Lesson video

Hello, how are you? My name is Dr.

Shorrock, and I am really excited to be learning with you today.

This lesson is from our unit, rounding and solving problems with numbers with up to seven digits.

The lesson is called, "Solve Problems," explaining which strategy is most efficient.

As we progress through the learning today, we're going to learn strategies to help us decide when or if we should use a mental or a written method.

And then we're going to look at how we can apply this to finding missing information.

Now, sometimes new learning can be a little bit tricky, but it's okay, because I am here to guide you and I know if we work really hard together, then we can be successful.

Let's get started then, shall we? How do we solve problems, explaining which strategy is most efficient? The keywords for our learning today are subtrahend and efficient.

It's always good practise to say new words aloud.

So let's have a go at this together.

My turn, subtrahend, your turn.

Nice.

My turn, efficient, you turn.

Well done.

The subtrahend, well that's the number that's to be subtracted.

It's the second number in a subtraction, also known as a part.

And being efficient means finding a way to solve a problem quickly, but by also being accurate.

Let's get started with our learning today then shall we? We're going to start by looking at a mental strategy or written method.

How do we decide? And in our learning today we have Aisha and Lucas to help us.

Lucas is trying to decide if he should solve these calculations using a mental strategy or a written method.

Which method do you think he should use for each of these? What would you do? The calculations we have got are, 1,459,199 subtract 110,000, 50,000 subtract 1,998, 500,000 subtract 178,362, 213 add 1,200,000 add 11,000, and 498,107 add 1,229,075.

What would you do for each of those? Let's start by looking at the numbers in each expression.

We'll start with this calculation.

What do you notice about these numbers? Lucas notices that the subtrahend, so that is the part we are subtracting, is a multiple of 10,000.

Hmm, does that help us decide which strategy to use? That's right, we could just use partitioning to calculate with this example.

We've got our whole 1,459,199.

We could partition the part into 100,000 and 10,000 and that makes it easier for us to calculate mentally.

If we subtract the 100,000, we're left with 1,359,199, then we can subtract the 10,000, 1,349,199.

So this time it was more efficient to calculate you using a mental strategy.

When we say mental strategy, you are okay to do some jottings as well.

We don't expect everything to be held in your head.

I know I couldn't hold it in my head.

I have to do jottings.

Let's look at the next calculation.

Look at the numbers.

What do you notice? That's right, Lucas has noticed that the subtrahend is close to a multiple of power of 10.

And the minuend itself is a multiple of a power of 10.

So how does that help us? Well, we can use a number line as our jottings and we can count on.

We can set up our number line and we know that 1,998 is only two away from the next multiple of 1,000.

And then we can add 48,000 to take us to 50,000.

So it's much more efficient here to use a mental strategy with jottings.

And the difference here would be 48,002.

Let's look at the next calculation.

What do you notice? Look at the numbers.

Lucas has noticed that the minuend is a multiple of a power of 10.

So that's the whole, that's a multiple of a power of 10.

What do you notice about the subtrahend or the part? It's quite a precise number, isn't it? And it's not really close to anything, so we wouldn't really know what to add or subtract if we use in number line.

So what else can we do? That's right, we can use the constant difference to avoid lots of regrouping.

We are still going to have to look at using a formal column subtraction algorithm, but we can make it simpler for ourselves by adjusting the minuend and the subtrahend by the same amount.

And then if we did 499,999 - 178,361, well, we'd still need to use a column method, but this calculation is more efficient.

There will be less regrouping.

Let's have a look at this next calculation.

Look at the numbers.

What do you notice? That's right, the numbers can just be recombined.

We can add them together and we can just use our knowledge of place value positions to help us.

So we can combine the 11,000 to get 1,211,000 and then combine the 213, 1,211,213.

This is more efficient to calculate using a mental strategy and you might like to do some jottings.

Let's look at this next calculation.

Look at the numbers.

What do you notice? The numbers really are quite precise values, aren't they? So this time it's more efficient to use a formal written method.

Let's check your understanding with this.

True or false.

Is 20,000 subtract 998 best calculated using a formal written method? Pause the video while you decide and when you are ready to hear the answer, press play.

How did you get on? Did you decide that was false? But why is it false? Is it A, it's more efficient to calculate mentally using jottings by partitioning 998 then subtracting each part? Or is it B, it's more efficient to calculate mentally using a number line as jottings.

998 is close to 1,000 so it's easy to know what to add first.

Pause the video, maybe find someone to talk to about those two different options and when you're ready to hear the answer, press play.

How did you get on? Did you say B? This time it would be more efficient to use a number line, because 998 is close to the nearest power of 10.

It's your turn to practise now.

For question one, could you sort these calculations into the table to show the most efficient strategy, giving reasons for your choice? So for example, 308,724 subtract 10,000.

If you think you could do that more efficiently with a mental strategy, write it in that column.

If you think actually you need to use a formal written method, then write it in that column.

For question two, could you read these problems and decide if you would choose a mental strategy with jottings or a formal written column algorithm to be efficient? Part A, a new RnB artist released a song.

On its first day it was streamed 147,607 times.

The next day it was streamed a further 78,683 times.

How many times was the song streamed over the two days? Part B, a charity has £187,412 in funding and uses £18,100 to buy food packages.

How much money does it have left? And part C, a football stadium expects an average of 21,000 fans.

The figure is 1,387 fewer than this.

How many fans attended? Pause the video while you have a go at both of those questions and when you are ready for the answers, press play.

How did you get on? Let's have a look.

Remember, your choices may have been different.

This is my opinion on whether I think a mental or a formal written method is most efficient.

308,724 subtract 10,000.

Well, I can use unitizing to help me there.

I've got 30, 10,000s I'm gonna subtract 10,000, so I'd be left with 29, 10,000s.

103,436 add 45,618.

Gosh, they're quite precise values, aren't they? So I'm going to use a formal written method there.

9 million subtract 437,208.

I'm going to use a formal written method there, but I might use the constant difference to adjust the minuend and the subtrahend to make the column subtraction simpler for me.

43,701 subtract 34,067.

While it would be at best to adjust this calculation using constant difference before we use a formal written method.

20,000 subtract 9,999.

While I could use a mental strategy with jotting there, I could use a number I couldn't I because 9,999 is close to the nearest multiple of 10,000.

I just need to add one.

1,070,640 subtract 65,231.

That would definitely.

I would use that as a formal written method and I would do a column subtraction for that.

Then 78,921 subtract 3,000.

I'm only subtracting 3,000 from 8,000 so that can be mental.

And the last one, I am recombining the part so I could do that with a mental strategy with jottings.

You might have given reasons like you were looking at the numbers and that helped you decide which strategy to use.

The calculations that can be solved using a mental strategy, have numbers that are rounded or have numbers that are multiples of powers of 10 and that makes calculations easier.

You might have said that calculations with precise numbers are best solved using a written method.

For question two, you had some strategies to decide for these word problems. For part A, you might have said that the numbers are precise and a written method would be most efficient.

For part B, you might have said a partitioning strategy is most efficient here and you could partition the subtrahend into 10,000, then 8,000, then 100.

For part C, you might have said that you would use a column subtraction algorithm, but that you would use the constant difference concept rewriting the expression as 20,999 subtract 1,386.

You would then have used the written method but there would've be less regrouping.

How did you get on with those questions? Well done.

Fantastic learning so far.

I'm really proud of how hard you are trying.

We're going to move on now and have a look at solving addition and subtraction problems. Sometimes equations have missing information.

Can you see here we've got 786,546, subtract something is 702,300.

In this case, the subtrahend is missing isn't it, that part is missing.

So what strategy can we use here? Well, two numbers have a difference of 702,300 and one of the numbers is unknown and we can rearrange the equation to find a missing subtrahend.

We subtract the difference from the minuend or we subtract the known part from the whole.

786,546 subtract 702,300.

Partitioning is more efficient to use here.

We don't need to use a written method.

We can subtract 700,000 first, then we can subtract 2,300.

If we subtract the 700,000, we're left with 86,546 and then subtract the remaining 2,300, which leaves us with 84,246.

Let's check your understanding with this.

Could you explain how you would find the missing number in this calculation? Include the strategy you would use.

You've got 407,612 is equal to something, subtract 102,300.

My clue for you is think about what have you got? Have you got the whole, have you got parts? Have you got a minuend, the subtrahend, the difference? And that might help you decide what to do.

Pause the video while you have a go and when you are ready to go through the answer, press play.

How did you get on with that? So you might have started by noticing that you were trying to find the whole and you had two parts.

If we've tried to find the whole, then we need to add the parts together.

You might then have used place value knowledge or partitioning to add, and we could partition 102,300 into its constituent parts 100,000, 2,000 and 300 and then the missing whole is 509,912.

Sometimes equations have more than one step.

Look at this equation.

What do you notice? Did you notice that in this case there is an addition step and a subtraction step? So what strategy can we use here to solve this? Well, that's right.

We could either subtract the 31,212 from the 786,546 first, or we could add the 3,000 first.

It doesn't really matter.

Let's rewrite the expression in the order that we want to do it.

So I have decided to subtract the 31,212 from the 786,546 first.

Then I'll add the 3000.

There's no regrouping here, so I could complete this mentally or maybe I would choose to use a column method to be more efficient.

If I subtract the 31,212, my difference is 755,334, then I need to add the 3,000 and using my place value knowledge here would be more efficient.

I can just add three to the 1,000s column.

758,334.

It's your turn to practise.

Now for question one, could you find the missing numbers in each equation and use an efficient strategy to calculate each time.

For question two, could you calculate the multi-step equations? Think about the strategy which will be most efficient.

And for question three, two numbers have a total of 3,456,789 and a difference of 987,655.

What are the two numbers? Pause a video while you have a go at these problems. And when you are ready for the answers, press play.

How did you get on? Let's have a look.

So for question one, did you think about the strategy you needed to use? Some of these could be calculated using a mental strategy.

Part A 3,207,412.

Well that's equal to 2,101,300 add 1,106,112.

Part B, we needed to find the missing part so we can subtract the known part from the whole.

3,207,412 subtract 1,334,010.

For part C, again, we were trying to find the missing part.

1,107,308 is equal to 3,207,412 subtract 2,100,104.

And for Part D, we needed to find the missing part so we know we can subtract the known part from the whole.

3,207,412 is equal to 1,207,415, add 1,999,997.

For question two, remember your strategy might have been different or you may have just adjusted the addend.

For part A, I chose to reorder the equation and subtract 100,000 first, which gave me 217,409.

Then I chose to add 399,999 by adjusting that part by one, subtracting one off the sum, which gave me 617,408.

For part B, you might have partitioned to subtract or use the column method.

I chose to add 12,100 first by partitioning, which gave me 419,709.

And then I subtracted by using a column method which gave me 337,209.

For part C, again, your strategy may have been different to the one I've used.

You might have found a column method more efficient for this subtraction.

I chose to add the parts I was subtracting together first, 1,333,375 and then subtract that from the whole, which gave me 4,051,651.

For question three, a problem to solve, you had to figure out what the two numbers were that had a total of 3,456,789.

Did you notice something about that number? Look at the digits, they go 3456789.

And these numbers had to have a difference of 987,655.

That's nearly the same, isn't it? Look, 98765.

Let's represent this in a bar model to begin with.

We know we've got two numbers.

I'm gonna call them A and B, and they have a sum of 3,456,789.

So I can represent that in a bar model.

But then we know that the difference between them is 987,655.

So that must be the part.

First, we can make the unknown parts the same by subtracting the difference.

So 3,456,789 subtract 987,655.

A formal written method would be more efficient there, wouldn't it? The numbers are so precise.

When I did my column subtraction, I found that the part I was looking for, the two parts were equivalent to 2,469,134.

So one of the numbers must be half of that number and that's 1,234,567.

Again, you notice the digits in that number? So to find the second number, we need to subtract 1,234,567 from the total.

And we could do that in a formal column method because the numbers are really precise.

Nine ones, subtract seven ones is two ones, eight 10s subtract six 10s is two 10s.

Seven 100, subtract five 100s is two 100s.

Six 1,000s subtract four 1,000s is two 1,000s.

Five 10,000s subtract three 10,000 is two 10,000.

four 100,000s subtract two 100,000s is two 100,000s.

Oh, do you spot something here? That's right.

And then three millions subtract 1 million is 2 million.

So the second number is 2,222,222.

Look at all those numbers.

I think that's quite fantastic, isn't it? We've got 3456789 as the whole We've got 1234567 as one of the part and then 2,222,222 as the other part.

I hope you enjoyed that as much as I did.

Fantastic learning today, you have really made good progress with how you can solve problems and explaining which strategy is most efficient.

We know different strategies for addition and subtraction, including mental and written mission strategies.

We know, but looking at the numbers helps us see which strategy is most efficient and we know missing number problems can be a rearranged to identify an efficient strategy to solve the problem.

Well done on how hard you have tried today.

I'm really proud of you and I hope you are proud of yourselves.

I have had great fun and I look forward to learning with you again soon.