centimetres.

Now we know baby Emmett's length, we can work out Evan's length.

585 subtract 168.

This time, there wasn't a number near to 100 that we could use.

There was quite a lot of regrouping to do, so it was best to use a column subtraction here.

And we had to regroup at one 10 for 10 ones.

So Evan has a length of 417 centimetres.

Now we know Evan's length, we can work out baby Ella's length because their total length was 633 centimetres.

And again, a column subtraction was probably the best strategy to use here.

And our column subtraction showed us that Ella's length was 216 centimetres.

Now we know about Ella, we can work out Amelia's length.

Again, a column subtraction was a good way of working here.

583 subtract 216 is equal to 367, so Amelia's length is 367 centimetres.

And now we can work out Ezra's length because we know Amelia's length.

Now here, 568 and 367.

We've got that 68, 67.

So we could use a counting on strategy.

200 centimetres would give us 567 centimetres.

And one more for 568.

So Ezra's length was 201 centimetres.

I wonder which different strategies you used.

Did you manage to use strategies that weren't just column subtraction, I wonder? It's always worth looking at the numbers involved in a calculation to make sure that you are using the most efficient strategy.

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

We've been deciding on the most efficient subtraction strategy and including column subtraction in that.

So what have we learned about? We've learned to look carefully at the numbers in a calculation.

Column subtraction might be the most efficient method to use if regrouping is needed, but we can use a mental strategy where it would be more efficient, where one of the numbers perhaps was close to 100 or a multiple of 100, or where the two numbers were very close together, so the difference was a very small number.

And then counting on could be an efficient strategy.

I hope you've enjoyed exploring the problems that we've looked at today and enjoyed discussing efficient strategies.

I hope also in the future you'll look carefully at the numbers and make sure that you choose the most efficient strategy.

Thank you for all your hard work today and I hope I get to work with you again soon.

Bye-bye.