Lesson video

Hello, everyone.

Welcome back to another maths lesson with me, Mrs. Pochciol.

As always, I can't wait to learn lots of new things and hopefully have lots of fun.

So let's get started.

This lesson is called Use strategies to make solving calculations more efficient, and it comes from the unit Column addition and subtraction with four-digit numbers.

By the end of this lesson, you should be able to use strategies to make solving calculations more efficient.

Let's have a look at this lesson's keywords.

Efficient, equivalent, and inverse.

Let's practise saying them.

My turn efficient, your turn.

My turn equivalent, your turn.

My turn inverse, your turn.

Fantastic.

Let's have a look at what they mean.

Working efficiently means finding a way to solve a problem quickly whilst also maintaining accuracy.

Equivalent is when two or more things have the same value.

And inverse means the opposite in effect.

The reverse of.

These three words are going to really help us in our learning today.

So let's get going.

Here is this lesson's outline.

In the first part of our learning, we're going to use efficient strategies to calculate with four-digit numbers, and in the second part of our learning, we're going to use inverse to find missing numbers.

Let's get started with using efficient strategies to calculate with four-digit numbers.

In this lesson, you're going to meet Sofia and Izzy.

Sofia and Izzy are discussing some four-digit equations.

Izzy thinks that we can use column method for all of them because they're all four-digit numbers.

Whereas Sofia thinks that she doesn't need to use the column method for all of them.

Have a look at the equations.

Who do you agree with? Hmm.

Let's have a look at this first one.

2,000 subtract 1,998.

Sofia notices that in this calculation the numbers are really close together so she could count on rather than using a column subtraction to find the difference.

On a second glance, Izzy has noticed that 1,998 is actually just two less than 2,000.

So she knows that 2,000 subtract 1,998 is equal to two.

She didn't need to use the column method at all for that question.

Are there any others that you can solve using a mental strategy rather than a column subtraction? Hmm, Izzy has noticed this one.

We could use our counting on strategy again to the difference here.

We notice that 10 more would be equal to 4,000 and then 1,000 more is equal to 5,000.

So 10 plus 1,000 is equal to 1,010.

So we know that the difference between 3,990 and 5,000 is 1,010.

So 5,000 subtract 3,990 must be equal to 1,010.

Again, no calculations necessary, just a mental strategy using what we already know.

Well done, Izzy and Sofia.

Izzy doesn't notice anything in the final two calculations.

So for those she has suggested that we use our column subtraction.

Sofia agrees.

So they're going to solve one each.

Let's have a look at Izzy and Sofia using column subtraction to solve the final two problems. Four ones subtract nine ones.

Hmm.

We can't do that, so we're going to have to regroup.

Now we have seven 10s but we do have 14 ones.

14 ones subtract nine ones is equal to five ones.

Seven 10s subtract two 10s is equal to five 10s.

100 subtract 300 we can't do that, so we're going to have to regroup.

11 100s subtract three 100s, now we can do that.

That is equal to eight 100s.

And four 1,000s subtract 1,000 is equal to 3,000.

So 5,184 subtract 1,329 is equal to 3,855.

Over to you then Sofia.

Let's see how you can solve yours.

Seven ones subtract four ones is equal to three ones.

Three 10s subtract nine 10s, we can't do that, so we're going to have to regroup.

Oh, but we don't have any 100s to regroup.

Sofia, what are we going to have to do? Oh, I see.

So we're going to regroup the 1,000 into 10 100s.

Now we have 10 100s, we can regroup one of those into 10 10s.

Did you see what Sofia had to do there? She had to go all the way to the thousands to regroup and regroup again.

Well done, Sofia.

Now we have 13 10s subtract nine 10s, we can do that.

That's four 10s.

Nine 100s subtract seven 100s is equal to two 100s.

And eight 1,000s subtract five 1,000s is equal to three 1,000s.

So we can see that 9,037 subtract 5,794 is equal to 3,243.

Well done, I'm super impressed at your column strategy there, guys.

Well done.

Over to you then.

Use an efficient method to calculate each of these.

Remember to look for any mental strategies you could use before using column subtraction.

Pause this video, calculate A, B, and C, and come on back when you're ready to see how Sofia solved each of those problems and whether your strategy was the most efficient.

Welcome back.

I hope you enjoyed finding the most efficient method there.

Let's have a look at how Sofia got on.

3,000 subtract 2,990.

Sofia noticed that 2,990 was 10 less than 3,000.

So 3,000 subtract 2,990 must be equal to 10.

Well done if you spotted that that was the most efficient method there.

For B, Sofia used column subtraction as she didn't notice anything that she could use to help her to solve this quickly.

And she found that the answer was 4,563.

Well done if you got that one.

And finally for C, she noticed that 4,993 was seven less than 5,000.

Seven more would be equal to the next thousand.

So 5,000 subtract 4,993 must be equal to seven.

Well done to you if you manage to solve all of those problems and then even more well done to you if you manage to use the most efficient method.

Izzy and Sofia now look at this problem.

They both think that they can solve this problem mentally.

They both solve the problem using what they know to help them.

Izzy thinks that the answer is 997.

She used her knowledge of number pairs to 10, but Sofia thinks that it's 993.

She used a number line to help her to visualise this problem along with using her knowledge of number pairs to 10.

Hmm, but who is correct? They both have different solutions.

Sofia shows Izzy her number line.

She starts at 1,003 and she noticed that this would bridge 1,000.

So she partitioned 10 into three and seven.

1,003 subtract three is equal to 1,000 and 1,000 subtract seven is equal to 993.

Izzy notice where she went wrong.

She saw three and thought seven and three is equal to 10, so it must be 997.

But a number line would've helped you to visualise that better, Izzy, and you would've been able to see that that wasn't quite right.

Well done, Izzy and Sofia.

I love how you use what you knew along with that number line to help you to solve that problem, Sofia.

Izzy and Sofia now look at this problem.

6,000 subtract 2,348.

Hmm, what strategy could we use to solve this? Izzy thinks that we could use column subtraction for this problem.

Sofia agrees, but there's something that we could do to make this easier as with lots of regrouping, it's easy to make lots of mistakes.

What do you think Izzy and Sofia could do to make this easier? Oh, Izzy is suggesting that we could adjust the calculation to make it easier.

What does that mean, Izzy? Izzy shows her what she's thinking.

If we subtract one from the whole and the part, the difference will remain the same.

Hmm.

So 10 subtract seven is equal to three.

If we subtract one from both the whole and the part which would give us nine subtract six.

The difference will remain the same, it's still three.

So if we subtract one from the whole and the part, we will be able to find the difference between 6,000 and 2,348.

Should we have a go? We can use an equivalent calculation to make the calculation easier.

We could add one or subtract one to the whole and the part.

So if we subtract one from both the whole and the part, we will keep the same difference, but that means it's going to be 5,999 subtract 2,347.

It's going to be a lot easier for us to use our column subtraction because there's not going to be any regrouping at all.

Nine ones subtract seven ones is equal to two ones.

Nine 10s subtract four 10s is equal to five 10s.

Nine 100s subtract three 100s is equal to six 100s.

And five 1,000s subtract two 1,000s is equal to 3,000.

So we can see that 5,999 subtract 2,347 is equal to 3,652.

So we also know that 6,000 subtract 2,348 will also be equal to 3,652.

How much easier was that than having to do all of that regrouping? Well done, Izzy.

A lovely idea there.

Over to you then to have a practise of this strategy.

How could we subtract one from this calculation to make it easier? Use the equivalent calculation to find the difference.

8,000 subtract 4,762.

Pause this video, adjust the calculation, complete the column subtraction, and find the difference between 8,000 and 4,762.

Come on back when you've completed it to see how you've got on.

Welcome back.

Let's have a look then at how Sofia adjusted this calculation.

If we subtract one from the whole and the part, the equivalent calculation will be 7,999 subtract 4,761.

Nine ones subtract one one is eight ones.

Nine 10s subtract six 10s is equal to three 10s.

Nine 100s subtract seven 100s is equal to two 100s.

And seven 1,000s subtract four 1,000s is equal to three 1,000s.

So if 7,999 subtract 4,761 is equal to 3,238, we also know that 8,000 subtract 4,762 is also equal to 3,238.

Well done to you if you got that calculation correct.

We can use equivalent calculations to make calculations easier.

Remember, we can add one or subtract one.

We've already practised subtracting one to make our calculation easier.

Now let's practise adding one.

Here we have 6,742 subtract 399.

If we add one to both the whole and the part, we can keep the same difference.

6,742 becomes 6,743 and 399 becomes 400, which is a lot easier to work with because we've replaced those nine 10s and nine ones with zero 10s and zero ones by adding one, which is a lot easier for us to work with.

So we can see that 6,743 subtract 400 is equal to 6,343.

So we know that 6,742 subtract 399 will also be equal to 6,343.

Can you see how adding one can also help us to make calculations easier? Let's have a practise of adding one.

How would we add one to this calculation to make it easier for us to solve? Use the equivalent calculation to find the difference.

So pause this video, adjust your calculation, work out the difference, and come on back to see how you've got on.

Welcome back.

Let's have a look then.

So if we add one to the whole and the part, the equivalent calculation will become 7,366 subtract 600.

So let's complete it.

Six ones subtract no ones is equal to six ones.

Six 10s subtract no 10s is equal to six 10s.

Three 100s subtract six 100s, now we can't do that so we have got some regrouping.

Now we have 13 100s subtract six 100s which is equal to seven 100s.

And we have six 1,000s subtract no 1,000s, which is equal to six 1,000s.

7,366 subtract 600 is equal to 6,766.

So we know that 7,365 subtract 599 is equal to 6,766.

Well done to you if you completed that calculation.

Over to you then with Task A.

Part one is to use the different strategies to solve and decide which is the most efficient.

So our calculation is 4,556 subtract 499.

Have a go at solving this using column subtraction.

Then have a go at solving it using adding one to the whole and the part and then have a go at solving this using finding the difference using a number line, the three strategies that we've looked at during our first learning cycle.

Once you've completed all three of them, it's up to you to decide which was the most efficient.

Part two is to then sort these problems into the most efficient strategy to solve.

Pause this video, have a go at Task A, part one and part two and then come on back to see how you've got on.

See you soon.

Welcome back.

I hope you enjoyed exploring the most efficient strategies there.

Now don't worry if your strategy was not the same as somebody else's because sometimes something that's more efficient for you might not be the most efficient for somebody else.

Let's have a look at how Sofia and Izzy got on with part one.

Part one was to use the different strategies to solve and decide which was the most efficient.

So let's have a look at our column subtraction.

Six ones subtract nine ones, we can't do that so we're going to regroup.

16 ones subtract nine ones is equal to seven ones.

Four 10s subtract nine 10s, we can't do that either, so we're going to have to regroup again.

14 10s subtract nine 10s, that's equal to five 10s.

Four 100s subtract four 100s is equal to zero 100s.

And four 1,000s subtract zero 1,000s is equal to 4,000.

We can see that the difference is 4,057, but was that our most efficient strategy? Let's try our next one.

Let's add one to the whole and the part and then subtract.

4,556 plus one is 4,557 and 499 plus one is equal to 500.

Well done.

We've got the same difference there, 4,057.

That strategy felt a little bit more efficient for me because there wasn't any regrouping so less risk of making a mistake.

Let's have a look at a third strategy.

Finding the difference using a number line.

499 plus one is equal to 500 plus 4,000 is equal to 4,500, and then we need to add that last bit of 56 to take us to 4,556.

To find the difference, we now add together those steps that we took.

So one plus 4,000 plus 56 is equal to 4,057.

So again, we have the same difference but a different strategy of finding the answer.

Which of those do you think was the most efficient strategy to solve that problem? I definitely think that the adjustment strategy or the number line was definitely more efficient for me so I would probably choose one of those as my most efficient strategy.

Which one did you find the most efficient? Let's have a look then at part two.

Sorting these problems into the most efficient strategy to solve.

7,000 there, adding or subtracting one will make that more manageable for me to work with.

5,523 plus 1,802, there isn't really a strategy that I can see there that's going to help me.

So column method would be the best strategy there.

1,996 plus 10, I can see that that's going to bridge a thousand so a number line would really help me to visualise that problem.

2008 subtract 100.

I can see that that's again going to bridge 1,000 so, the best strategy will be to use a number line.

9,523 subtract 299.

I can see that if I add one more to that 299, that will be 300, which would make it a lot easier for me to work with.

So that would be to add or subtract one to the whole or the part.

And finally 6,234 plus 2,526.

I can't see any strategies there and there's gonna be quite a bit of regrouping there, so column method would be the best strategy to use for that one.

Well done to you if you managed to sort them into the same categories that I did.

Let's move on then to the second part of our learning using inverse to find missing numbers.

Sofia and Izzy are discussing some four-digit calculations.

Let's help them to work out the missing digits.

Izzy can see that we're adding here.

So we're going to start with the ones just in case we have any regrouping.

What knowledge can we use to find the missing digits here? We can see this as something plus seven is equal to nine and Sofia knows that two plus seven is equal to nine.

So two must be the missing digit there.

Four plus something is equal to seven.

We know that four plus three is equal to seven, so three must be the missing digit here.

Here we can see this as something plus five is equal to eight.

We know that three plus five is equal to eight, so three must be the missing digit.

And finally we can see this as three plus something is equal to seven.

We know that three plus four is equal to seven so four must be the missing digit.

Here Sofia and Izzy use their addition facts to tend to help them to find the missing parts.

Well done to you.

Sofia and Izzy now have a go at another one.

Because we know the whole, we can use the subtraction, the inverse, to find the missing parts.

So have a look at the ones.

Something plus seven is equal to nine or we can see this as the whole subtract the part is equal to the part.

Nine subtract seven is equal to two so we know that that missing part must be two.

Let's have a look at our 10s column.

Four plus something cannot be equal to three, so it must be four plus something is equal to 13.

We must have had some regrouping.

We can solve 13 subtract four, which would give us the missing part.

13 subtract four is equal to nine so nine must be the missing part because four plus nine is equal to 13.

Well done Izzy.

I love how you used your knowledge there to help find that missing number.

Let's have a look at our 100s column then.

We can see this as something plus five plus two is equal to two? That cannot be.

So we know that there must have been some regrouping here.

Something plus five plus one is equal to 12.

That makes more sense, doesn't it? Five plus one is equal to six so we can see this as 12 subtract six, which is equal to six.

So six must be the missing digit here because six plus five plus one is equal to 12.

Well done, Sofia.

And finally, let's look at the 1,000s column.

Three 1,000s plus something plus one is equal to eight.

We know that three and one is equal to four and eight subtract four is equal to four.

So the missing digit must be four, three 1,000s plus four 1,000s plus 1,000 is equal to eight 1,000s.

Well done, Izzy and Sofia.

You completed all those missing numbers.

This time though you used your knowledge of inverse to help you.

If we know a whole subtract a part is equal to a part, then we know that a part plus a part is equal to the whole.

That knowledge can really help you to find missing numbers.

Over to you then.

Use your knowledge of inverse and our stem sentence to help find the missing digits in this column edition.

If I know mm subtract mm is equal to mm, then I know that mm plus mm is equal to mm.

Pause this video, have a go at finding all of those missing digits and come on back to see how you get on.

Welcome back.

I hope that stem sentence really helped you to find those missing digits there.

Let's have a look at how Sofia and Izzy got on.

If I know that nine subtract five is equal to four, then we know that four subtract five is equal to nine.

So four is the missing digit there.

Let's have a look at the 10s.

Four plus something cannot be two, so it must be four plus something is equal to 12.

If we know that 12 subtract four is equal to eight, then four plus eight is equal to 12.

So eight is that missing digit.

Let's have a look at those 100s then.

If we know that seven subtract five subtract one is equal to one, then we know that one plus five plus that regrouped one is equal to seven.

So one is the missing digit there.

Then let's have a look at the 1,000s.

If we know that five subtract three is equal to two, then we know that three plus two is equal to five.

So two is the missing digit there.

Well done for completing that check.

Sofia and Izzy now have a go at using their knowledge of inverse to find the missing numbers in this column subtraction.

So let's have a look.

We can see that we're subtracting here so let's start with the ones just in case we have any regrouping.

Something subtract four is equal to five.

We can use the inverse here.

We are missing the whole, so we know that four plus five is equal to nine.

So nine subtract four must be equal to five.

Nine is the missing digit.

Well done, Sofia.

I love how you noticed that the whole was missing so you could use the inverse of addition to add the parts together to find the whole.

Let's have a look at our 10s.

In the 10s we can see this is eight subtract something is equal to seven.

Here we are missing a part.

We know that eight is one more than seven, so eight subtract one is equal to seven.

One is the missing digit.

Well done, Izzy.

Let's have a look at our 100s then.

Something subtract two is equal to four.

Again, we're missing the whole here.

So we know that four plus two is equal to six and six subtract two is equal to four.

So six is our missing digit here.

And finally our 1,000s.

Again, we're missing our part.

We know that three and four is equal to seven.

So seven subtract three is equal to four.

Three is the missing digit.

Well done, Izzy and well done, Sofia.

The girls now have a go at this problem.

Let's have a look at the ones.

Eight subtract something is equal to five.

We know that eight subtract five, the other part, is equal to three.

So eight subtract three is equal to five.

Three is our missing digit.

Let's have a look at our 10s.

Something subtract five is equal to seven.

Here we are missing the whole.

Seven plus five is equal to 12 so we must have regrouped here.

One of the 100s must have been regrouped into 10 10s to give us 12.

Well done, Izzy.

I love how you notice that we must have regrouped there.

Let's have a look at our 100s then.

Six subtract something is equal to zero.

We know that when we subtract a number from itself, it's equal to zero.

So six must be the missing digit there.

Now let's have a look at our 1,000s.

Something subtract one is equal to three.

We know that three plus one is equal to four, so four must be that missing 1,000s digit.

Well done.

Let's continue to practise this strategy in Task B.

Task B, part one is to fill in the missing numbers in the column additions.

And part two is to fill in the missing numbers in the column subtractions using all of those strategies that we've practised throughout this lesson.

So pause this video, have a go at part one and part two, and come on back when you are ready to see how you've got on.

Welcome back.

Let's have a look at how you got on.

Here are all the missing numbers.

Izzy, which parts did you have to think carefully about? Oh, seven plus something couldn't have been equal to four, so it must have been regrouped.

Seven plus something was equal to 14.

The missing number must have been seven.

Over here Izzy noticed that six plus five was equal to 11.

Again, a regrouping required.

So 10 10s were regrouped as 100.

That then impacted the next missing digit because something plus nine plus one couldn't be equal to eight.

So it must have been something plus nine plus one was equal to 18.

We know that the missing digit was eight because nine plus one plus eight is equal to 18.

Well done for completing Task B, part one.

Let's have a look at part two then.

Here are your missing numbers.

Izzy, which parts did you have to think about a little bit more carefully with these ones? Oh, here.

Izzy noticed that the part that was left was more than the part that was subtracted.

So that means there must have been some regrouping here.

We had to regroup one of the 100s as 10 10s, so you can see that it was eight plus three, which was equal to 11.

11 subtract three is equal to eight.

Well done, Izzy.

In C Izzy noticed that nine plus nine was equal to 18, so we must have regrouped here.

One 10 is 10 ones.

With this one, seven subtract zero was equal to seven, but we know that we regrouped one of those 100s into the 10s column, so that means that the original must have been one more before it was regrouped, which would be eight.

Well done, Izzy and well done to you for completing Task B and finishing this lesson.

Let's have a look at what we've learned today.

You can use equivalent calculations with the same difference or same sum to make calculations easier.

You can use a number line to represent a more efficient method.

You can use inverse, the relationship between addition and subtraction, to solve missing number problems. Well done for all of your hard work today.

I hope that this lesson has highlighted some of the more efficient and easier strategies for you to solve missing number problems and column addition and subtraction.

Thank you for all of your hard work.

I can't wait to see you all again soon to continue our learning.

Goodbye.