Lesson video

Hello there, my name is Mr. Goldie.

Welcome to today's math lesson, and here is our learning outcome.

I can make efficient use of subtraction strategies including column subtraction and here are the keywords for today's lesson.

So I'm going to say the keywords, can you repeat them back? So the first key word is efficient.

The next key words are mental strategy and the last key word is regroup.

Let's take a look at what those words mean.

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

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

The process of unitizing and exchanging between place values is known as regrouping.

For example, 10 tens can be regrouped for 100, 100 can be regrouped for 10 tens and here is this lesson outline.

So the first part of the lesson is called which strategy, and the second part of the lesson is solving problems efficiently, let's get started.

In this lesson, you will meet Sam and Aisha who are going to be helping you with your math today and what's that Sam, you want to say something? "I love column subtraction." Sam has become a bit of a fan of column subtraction and I think he likes to use it whenever he can.

Sam and Aisha are thinking about subtraction.

"I think column subtraction is brilliant.

I'm going to use it whenever I can." says Sam, I told you that Sam was a bit of a fan of column subtraction.

Aisha says, "For each calculation you've got to look really carefully at the numbers involved.

Column subtraction could be the best strategy if regrouping is needed, but sometimes it's not the most efficient strategy." Let's take a look at some problems. How would you solve these? So we've got here four problems, 367 subtract 200, 566 subtract 199, 902 subtract 897 and 832 subtract 567.

I wonder how you would solve each of these, would you use column subtraction? Would you use a different method? Sam says, "I use column subtraction for all of them! Column subtraction is brilliant." Sam and Aisha look at the first calculation.

The first calculation is 367 subtract 200.

Aisha says, "This is a problem that you can easily solve using a mental strategy.

Only the hundreds digit is going to change." "I suppose you're right, Aisha." admits Sam, "I know 300s subtract 200s is equal to 100." So Aisha says, "You can quickly work out the answer.

367 subtract 200 is equal to 167." So already we found one calculation which is better to do using a mental strategy rather than column subtraction.

Sam and Aisha look at the next calculation.

So the next calculation is 566 subtract 199.

Sam says, "I definitely use column subtraction to work out the difference." So Sam writes it as a column subtraction with the subtrahend written below the minuend.

"I regroup one 10 as 10 ones.

There are now five tens and 16 ones." So Sam's already looked and seen that there are more ones in the subtrahend than there are in the minuend, so you have to regroup.

So here regroups one of the tens as 10 ones.

So are now five tens and 16 ones, 16 ones subtract nine ones is equal to seven ones.

Sam also needs to regroup in the tens, because we've got five tens subtract nine tens.

The tens number in the subtrahend is larger than the tens number in the minuend, so I regroup 100 as 10 tens.

There are now four hundreds and 15 tens.

There were five tens, 10 more tens have been added, so now 15 tens altogether.

15 tens subtract nine tens is equal to six tens.

And then 400 subtract 100 is equal to three hundreds.

So 566 subtract 199 is equal to 367.

Now Sam has worked out the correct answer, but was it the most efficient way to work out the difference? Aisha says, "I think a mental strategy is more efficient.

First I'd subtract 200 from 566 and jot down the answer.

To subtract 199, I can subtract 200, then add one." So Aisha works out what 566 subtract 200 would be, that would equal 366 and then she works out 366 add one and that is equal to 367.

Aisha has subtracted 200 and added one back on and that is the same as subtracting 199.

Now notice they both got the same answer.

It's a good way of checking a calculation into two different ways, but I think Aisha's method is more efficient.

Ah Sam agrees, "Your strategy was a more efficient way of finding the difference." Sam and Aisha look at the next calculation.

So next calculation is 902, subtract 897.

Sam says, "I would use column subtraction to work out the difference, because I need to regroup in the ones and tens." Now quite often when you need to regroup in the ones and tens, it is most sensible to use column subtraction, but not always.

You may have spotted something about those two numbers already.

Aisha says, "You could use column subtraction, but the numbers are actually very close together." 897, 902 are not very far apart.

Aisha says, "I would count on to find the difference." So Aisha says, "I would start at 897 and count on three to 900 and then count on two more to 902." So Aisha draws number line 897 add three is equal to 900 and then 900 add two is equal to 902.

What is Aisha added altogether? Altogether I added five 902 subtract 897 is equal to five, 897 add five is equal to 902.

Sam says, "I like that strategy." So Sam is realising of course that column subtraction is useful.

It's a good strategy to use, but it's not always the most efficient strategy to use, it all depends on the numbers involved in the calculation.

Sam and Aisha look at the last calculation.

The last calculation is 832, subtract 567.

Sam says, "I definitely use column subtraction to work out the difference." So he sets out who column subtraction, 832 is the minuend 567 is the subtrahend.

And then Sam of course has to regroup in the ones and the tens, so I regroup one 10 as 10 ones.

There are now two tens and 12 ones, 12 ones subtract seven ones is equal to five ones.

Then Sam also has to regroup in the hundreds, I regroup 100 as 10 tens.

There are now seven hundreds and 12 tens, 12 tens subtract six tens is equal to six tens.

Seven hundreds subtract five hundreds is equal to two hundreds.

832 subtract 567 is equal to 265.

Wonder what Aisha's going to say.

Aisha says, "I agree.

I think column subtraction is the most efficient strategy here, because regrouping is needed in the ones and the tens." That's not always true that when there's regrouping the ones and tens needed, you should use columns subtraction, but sometimes it is of course it all depends on the numbers.

And here is some problems for you to look out on your own, so how would you solve each problem? There are four calculations there for you to take a look at, how would you answer each of them? Would you use common subtraction? Would you use a mental strategy? You're going to sort each calculation into the table, so would you use column subtraction? Would you use a mental strategy including some jottings as well if you jot some things down that counts the mental strategy too.

Sam says, "Would you use column subtraction?" Aisha says, "Would you use another strategy?" So look at each calculation, how would you answer it? You don't need to answer it yet, but how would you work out the answer? Pause video and have a go at sorting those four calculations.

And welcome back, did you manage to sort them all? Do you think you've got them to the right place on the table? Now you might not completely agree with where Aisha and Sam have sorted them, but hopefully you have, because I think they've got the most efficient way of answering each question, let's take a look.

So if that first calculation 800 subtract 399, hopefully you said I'd use a mental strategy to work it out, you could adjust 399 to 400.

The next calculation, 791 subtract 293.

Hopefully you said I'd use column subtraction.

There is regrouping needed there or groupings needed in the ones, so probably the most efficient way to answer that question is by using column subtraction.

Let's take a look at the next calculation.

So 913, subtract 477.

Again, we'd use column subtraction and in fact for that calculation you have to regroup in the ones and in the tens.

And then lastly, last calculation 604 subtract 596.

The minuend and subtrahend are close together, very, very close together, very little difference in between them.

So in fact the easiest way to answer that question would be to start from 596 and to add on to get to 604 crossing over 600.

Hopefully you sorted those four calculations into the same places as Sam and Aisha.

Next we're going to take a look at two of those problems, so how would you calculate the difference? How would you work out the answer to each of those questions? So one of them, 791 subtract 283 and one of them 800 subtract 399, how would you solve each question? How would you find the difference between each pair of numbers? So pause the video, see if you can find the difference between each pair of numbers.

And welcome back, did you answer both questions? Did you use column subtraction for one? Did you use a mental strategy for the other? Let's take a look, see how you might have answered them.

So hopefully for that first one you probably said use column subtraction.

So we set it out like a column subtraction with a subtrahend written beneath the minuend and then we can try to work out the difference.

So Sam says 791 subtract 283 is best solved using column subtraction.

Regroup one 10 as 10 ones.

There are now eight tens and 11 ones.

11 ones subtract three ones is equal to eight ones.

Eight tens subtract eight tens is equal to zero tens and then finally seven hundreds subtract two hundreds is equal to five hundreds.

So Sam says, "791 subtract 283 is equal to 508." hope that's the answer you got too.

Aisha says, "It is more efficient to solve 800, subtract 399 using a mental strategy." Aisha says, "She knows 800 subtract 400 equals 400." So 800 subtract 399 is equal to 401.

Subtracting 399 is the same as subtracting 400, then adding one back on.

So for that calculation is much better to use a mental strategy to work out the answer.

So very well done if you thought really carefully about how to answer those questions and you've got the right answer in an efficient way.

Let's take a look at task A.

So task A, you're going to sort each calculation into the table thinking carefully about would you use column subtraction? Would you use another strategy? Now if you've managed two sort the calculations, have a go trying to answer 'em as about can you find the difference between the two numbers? And you might want to do that as you go along.

So each time you sort a calculation, you might want to answer it straight away.

Here are the 12 calculations you are going to be sorting.

For some of them it's more efficient to find the difference using a mental strategy, for some of them it's more efficient to find the difference by using column subtraction.

So you gotta think really carefully, look really carefully at those numbers.

Pause the video and have a go at task A.

And welcome back.

And let's take a look at those answers.

So here are the answers for task A and this is how you probably sorted those calculations, you might not agree in every single one.

You might have done some of them in a slightly different way, but this is probably the most efficient way to solve each of the problems. So for 761 subtract 356, probably most efficient to use column subtraction.

For 765 subtract 299, it's definitely more efficient to use a mental strategy, because you can use adjustment, you can subtract 300, add one back on again.

So hopefully you thought really, really carefully about each of those calculations and hopefully manage to answer at least some of them as well, so very well done on task A.

And let's move on to the second part of the lesson, which is solving problems efficiently.

Some pandas are at different heights on a mountain, so we've got Poly, Poly is at 198 metres.

We've got Ping, Ping is at 302 metres.

Peter is at 759 metres.

Priya is at 765 metres.

Pedro is at 891 metres and finally Paul is right near the top of the mountain at 903 metres.

We are going to be using these six pandas and their different heights to solve some problems and here is the first problem.

How much higher is Ping than Polly? So Polly is at 198 metres, Ping is at 302 metres.

"We need to calculate the difference between 198 metres and 302 metres." says Aisha.

And then we'd know how much higher Ping is than Polly.

Sam calculates 302 metres subtract 198 metres.

I wonder how Sam's going to do that.

"I would use a mental strategy." says Sam, "First I'd subtract 200 from 302 and jot down the answer." It's nice to see that Sam isn't just using column subtract anymore, isn't it? So first of all, Sam jots down 302 subtract 198, 'cause that's the calculation we're trying to answer.

And then Sam jots down 302 subtract 200, that is equal to 102.

How's Sam going to work out the difference between 302 and 198? To subtract 198 I can subtract 200, then add two.

So subtracting 198 is the same as subtracting 200 and then adding two back on again.

So 102 add two is equal to 104.

So same has subtracted 200 from 302, I got the answer 102 and then Sam has added 2 to 102.

Got the answer 104.

It's a very efficient way of working out that calculation, well done Sam.

302 metres subtract 198 metres is equal to 104 metres.

"I think you are right Sam" says Aisha "Column subtraction is not the most efficient strategy here." So it's still really important to be thinking about those most efficient strategies, what is the best strategy to use? And the question was asking us how much higher is Ping than Polly, Ping is 104 metres higher than polly.

How much higher is Paul than Pedro? Pedro is at 891 metres.

Paul is at 903 metres.

How much higher is Paul than Pedro? We need to calculate the difference between 891 metres and 903 metres is Aisha, I wonder how you do that.

Aisha calculates 903 metres, subtract 891 metres.

I wonder if she's going to use column subtraction, what do you think.

"I would count on to find the difference." says Aisha.

The numbers are quite close together, aren't they? "I would start on 891 and count on nine to 900 and then count on three more to 903." So she draws number line, she starts on 891, she counts on nine to get to 900.

It's all about crossing through that hundreds number and then she adds on three to go from 900 to 903.

What has she added on altogether? Altogether I added 12, I did nine and added three, so altogether I added 12.

So 903 subtract 891 is equal to 12.

Paul is 12 metres higher than Pedro.

Here's one for you to try on your own.

How much higher is Paul than Peter? What do you think? Let's find out where they are first of all.

So Peter is at 759 metres, Paul is at 903 metres.

How will you calculate the difference? How will you work out the answer? So what is 903 subtract 759? How will you work out the difference between those two numbers? Pause the video, see if you can calculate the answer and think really carefully about the most efficient way of finding the answer.

And welcome back, how did you get on? Did you find the answer? Did you definitely answer it using the most efficient strategy? Let's take a look.

Sam says, "I'd find the difference using column subtraction." So Sam says, "There aren't any tens to regroup, so we need to regroup the hundreds first." So regroup 100 as 10 tens, there are now eight hundreds and 10 tens and then regroup one 10 as 10 ones.

There are now nine tens and 13 ones, 13 ones subtract nine ones is equal to four ones.

Nine tens, subtract five tens is equal to four tens and eight hundreds subtract seven hundreds is equal to 100.

So 903, subtract 759 is equal to 144.

Very well done, if you've got 144 is the answer and hopefully use column subtraction.

You may have used a different method, but have a good think about it.

Was it more efficient than using column subtraction? So Paul is 144 metres higher than Peter, that's the answer to the question and let's take a look at task B.

So task B is similar questions the ones we've just been looking at, some pandas are at different heights on the mountain.

So we've got our six pandas there and we've got the heights that they are each at.

You've got to think carefully about how to solve each problem.

So question A for example is how much higher is Pedro than Polly? Question B is how much higher is Paul than Ping? So have a good look at the numbers, what's the most efficient strategy to use to solve the problem? Would you use column subtraction? Would you use another strategy, possibly a mental strategy, probably a mental strategy with some jottings.

So pause the video and have a go at answering those five questions, thinking really carefully about the most efficient way to answer them.

And welcome back, how did you get on? Did you get to question D? Did you get to question E? Very well done if you did.

Did you think really carefully about the most efficient strategy you can use to answer each question? Let's take a look.

So here are some solutions and your solutions may be different, because you might have solved the problems differently.

So for question A, how much higher is Pedro than Polly? So the calculation was 891 metres subtract 198 metres.

Hopefully you subtracted 200 and added two back on again, and that would've given you the answer 693 metres.

For the second calculation.

Well, there's different ways of doing that one, you could have used column subtraction, but it's pretty straightforward calculation you could probably have done mentally, the answer would be 601 metres.

Question C, you probably used a column subtraction for so 891 metres subtract 765 metres, that is equal to 126 metres, that was regrouping there in the tens.

How much higher is Priya than Peter? This is question D.

Well the numbers are very, very close together, so probably you added on from the small number to get to the large number.

Priya is only six metres higher than Peter.

And lastly, question E.

And again, it was used in that same number again, 198.

So again, we can subtract 200 and then add two back on again.

So very, very well done.

If you managed to get to question E and you managed to solve that one as well and hopefully you are gonna think a little bit more next time you are faced with a subtraction calculation about which strategy you would use, would you use column subtraction? Would you use a mental strategy? And sometimes you might want to use both.

You might want to use a column subtraction to work out the answer and then use a mental strategy to check your answer.

Very well done today, excellent work, I hope you enjoyed that lesson.

And let's take a look at our lesson summary.

So look carefully at the numbers in a calculation.

Column subtraction might be the most efficient method to use if regrouping is needed, and use a mental strategy where it would be more efficient.