Lesson video

Hi there, my name is Mr. Tazzyman, and I'm really looking forward to teaching you the lesson today from the unit that's all about equivalence, compensation, and subtraction.

If you're ready, we can get started.

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

By the end, we want you to be able to say, "I can calculate the difference using knowledge of an adjusted subtrahend, different structure." Here are the keywords that you might hear.

We'll need you to understand them, but we'll also need you to be able to say them as well, so I'm gonna get you to repeat them back to me.

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

Understand? Okay, let's go for it.

My turn, minuend, your turn.

My turn, subtrahend, your turn.

My turn, difference, your turn.

My turn, adjust, your turn.

Here are the definitions for each of those words then.

The minuend is the number being subtracted from.

A subtrahend is a number subtracted from another.

The difference is the result after subtracting one number from another, so the minuend in this equation was seven, the subtrahend is three, and the difference is four.

So that reads as seven, subtract three is equal to four.

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

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

This is the outline then for today's lesson.

We're gonna start by calculating the adjusted subtrahend.

Then we're gonna move on to calculating adjusted subtrahends or differences.

We're gonna have some help along the way from these two.

Hi, Laura, hi, Jun.

They're here to give us some discussion, explanation, hints, prompts, and tips for the maths that we're gonna learn today.

Follow them along, and you'll learn superbly.

All right, let's get started.

Laura has 75 jelly beans.

35 are strawberry flavoured, and 40 are blueberry flavoured.

Jun also has 75 jelly beans.

Some are strawberry flavoured, and some are blueberry flavoured.

He has 10 more strawberry jelly beans than Laura.

How many blueberry jelly beans does Jun have? It's quite a lengthy worded problem that.

We might need to explore this a bit further.

"I'll model this using a part-part-whole model." Good idea, Jun, sometimes it's best to turn something into a visual representation just to clarify your thinking.

There's Laura, and there's Jun.

They've both got 75 as their whole.

Laura, we know, has 35 strawberry-flavored jelly beans and 40 blueberry-flavored ones.

Jun we know has 35 plus 10 strawberry-flavored ones, but we don't yet know how many blueberry ones he has.

The minuends are the same because we both have 75.

"If I adjust the subtrahend by adding 10," you can see he's made that adjustment now, so he knows he's got 45 strawberry jelly beans, "Then I need to adjust the difference by subtracting 10." So he's taken Laura's difference, and he's gonna subtract 10 from it.

It's 30.

Can double-check that by seeing that 45 and 30 added together equal 75.

Laura decides to turn the part-part-whole models into equations and jottings.

Great idea, Laura, it's always good to try to represent something in a couple of ways to show that you've really understood the structure.

"Here was the number of blueberry jelly beans I had," Laura, 75, subtract 35, which is equal to 40.

"You had the same total number but 10 more strawberry," Jun, 75 subtract 45, and she's written in the adjustment there.

It's gone from 35 strawberry jelly beans to 45 strawberry jelly beans, which is what Jun had.

"So that meant you had 10 fewer blueberry," and again, there's that adjustment written in, a subtraction of 10.

40 subtract 10 is equal to 30.

Okay, let's check your understanding so far.

Can you spot a mistake in the jottings below? 100 subtract 46 is equal to 54.

100 subtract 58 is equal to 66, and there are two adjustments written in there as well.

Pause the video and see if you can spot the mistake.

Welcome back, here was the mistake.

The adjustments to the difference should be subtract, and that's because it should be the inverse.

If the minuend stays the same, and the subtrahend is increased, then the difference is adjusted using the inverse operation.

Here's another worded problem.

Laura gets two pounds a day to spend on snacks at the school residential.

She wants to save some money for a souvenir at the end of the week.

On Monday, she spends £1.

50, so she's left with 50 p to save.

On Tuesday, Laura spends 30 p less than she did on Monday.

How much has she saved on Tuesday? "I'll try this with a part-part-whole model this time," says Laura.

There's Monday, and there's Tuesday.

She has two pounds available to spend on each of those days.

On Monday, she spends £1.

50, so she saves 50 pence.

On Tuesday, she spends £1.

50, subtract 30 pence, and we've got to work out how much she's got left to save.

"The minuends are the same because I had two pounds each day.

If I adjust the subtrahend by subtracting 30 pence," and you can see she's made that subtraction now, leaving her with £1.

20 pence, "Then I need to adjust the difference by adding 30 p." So she's taken the difference from Monday, which was 50 p, and added 30 p to that.

That's 80 pence.

Jun decides to turn the part-part-whole models into equations and jottings.

"Here was the savings equation for Monday," Monday, two pounds subtract £1.

50 is equal to 50 pence.

For Tuesday, he says, "You spent 30 pence less on Tuesday," so he's changed the subtrahend to £1.

20, "So that meant you saved 30 p more on Tuesday." It's gone from 50 pence to 80 pence.

Okay, time to check your understanding.

Can you spot a mistake in the jottings below? Five pounds subtract £2.

50 is equal to £2.

50, and then in the next equation, we've got five pounds subtract £1.

50 is equal to £1.

50.

We've got some adjustments that have been jotted on there as well.

Pause the video and see if you can spot the mistake.

Welcome back.

"The adjustment to the difference should be add.

If the minuend stays the same and the subtrahend is decreased, then the difference is adjusted using the inverse operation." We can see that whoever made these jottings used the same operation for both adjustments, but they need to be the inverse.

Okay, it's time for your first practise task.

For number one, we've got a word problem, which I'll read to you now.

Jun and Laura are flipping coins and recording the results as they go.

They each flip the coin 54 times.

Jun gets heads 18 times and tails 36 times.

Laura gets heads nine times more than Jun.

How many times did Laura get tails? Here's another important instruction, though.

Calculate the answer by firstly drawing part-part-whole models and then using jottings," so you've got to represent your working out in two different ways here.

Here's number two, another worded problem.

Jun and Laura are practising taking shots in netball.

They take it in turns and each take 46 shots at the goal ring in total.

Jun scores 12 but misses 34 shots.

Laura scores five more than Jun.

How many did Laura miss?" Again, "Calculate the answer by firstly drawing part-part-whole models and then using jottings." Finally, number three, a worded problem as well, "Jun gets £3.

20 a day to spend on snacks at the school residential.

He wants to save some money for a gift for his family at the end of the week.

On Monday, he spends £2.

55 pence, so he is left with 65 pence to save.

On Tuesday, Jun spends 25 pence less than he did on Monday.

How much has he saved on Tuesday? Again, calculate the answer by firstly drawing part-part-whole models and then using jottings.

Good luck with those.

Pause the video here, and I'll be back to give you some feedback in a little while.

Welcome back.

Let's look at number one to begin with.

Here were the part-part-whole models that you might have drawn.

We had Jun who had 54 and Laura who had 54 as the minuend.

That's because both of them flipped the coin the same number of times.

Jun's was split into two separate parts.

The first was 18, and the second part was 36.

He got heads 18 times and tails 36 times.

Now Laura, we know, got heads nine times more than Jun's.

That's 18 plus nine.

Consequently, because the minuend was the same, the total number of coin flips they had at 54.

Then we also had to do 36 subtract nine.

Here in the jottings then, you can see that Jun flipped it 54 times, and in that, he got 18 times heads, and tails was 36 times.

That was the difference.

If we adjust the number of heads that he got by nine, we can see that Laura must have got heads 27 times.

She flipped the coin 54 times, so 54 subtract 27 is equal to 27.

She got tails 27 times.

She got half tails and half heads exactly.

Number two then, here are the part-part-whole models.

Jun had 12 and 34, and Laura had 12 plus five and 34 subtract five.

If we look at that as jottings, we can see the same thing.

The adjustment made was plus five, and then we had to subtract five to get the difference, which meant that Laura missed 29 times.

For number three, well, here's our part-part-whole models again.

Monday could be split into two parts of £2.

55 and 65 pence, and on Tuesday, it was £2.

55 subtract 25 pence, and then 65 pence plus 25 pence.

If we show on our jottings what that meant in the end, £3.

20 subtract £2.

30 was equal to 90 pence, so Jun saved 90 pence.

Now it's time to move to the second part of the lesson, calculating adjusted subtrahends or differences.

Laura and Jun look at a sequence of subtraction equations and describe the changes.

The minuend is constant and stays the same.

It's 168.

The subtrahend is increasing by one each time.

You can see that here, 71, 72, 73, 74, 75.

I'm reading down through the subtrahends there, so the difference has to decrease by one each time.

Again, I'll readjust the differences here, 97, 96, 95, 94, 93, Laura and Jun look at a new sequence of subtraction equations and describe the changes.

Again, the minuend is constant and stays the same.

This time the subtrahend is decreasing by one each time, 56, 55, 54, 53, 52, so the difference has to increase by one each time, 540, 541, 542, 543, 544.

Okay, let's check your understanding then.

Look at the sequence below and describe the changes by completing the stem sentence.

You can see the sequence of expressions and equations there.

Underneath is the stem sentence.

Can you fill it incorrectly? Pause the video and have a go.

Welcome back.

Here's how it should have read.

The minuend is constant and stays the same, but the subtrahend is decreasing by two each time.

Let's just have a look at that.

These are the subheads.

150, 148, 146, 144, 142.

Yes, they're decreasing by two each time, so the second sentence read, this means that the difference must increase by two each time, and if you have a look and listen carefully, you'll see that that's the case.

300, 302, 304, 306, 308.

Laura and Jun look at a new sequence of subtraction equations that feature missing numbers.

The top equation has been given to them, 234 subtract 71 is equal to 163.

The minuend is constant.

Let's look for any patterns as the sequence goes down.

The subtrahend is increasing by three each time, 71, 74, 77, 80, 83.

Laura realises the difference will decrease by three each time then, so they can start to fill in those numbers.

163, 160, 157, 154, and 151.

What do you notice this time? There isn't a regular pattern to the increases in the subtrahend.

We will have to work out each increase individually and then decrease the difference by the same amount, so there's an increase of one, which means there's a decrease of one.

162.

The subtrahend this time increases by 10, so the difference needs to decrease by 10.

152.

On this one, the subtrahend increases by two, so the difference has to decrease by two, 150.

And on the last one, the subtrahend is increased by five, so the difference has to decrease by five.

145.

What do you notice this time? The missing numbers are a mix here.

They are either the subtrahend or the difference.

We will have to calculate each missing number and then the adjustments, so the first missing number they've calculated is 163.

They notice that 163 subtract 11 is 152, so that means they need to add 11 to the subtrahend, giving them 82.

Now they can see that there's an adjustment of 12 to be made to the subtrahend by adding 12 on, and that means you need to subtract 12 from the difference.

That gives 140.

Now they can compare the difference of 140 and 139.

That's an adjustment of takeaway one, which means we need to add one to the subtrahend to give 95.

And lastly, you can see that there's an adjustment of adding 0.

5 to the subtrahend, so that means 0.

5 needs to be taken away from the difference, giving 138.

5.

Okay, let's do the practise task now.

For number one, you need to use your understanding of the relationship between the subtrahend and the difference to find the missing numbers in these sequences.

For number two, it's the same thing, but this time, there's slightly larger numbers.

For number three, again, same thing, but this time, it's decimal fractions.

Pause the video here, have a go at those and enjoy.

I'll be back shortly with some feedback.

Okay, time to mark number one then.

Here's A, 88 with an adjustment then of 10.

The next number was 37.

Then there was an adjustment of nine, leaving 107.

Then there was an adjustment of 50, leaving 78.

Then there was an adjustment of 22, leaving 100.

For B, we had 542.

There was an adjustment of nine, giving 35, an adjustment of 23, giving 556, an adjustment of 100, giving 112 and an adjustment of 88, giving 368.

Here's number two then.

The first missing number was 72,018, and you could see that because there was an adjustment of subtract 1,000 in the difference, meaning that the subtrahend had to have 1,000 added to it.

The next one was 2018.

That's because the difference had had 70,000 added to it, meaning that the subtrahend needed to subtract 70,000.

On the next one, it was 458,103.

The subtrahend reduced by 80, which meant that the difference had to increase by 80.

And on the last one, we had 200.

That's because there was a decrease in the difference of 1,800.

Here's number three then.

I'll read through these missing numbers.

4.

88, 1.

07, 4.

68, 4.

74, 4.

95.

If you need a bit longer, pause the video now.

That brings us to the end of the lesson.

Here's a summary of our learning.

If the minuend remains constant and the subtrahend is increased or decreased, then the difference will need to be adjusted by the same amount using the inverse operation.

It follows that it is also true that if the minuend remains constant and the difference is increased or decreased, then the subtrahend will need to be adjusted by the same amount using the inverse operation.

This concept can be useful for calculation and reasoning about sequences of equations with missing numbers.

My name's Mr. Tazzyman.

Hope you enjoyed that.

I definitely did, and maybe I'll see you again in the future in more maths lessons.

Bye for now.