Lesson video

Hello, I'm Mr. Tazzyman, 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 of the lesson, we want you to be able to say, "I can explain how increasing or decreasing the minuend affects the difference." These are the keywords that you are going to hear during the lesson, and it's important that you know how to say them and that you understand their meaning.

We'll start with you repeating them back to me.

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

Clear? Okay, let's do it.

My turn, minuend, your turn.

My turn, subtrahend, your turn.

My turn, difference, your turn.

My turn, constant, your turn.

Well done.

Let's see what each of those means.

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.

And the equation at the bottom is labelled with each of those keywords.

We've got 7 subtract 3 is equal to 4.

The minuend is the 7, the subtrahend is the 3, the difference is 4.

A constant is a quantity that has a fixed value that does not change or vary, such as a number.

Here's the outline then for today's lesson, we're gonna start by thinking about adjusting the minuend.

Then we're gonna move on to looking at larger numbers and decimal fractions.

We've got two friends here that are gonna help us along the way.

Hi, Alex! Hi, Jun! They're gonna be discussing some of the prompts.

They'll be giving us some hints and tips.

And they might even reveal some of the answers when we come to do some feedback.

Let's start with this, 6 subtract 3 is equal to 3.

We've got a representation of that on the left using a 10 frame and counters, and then we've got the equation form on the right.

Hm, slightly different.

16 subtract 3 is equal to 13.

Different again, 26 subtract 3 is equal to 23.

What's the same and what's different between each of these representations and their accompanying equations? Well, Jun says, "The subtrahend is the same in each representation." You can see that the number we're subtracting is the same each time.

It's 3.

The minuend of difference increase by 10 each time.

Okay, here are the same equations, but written in a kind of jottings format.

This is the same as before, but represented differently.

The minuend difference increase in the same way.

The subtrahend is still constant.

And remember, that word means that it stays the same.

Alex creates a table with subtraction equations.

What can you generalise? So what can you say about each row of the equation that is true of all the others? If you increase the minuend and the subtrahend stays the same, the difference must increase by the same amount.

Okay, look at this one then.

What's the same and what's different here? We've got three equations, and we've got a similar way of representing it in that jotting style again.

"This time," says Alex, "the minuend and difference decrease equally." The subtrahend is still constant.

Jun creates a table with subtraction equations.

What's different? What can you generalise? So again, look at each row and compare them.

What can you say is true across the whole table and is true of each row? If you decrease the minuend and the subtrahend remains constant, it is constant there, isn't it? It's 3 all the way down.

The difference must decrease by the same amount.

Okay, let's check your understanding so far.

We've got a true or false here regarding this statement.

If I adjust the menu and the subtrahend stays the same, then I have to adjust the difference by the same amount to maintain a balanced equation.

Is that true or false? Pause the video and decide.

Welcome back.

That was true, but why? It's important to have justifications as mathematicians.

So here are two, and you've got to decide which one you think is the best justification.

Is it A, because the minuend and the subtrahend are never equals so the difference needs changing? Or is it B, because the subtrahend is constant, the difference had to be adjusted to keep the equation balanced.

Pause the video, maybe have a discussion about it, and decide which justification you would select.

Welcome back.

B was the correct justification here, because the subtrahend is constant, the difference had to be adjusted to keep the equation balanced.

Here's a worded problem.

Alex has 36 pence and Jun has 52 pence before Jun finds 21 pence down the back of his sofa.

I love it when I find money down the back of the sofa.

How many more pence does Jun have than Alex now? Jun says, "I'll represent this using a bar model." So watch closely.

There it is.

We've got 52 pence, we've got 36 pence, and we've got difference.

That's 16 pence.

Then we've got 21 pence added onto the 52 pence.

That's representing that 21 pence that Jun found down the back of the sofa.

He did have 52 pence, he's also got 21 pence more now.

I've added to the minuend, so I have to add to the difference too.

He's got 73 pence altogether.

And the difference is 16 pence plus 21 pence.

That's 37 pence.

Now, I have 37 p more than Alex.

Lucky you.

We started with the bar model at the top and then we adjusted it to the bar model below.

Can you describe the change? So look at that top bar model, how did it change going down to the bottom? Sometimes when you're thinking about change, it's important to also see what is it that remains constant, what was it that stayed the same.

I added 21 p to the minuend and kept the subtrahend the same.

So I had to add 21 p to the difference.

"I might use different language here," says Alex.

"You added 21 p to one part and kept the other part the same, so you had to add 21 p to the whole as well." So Alex has recognised that in some situations, the terms part and whole can also be appropriate, and they can replace the terms minuend, subtrahend, and difference.

Jun then buys a cupcake for 20 pence.

How many more pence does Jun have now? We've got another adjustment here.

"I'll represent this using a bar model," says Alex.

There's the bar model initially.

We've just had that because we worked out by adding on the number of pence that were found at the back of the sofa.

But now, we know there's been a reduction of 20 pence, which means that there also needs to be a reduction of 20 pence in the difference.

That means we've now got a bar model that looks like this.

53 pence made up of 36 pence and 17 pence.

Now you have 17 p more.

There's the initial bar model and there's the changed, adjusted bar model.

Can you describe the change? So think about the language that we just talked about.

Could you describe that change using the correct terminology? I subtracted 20 p from the minuend and kept the subtrahend the same.

So I had to subtract 20 p from the difference.

"I might use different language again here," says Alex.

"You subtracted 20 p from one part and kept the other part the same, so you had to subtract 20 p from the whole as well." Okay, it's time for the first practise task then.

Fill in the blanks in the tables and explain the pattern.

There's A and there's B.

Number two, use the bar models to complete the sentences describing the change.

So you can see that we've got some bar models here with an arrow between them that's showing that we've adjusted them slightly.

Underneath, there are some sentences with some blank parts for you to fill in, describing that change.

For number three, you're gonna do a similar thing, but this time, instead of filling in the sentences, you'll notice they've already been completed for you.

Your task is going to be to draw out the bar model after those adjustments have been made.

Okay, enjoy those questions.

Good luck.

Pause the video, and I'll be back shortly with some feedback.

Welcome back.

Let's look to begin with at 1A.

The minuend and difference are decreasing by 24 in each row.

So we've got 284 in that first row, 275 as the minuend in the second, 236 is the difference in the third, 227 as the minuend in the fourth, 188 is the difference in the fifth, and 179 as the minuend in the last row.

Okay, let's look at 1B.

Here's B.

The minuend and difference are increasing by 18 each row.

In the top row, 17 was the missing number, which was the subtrahend for all of the rows.

Then we had a difference in the second row of 225.

The minuend was 260 in the third row.

The difference was 261 in the fourth row.

296 was the minuend in the fifth row.

And 294 was the difference in the last row.

Let's look at number two then.

We were being asked to describe the change in bar models using the sentences below.

We had to fill in the blanks.

In the first one, it should have read, "They subtracted 15 p from the minuend and kept the subtrahend the same, so they had to subtract 15 p from the difference." And for B, it should have read as follows.

"They added 19 p to the minuend and kept the subhead the same, so they had to add 19 p to the difference." Here's number three then.

This time, we were drawing out the bar models.

Don't worry too much about whether the bars themselves have been drawn completely accurately.

They don't need to be totally proportional.

Here's the first one.

We had the subtrahend of 39 pence, a minuend of 44 pence, and a difference of 5 pence.

Both the minuend and the difference had been adjusted by subtracting 19 pence and the subtrahend remained constant.

Let's look at B.

We had a subtrahend of 30 pence because it remained constant.

We had a new minuend of 64 pence, and a new difference of 34 pence because they've both been adjusted, the minuend and difference that is, by adding 25 pence.

Okay, I hope you got 'em really well there, let's move on to the second part of the lesson now.

We are looking at larger numbers and decimal fractions.

Have a look at these.

What's the same and what's different between these three equations and the adjustments? Jun says, "This time, the minuend and difference increase equally, though the numbers are much larger than before." If we turn the arrows around and use the inverse, we can show them decreasing equally as well.

Great thinking, Alex.

We are showing both increases and decreases here.

Alex creates a table with subtraction equations.

What is the change in each row? Have a look.

What do you think? Compare the rows.

What changes are being made here? If you adjust the minuend and the subhead stays the same, the difference must adjust by the same amount.

The adjustments here were 1,000 each time.

You can see that as you go down the table, the minuend, and therefore the difference as well, increase by 1,000, but the arrow there shows us that we don't just have to look down.

We can also go up and see that there's a decrease of 1,000 each time.

The important thing here is that the subtrahend remain constant, so the minuend and difference had to adjust by the same amount.

* Okay, your turn to check your understanding, Alex creates a table with subtraction equations.

What is happening? Can you explain it? Pause the video and have a go.

Welcome back.

Here's Alex explaining what's going on.

"The minuend is adjusting by 3,000 and the subtrahend is constant, so the difference is also adjusting by 3,000." Remember that you can look at the table in both directions going up or down, and that changes whether you are using addition, or increasing it, or subtraction, decreasing it.

Okay, look at these ones.

We've got decimal fractions this time.

What's the same? What's different? Have a good look.

Compare each of those.

This time the minuend and difference increase equally, and these numbers have decimal fractions.

Let's turn the arrow around and use the inverse, same trick as you completed last time, to show them decreasing equally as well.

Jun creates a table with subtraction equations.

What is the change in each row? Hm.

If you adjust the minuend on the subtrahend stays the same, the difference must adjust by the same amount.

So if we have a look at the minuend going down the table, we can see that the decimal fraction part remains constant.

It's the inter integer part that's changing.

We're going from 13 to 18 to 23.

Hm, oh, that's a difference of five each time.

So I know as we go down the table, the minuend is increasing by five.

The subtrahend remains constant, so the difference is also increasing by five.

Similarly, if we go up the table, we can see decreases of five each time to the minuend and difference, with the subtrahend remaining constant.

Okay, your turn then.

Jun, create a table with subtraction equations, what is happening? Pause the video here and have a go at explaining that.

Welcome back.

Here's what Jun says.

"The minuend is adjusting by 0.

5 and the subtrahend is constant, so the difference is also adjusting by 0.

5." Did you manage to see that? I hope so.

Here's a worded problem.

Jun and Alex play an arcade game against one another.

Jun scores 63,500 points and Alex scores 43,200 points.

At the end of the game, Jun gets a bonus of 15,000 points for using a special move.

How much did Jun win by? "I'll use a bar model again," says Jun.

Here it is.

We've got 63,500, which is Jun's score, as the minuend, we've got 43,200, which is Alex's score, as a subtrahend, and then we've got the difference.

It's 20,300.

Now, Jun also gets a bonus of 15,000, so he inputs that next to the minuend.

The subtrahend stays the same, so, of course, we also need to put 15,000 next to the difference.

He's calculated his score of 78,500.

The difference is going to be 20,300 plus 15,000.

That's 35,300.

He's won by 35,300 points.

Here's another worded problem.

At the gift shop on a residential week, Alex has 12.

50 pounds and Jun has 7.

35 pounds left to spend.

Alex spends 2.

3 pounds on penny sweets and chocolate.

Oh, that's gonna be a lot.

How much more does Alex have now? "I'll use a bar model again," says Alex.

And there it is.

12.

50 pounds, his spending as the minuend, 7.

35 pounds is what Jun has left to spend, and the difference labelled.

Then he decides he's going to remove 2.

3 pounds from the minuend because that's what he spends on chocolate and penny sweets.

He needs to remove that from the difference as well.

So he ends up with a bar model that looks like this, and a difference of 3.

12 pounds.

"I have 3.

12 pounds more," he says.

Okay, it is time for your second practise task.

Use the bar models to complete the sentences describing the change.

This is very similar to what you did in your first practise task.

Number two, Jun and Alex play an arcade game against one another again.

Jun scores 24,710 points and Alex scores 18,206 points.

At the end of the game, Jun gets a penalty points reduction of 2,500 points for bashing the buttons too hard.

How much did Jun win by? Number three, at the gift shop on a residential week, Alex has 10.

47 pounds and Jun has 7.

35 pounds left to spend.

Alex wins at 5 pound shop gift voucher in a dress-up-as-an-animal competition.

How much more does Alex have now? There he is, dressed as a panda look.

For number four, use your understanding of what happens to the difference when adjusting the minuend and the subtrahend stays constant to find the missing numbers in these sets of equations.

It's really useful to look at the equation above to help you with the equation you are working on here.

Just a little tip.

Okay, pause the video, enjoy the questions, and I'll be back shortly for some feedback.

Good luck.

Welcome back.

We'll start with number one.

The description for 1A was they subtracted 100,000 from the minuend and kept the subtrahend the same, so they have subtracted 100,000 from the difference.

And for B, they added 0.

5 to the minuend and kept the subtrahend the same, so they have added 0.

5 to the difference.

Here's number two then, we had our worded problem about the arcade game.

We might have started with a bar model that looked like this, 24,710, 18,206 as the subtrahend, and then the difference.

Then we needed to make sure that we were getting the penalty points put in, so we were subtracting 2,500.

We ended up with 22,210 as the minuend, so the difference was 4,004.

Jun one by 4,004 points.

Here's number three.

We started with a bar model that looked like this, 10.

47 pounds as the minuend, 7.

35 pounds as the subtrahend.

We knew that the difference was then 3.

12 pounds, but we also needed to add on the 5 pounds to the minuend, giving us 15.

47 pounds.

And that meant that the difference needed to be 3.

12 pounds plus 5 pounds, which is 8.

12 pounds.

Alex has 8.

12 pounds more.

Here's number four then.

The missing numbers were as follows, 43,287, 66,922, 33,635, 32,735.

For B, we had 178.

21, 104.

47, 104.

77, 99.

71.

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

We've reached the end of the lesson then.

Here's a summary of all of our learning.

If the minuend is adjusted and the subhead stays constant, then the difference has to be adjusted by the same amount to keep an equation balanced.

This can be useful to find missing numbers and solve worded problems that feature adjustments to the minuend.

My name is Mr. Tazzyman.

I hope you've enjoyed today's lesson, I know I have.

And I hope that I'll be able to see you again soon in another maths lesson.

Bye for now.