Lesson video

Hello, I'm Mr. Taziman, and today I'm going to teach you this lesson from the unit that's all about equivalent compensation and subtraction.

So sit back, be ready to listen and engage.

Let's do this.

Here's the outcome for today's lesson then.

By the end, we want you to be able to say, I can explain how adjusting the minuend can make mental calculation easier.

These are the key words that you might hear during the lesson.

I'm gonna say them and I want you to repeat them back to me.

So I'll say my turn, say the word and then I'll say your turn and you can say it back.

Ready, my turn, minuend, your turn.

My turn, subtrahend.

Your turn, my turn, adjust, your turn, my turn, inverse, your turn.

Let's look at the meanings of these words then to make sure that we have clear understanding.

The minuend is the number being subtracted from, a subtrahend is a number subtracted from another, and there's an example at the bottom that you can see where we've written out a subtraction equation.

Seven subtract three is equal to four.

In this equation, seven is the minuend and three is the subtrahend.

When you adjust, you make a change to a number.

This is done to make a calculation easier to solve mentally.

The inverse is the opposite or reverse operation, for example, subtraction is the inverse operation of addition.

Here's the outline then for today, we're gonna start by adjusting the minuend for efficiency and then we're gonna look at adjusting the minuend in context.

We've got two friends here to meet, Andeep and Aisha, hiya you two.

They're gonna help us today by responding to maths prompts, giving us some of their thinking and revealing some hints and tips to help us along the way.

All right, you sitting comfortably and are you ready to learn? Let's do this.

Aisha and Andeep are comparing two subtraction expressions to see which they think is quicker to solve.

68, subtract 28 or 64, subtract 28.

What do you think? Which of those do you think is easiest to solve mentally? Aisha says 68, subtract 28 is quicker to solve I think, the ones are the same, so we only need to calculate a new tens digit.

Andeep says, I agree, we would have to regroup for 64 subtract 28 because eight is greater than four.

Aisha and Andeep consider mental calculation strategies to solve 183 take away 47.

How would you solve it? I'd use constant to transform the subtraction, says Aisha.

She writes down 183, subtract 47.

She looks at adding three to the subtrahend, so then she adds three as well to the minuend.

Now I only have to calculate the tens column she says, it's 136, Andeep says I'd adjust the minuend so it matched the ones in the subtrahend, so he takes 183, subtract 47, he adds four to the minuend so that the ones digit is now a seven.

Then I can calculate the tens column and adjust using the inverse, so he knows that it will be 140 and he can adjust that by subtracting four to give him the original difference, which was 136.

Which of those two methods do you prefer? Aisha said, I've never tried adjusting the minuend, but I'm intrigued.

It's always good to try new mental strategies.

I agree, it makes us more fluid mathematicians because we have more choice.

Aisha and Andeep adjust the minuend to solve 185 subtract 46.

They write out the expression first.

They add one to the minuend so that it's 186 now and look, the ones now matches the subtrahend ones.

That's equal to 140 and then they subtract one to give them 139.

They're adjusting the difference.

Okay, it's your turn.

Try and use that same method, adjust the minuend to solve 173 subtract 48, pause the video here and give it a go.

Welcome back, well, to start with, you might have adjusted the minuend by adding five so that it was 178.

The ones column now matches the subtrahend ones column.

That makes it easier to work out the difference, which was 130, but that now needs adjusting by using the inverse and subtracting five, which equals 125.

Did you get it? I hope so.

Aisha and Andeep adjust the minuend to solve 256 subtract 43, they subtract three from the minuend.

That gives them a difference of 210.

Then they use the inverse to add three, so they get 213.

Aisha and Andeep compare some subtraction calculations.

What's the same and what's different? Have a look at those subtraction calculations on the left hand side there and compare them with the ones on the right.

What do you notice? In the first one, we adjusted the minuend by subtracting says Aisha.

In the second one, we adjusted the minuend by adding, adjusting can be adding or subtracting says Andeep.

Then you use the inverse to adjust the difference.

Okay, it's time for you to have another go.

Adjust the minuend to solve 166 subtract 42, pause the video and give it a go.

Welcome back, you probably started by subtracting four from the minuend so that the ones in the minuend match the ones in the subtrahend.

162 subtract 42, that's nice and easy to calculate mentally, it gives 120, but now we need to adjust that to get the original difference.

We add four and we get 124.

Did you get it? Hope so, Aisha and Andeep look at another subtraction.

22 subtract 0.

83.

This one has a decimal fraction, says Aisha.

We can still use adjustment and decimal compliments to one.

They subtract 21 from the minuend, giving them one, they know using their decimal compliments that one subtract 0.

83 is equal to 0.

17.

Now they need to adjust that by using the inverse and adding 21.

That gives them 21.

17.

Here's another one, 345,000, subtract 36,000.

These numbers are larger.

Should we use a written method? We can still use adjustment.

We just need to adjust the 1000s instead of the ones, 345 thousands subtract 36 thousands, so they adjust it by adding 1000.

Now the thousands columns match.

They both got six as the digit, that equals 310,000.

Now they need to adjust that difference by subtracting 1000, which is the inverse of the adjustment they made to the minuend.

There it is, that gives them 309,000.

Here's another one, 345,512 subtract 36,826.

This one isn't good for adjustment because they're large numbers and a range of digits.

I agree, I'd use a written method for this one.

The answer was 308,686.

All right, it's time for your first practise task then.

For number one, you need to fill in the missing parts for each of the jottings showing the of the minuend in the calculations, so you can see you've got A, B, C, and D, and there are some blank boxes there for you to fill in.

Some of them involve finding the difference, but some of them show your understanding of what adjustments are taking place and how they are changing some of the numbers.

For number two, you need to solve each of these calculations mentally by adjusting the minuend and please do have a look at some of the links between the equations because the equation you would have just completed might help you with the next one.

Okay, pause the video here and give those a good go.

Enjoy.

Welcome back, let's start by marking number one.

For A, we had 299.

The adjustment there that was missing was subtract one and the minuend in the bottom equation was 347.

For B, the original difference was 725.

The adjustments were subtract five and add five, and we had 784 as the adjusted minuend, for C, the difference was 44.

66.

The adjustments were firstly subtract 44 and then add 44, and the difference on the adjusted equation was 0.

66.

D, we had some larger numbers here, so we were subtracting 38,000 to give a difference of 636,000, and we found that by initially adding 4,000 and then subtracting 4,000 and on that bottom equation, the minuend was 678,000 and the difference was 640,000.

Let's do number two, then.

We had some missing numbers here.

508, 513, 1,508, 1513, 50.

44 and 2050.

44.

for B, 132, 132,000, 932, 932,000, 7.

54 and 75,400.

You might have noticed that these were in pairs.

The digits were similar, but the place value was very different.

Okay, pause the video here should you need some extra time to mark those accurately.

It's time for the second part of the lesson then, adjusting the minuend in context.

Aisha Andeep are studying the Victorian era.

They're looking at the population data of two cities to the nearest thousand from 1881 and the increase since 1861.

Their teacher asks them to calculate which city had the greatest population in 1861.

You can see the table there.

The headings are city, 1861 population, 1881 population, increase from 1861.

We had the city of Newcastle.

We don't know it's 1861 population yet, 1881 population was 145,000 and the increase was 36,000 from 1861.

We also had Bradford.

Again, we didn't know the 1861 population.

That's what their teacher was asking them to calculate.

The 1881 population was 183,000 and the increase of 1861 was 77,000.

Lots of information there to work through.

Let's see how they get on with it.

I'll start by writing it as an expression says Aisha, 145,000 plus 36,000.

Hang on, that's not correct.

What's the mistake? Aisha's been asked to work out the 1861 population.

She's looking at Newcastle.

You can tell from the numbers, what mistake has she made in the way that she's written this expression? We need to use the inverse instead says Andeep.

Oh, I see, we are going back in time.

She switches the symbol from add to subtract because that is the inverse.

Let's adjust it so the thousands match, so they adjust it by adding 1000 to give a new expression of 146,000, subtract 36,000.

That equals 110,000.

Now they need to adjust that by using the inverse, just as Andeep says.

So they subtract 1000, giving them 109,000.

That was the population of Newcastle to the nearest thousand in 1861.

Okay, first part done.

Now it's time to do Bradford, 183,000, subtract 77,000.

Now calculate Bradford by adjusting the minuend.

Again, let's adjust it so the thousands match.

They add 4,000 this time, giving a new calculation of 187,000 subtract 77,000, nice and easy to do mentally.

That gives you 110,000.

Then there's an adjustment using the inverse.

They subtract 4,000.

That gives them 106,000, so Bradford's population to the nearest thousand in 1861 was 106,000.

Newcastle was more populated in 1861.

Okay, your turn then adjust the minuend to calculate the population of Plymouth in 1861, pause the video and give it a go.

Welcome back, let's see how you got on.

Here's the initial expression that you might have written.

139,000, subtract 26,000.

Make sure there that you did write subtract and you didn't write add.

Then you might have adjusted the minuend by subtracting 3000 so that the thousands column matched that in the subtrahend, the digit six.

That gave you 110,000, so now you needed to adjust that by using the inverse and adding 3000, 113,000, that was the population of Plymouth in 1861 to the nearest thousand.

Aisha and Andeep each help on a stall at the summer fair.

Aisha runs the beat the goalie stall, and Andeep helps out with the lucky dip.

The chart below shows how much money the stalls have at the end of the day, which stall has the most money? This is a pictogram.

You might not have seen one of these for a while, but you can see that the circle represents 10 pounds.

I can see that because there's a little key there that says circle is equal to 10 pounds.

Okay, so now you need to try to think about how much money each of them made.

I had the least, but I might have made more, says Andeep.

Each of them started with a float, which is a small amount of money in coins that can be used to give change to the first few people who pay.

Can you see the table there? It says stall, beat the goalie and Lucky Dip, and then it says float, beat the goalie had a 34 pound float.

And lucky dip had an 18 pound float, so the float has to be subtracted at the end.

I think I did make more money, says Andeep.

What do you think? It's clear you can see from the pictogram that beat the goalie had more money at the end than lucky dip, but there's the float to think about which needs to be subtracted.

Andeep calculates which stall made the most.

I'll start by labelling the pictogram.

He says, can you calculate how much each stall had from the pictogram? So look closely at the pictogram now, you can see that there are 10 tens in each row.

Well, there are 10 tens in a full row I should say, and in the second row you can see that beat the goalie has got six complete circles and one half circle.

If each of those is worth 10 pounds, I wonder how much beat the goalie will have made.

It's 165 pounds, 16 full tens, and then a half 10.

Now, lucky dip was very similar, but what you can see is that it had two full circles less, so it was 145 pounds.

Did you manage to get that.

Now I'll use adjustment of the minuend says Andeep.

I'll start with beat the goalie, 165 pounds, subtract 34 pounds, so that's the amount of money they had at the end of the day, subtracting the float that they started with Andeep adjust the minuend by subtracting one so that the ones column, the pounds match, that gives 130 pounds.

He adjusts that difference by adding a pound, which is the inverse, so he knows that Beat the Goalie in total made 131 pounds.

He writes that down.

Now I'll calculate Lucky Dip.

He says 145 pounds subtract 18 pounds.

I wonder what adjustment he'll need to make.

Well, he adds three pounds to the minuend so that the one's column matches.

That gives him a difference of 130 pounds, but he needs to adjust that by using the inverse and subtracting three, 127 pounds.

The lucky dip stall made 127 pounds.

Looks like Aisha still made more money, he says, at least it all goes to school funds.

Okay, it's your turn to complete your second practise task For number one, the table below shows the population of some towns and cities in 1921 and 1900.

Complete the table below by calculating the 1900 populations by adjusting the minuend.

For number two, Oak Pupils helped out with many other stores at the summer fair, including the Tombola and Splat The Rat.

Below is a pictogram showing how much money these stores had at the end of the day and a table showing the float they started with, which stall made the most money? Remember, that's not which stall had the most money at the end of the day, it's which stall made the most.

You need to ensure that you subtract the float.

Okay, pause the video here and have a go at those questions.

Enjoy.

Welcome back, let's start by marking the first one.

We'll look at Leeds to begin with.

You might have written this expression to start off with, 458,000, subtract 29,000.

You might have adjusted that by adding 1000 so that the thousands columns match.

That gave a difference of 430,000, which needs adjusting by subtracting 1000 because that's the inverse, that gives you 429,000.

Okay, let's look at the answers in the other boxes then.

Bristol was 329,000.

Lester was 212,000.

Birkenhead was 111,000, Southampton was 105,000.

Pause the video here if you need extra time to mark those.

Number two now, which stall made the most money? You might have started by reading the pictogram carefully to get the values of how much money was on the table at the end of the day, Tombola had 145 pounds and Splat the Rat had 175 pounds, but remember, that wasn't the money that they made.

That was the money they had.

We needed to take into account the float, so for the Tombola, you might have done 145 pounds minus 13 pounds.

You could adjust 145 to 143 by subtracting two.

That gave a difference of 130, and then you might have added two to that.

That gave you 132 pounds, Splat the rat, however, started with 175 pounds, subtracted 37 pounds for the float.

You might have added two so that the ones column matched.

That gave you a difference of 140 pounds and then you needed to adjust by subtracting two, because that was the inverse.

That's 138 pounds.

Splat the Rat made more money in total.

Okay, that brings us to the end of the lesson.

Here's a summary of the things that you've learned today.

When looking at subtraction calculations, it is easy to go straight to using a written method.

However, there are more efficient methods available with closer inspection of the minuend and subtrahend.

By adjusting the minuend to match a part of the subtrahend, you can transform a calculation into something easier to solve and so quicker and more efficient.

This can be used in a range of different contexts.

My name is Mr. Taziman.

I hope you enjoyed that today and I hope that I'll see you again soon in another maths lesson.

Bye for now.