Lesson video

Hello, my name is Mr. Tazzyman and I'm really excited to be working with you on this lesson today.

If you are ready, let's get started.

The outcome will be for you to be able to say, I can subtract a pair of three digit numbers by finding the difference.

We've got some keywords that we need to know about in order to understand this lesson really well.

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

I'll say my turn, say the word, and then I'll say your turn and you repeat it, ready? My turn, minuend, your turn.

My turn, subtrahend, your turn.

My turn, difference, your turn.

Now we know how to say them, let's see if we can understand them.

Here are the explanations for each of the terms. 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.

You can see there's an equation at the bottom, seven subtract three is equal to four.

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

In today's lesson, subtracting three digit multiples of 10 by finding the difference between them, we are going to have two parts.

The first part is going to be doing all of this without any bridging, and the second part is going to be looking at what we will do if we do have some bridging.

Let's get going with the first part.

Here are two maths friends that you are going to meet, Lucas and Laura, they're going to help us by discussing some of the questions and prompts in these slides.

If you you're not sure, make sure you listen out for them really well, because they're gonna help.

We can see here an adult penguin and a penguin chick.

What is the difference in height between this adult penguin and the penguin chick? Laura says, "What does the question mean? The adult penguin is taller than the penguin chick.

How can I think about the difference?" Lucas replies, he says, "If I represent the heights with bars, the difference is the gap between them." He puts two bars next to the adult penguin and baby penguin.

Then he moves them over and he draws an arrow to represent the difference between the two heights.

This is a really good representation of the question above, what is the difference in height between this adult penguin and the penguin chick? We've got a new context now.

Lucas and Laura have been growing sunflowers.

Lucas decides to compare his to Laura's to see which sunflower is the tallest.

I think they're pretty close, but one is just slightly taller.

Laura says, "So what do we need to do then? Lucas replies, "We need to find the difference.

Look at them as a bar model." Two bars have been drawn on again to help us to think about the difference.

Lucas says, "The difference is the gap between them, but it's not very long." You are right Lucas, both those sunflowers are really close together in terms of height.

Laura says, "Shall we measure the height of each of them?" Lucas replies, "Okay, then see if we can find the difference using the heights." So they put out a ruler.

You can see it there just to the left hand side of the tallest sunflower.

Laura measures across and she says, "My sunflower is 98 centimetres tall." Lucas says, "My sunflower is only 91 centimetres tall, which means that yours is taller." "By how much I wonder?" Laura wants to know how much she's won by.

Lucas says, "Well, yours is the minuend and mine is the subtrahend." Laura says, "So our expression is 98 centimetres subtract 91 centimetres." "I know 91 plus seven equals 98, so the difference is seven centimetres." Lucas scored 380 points on a computer game.

Laura scored 320 points.

What is the difference between their points? How many more points did Lucas get? Lucas says, "If I represent the points with bars, the difference is the gap between them." He's drawn it out there.

"We can work out how many more by calculating the value of the gap.

Although they're multiples of 10, our scores are really close together.

The gap is the difference.

The top bar is the minuend and the bottom bar is the subtrahend." He writes it out as an equation with an unknown.

"I can show the difference on a number line.

What step can be made between the two? What do we subtract from 380 to get to 320? Or what can we add on to 320 to get to 380?" Lucas draws a clearer number line to think about the difference between 320 and 380.

He says, "I will start on 380 and count back in tens because ones would take too long.

I end up on 320 having counted back six lots of 10 in total.

Six lots of 10 makes 60, so I counted back 60.

The difference between 380 and 320 is 60." He writes it into his equation to replace the unknown.

"I think I can also count forwards to find the difference and the result will be the same.

I was right, I counted on six lots of 10, which is 60." Okay, it is time for you to have a go so we can quickly check that you've understood what we've done so far.

Lucas scored 710 points on the game.

Laura scored 760 points.

What is the difference between their points? How much did Laura win by? And Laura says, "I know that six takeaway one equals five, which is useful here." Pause the video and come back in a moment so that you can see how you've got on.

Welcome back, let's give you some feedback.

We've drawn out the number line here with the equation below featuring the unknown quantity, the difference.

You can see that we can make one big jump counting back of 50.

760 takeaway 50 is equal to 710.

That means that 760 takeaway 710 is equal to 50.

I hope you got it, it might be that some of you decided to count back in tens rather than in one big jump.

That's okay, as long as you've got the correct answer and you know that you can do it speedily to be efficient.

Let's move on.

It's time for you to have a practise now.

Below is a table of computer game scores.

For each turn, say who won and then find the difference to say by how much.

You can see the table below.

In the first column, we've got Lucas's scores.

In the second column, we've got Laura's, and you need to, in the third column, write down the name of the child who won and then calculate the difference between the two scores to see how much that child won by.

Pause the video here, have a good go at these calculations, finding these differences, and I'll be back in a little while to give you some feedback, good luck.

Let's do some feedback to see how you got on.

In the first game, Laura won by a difference of 50.

Here's a number line that might represent how you thought about this question.

Did you start on 590 and count back 50 to get to 540? If you did, well done.

You may have counted back in tens.

You might have started on 540 and counted forwards.

All of these are good strategies provided that they're quick and accurate for you.

Let's list down the rest of the differences.

In the second match, Laura won by 70 points.

In the third match, Lucas won by 50 points.

And in the fourth match, Laura won by 70 points.

Looks like Laura won more games than Lucas.

Okay, we're ready to start the second part of the lesson, we're gonna look at subtracting three digit multiples of 10 by finding the difference between them, but this time there's going to be some bridging, ready? Okay, let's go for it.

Lucas and Laura play the computer game again.

This time Lucas scored 420 and Laura scored 360.

What is the difference between their scores this time? Lucas says, "If I represent the points with bars, the difference is the gap between them." And there it is, he draws it out.

"We can work out how many more by calculating the value of the gap." So no changes here so far from what we were learning about in the first half of the lesson.

"Our scores are really close together, but I'll need to bridge across 100." Aha, now that's slightly different.

Lucas draws a clearer number line to think about the difference between 360 and 420.

You can see at the bottom he's written out the equation with an unknown again, he says, "I could count back in steps of 10 to see what the difference is, but I think I can be more efficient and partition.

I can count back, 420 subtract 20 is 400, which is an easy 100s number to work from.

400 subtract 40 is 360.

I have subtracted 60 altogether.

The difference between 360 and 420 is 60." Well done Lucas, that looks like a sensible method to me.

I think it could be quite efficient.

"I think I can also count forwards to find the difference and the result will be the same.

360 add 40 is 400, which is an easy 100s number to work with.

400 add 20 is 420, I have added 60.

The difference between 360 and 420 is 60." And that's exactly what he found last time.

You can count on or you can count back, it depends which one you prefer.

Okay, time to check your understanding of that.

Lucas and Laura play the computer game once more, must be a really good game.

This time, Lucas scored 250 and Laura scored 330.

Find the difference between their scores.

Have a go at that, pause the video, and I'll be back in a moment to see how you've got on.

Welcome back, let's see how you did.

We've drawn out a number line here to represent this problem.

We know that we've got Lucas who scored 250 and Laura who scored 330.

We've also written out the equation below with an unknown.

We are counting on here, we count on 50 to get to 300, a nice easy 100s number to work from, and then we add on 30 to get to 330.

If we total up what we've added on, we can see that altogether we've added 80.

So the difference between 330 and 250 is 80.

330 subtract 250 is equal to 80.

Did you get it? I hope so.

Lucas and Laura play a game using a spinner.

They each create two 3-digit numbers.

The winner is the person with the greatest difference between the two numbers.

Lucas says, "I think this is too tricky for finding the difference.

Can we make it easier to calculate mentally? Let's put placeholders in the 1s column.

Then they'll be multiples of 10.

They are best for finding the difference." "Great idea," says Laura.

And there they are, the placeholders in each of their three digit numbers in the 1s column.

Lucas and Laura both spin to create their numbers.

Who has the greatest difference? Who has won? There's Lucas's numbers, and there's Laura's numbers.

Lucas has got 380 and 510, and Laura's got 380 and 420.

"Oh no," says Laura, "I already know that I've lost without calculating." Hmm, I wonder how she's managed to know that straight away.

How does Laura know that she has already lost? Lucas replies, "Our subtrahends are equal, but your minuend is lower.

That means that you have a smaller difference." Lucas and Laura both spin again.

Laura is determined to win this time.

Has she managed to win? Let's see.

So Lucas has got 380 and 510, and Laura's got 290 and 430.

"Closer this time.

I'll need to find the difference," says Lucas.

Lucas finds the difference between his numbers.

He says 510 is the largest number, so that is the minuend, 380 is the subtrahend, so now I can write an equation.

510 subtract 380 is equal to an unknown, question mark to represent that.

"I'll use a number line to help my thinking and I'll count back from 510.

First, I will subtract 10 to get to 500." He's also writing out the jottings underneath his equation.

510 subtract 10 is equal to 500.

"Then, I will subtract 100 to get to 400." And again, he's written that out as a jotting.

500 subtract 100 is equal to 400.

"Finally, I will subtract 20 to get to 380." 400 subtract 20 is equal to 380.

"So I counted back in three parts of 10, 100, and 20, which is 130 altogether.

The difference was 130, so that was my score." Laura finds the difference between her numbers.

"430 is the largest number, so that is the minuend.

290 is the subtrahend, I'll write my equation." And she's done that.

430 subtract 290 is equal to question mark, an unknown.

"I'm going to use a number line too, but I'll count on instead.

First, I will add 10 to get to 300.

Then, I'll add 100 to get to 400.

Finally, I will add 30 to get to 430.

I counted on in three parts of 10, 100, and 30, which is 140 altogether.

The difference was 140, so that was my score.

I won," she says.

Okay, it's your turn, just to give you a little check for how much you've understood of what we've just been learning about.

Below is a number line.

Write out the subtraction equation that the number line represents.

Pause the video here, have a look closely at the number line, and I'll be back in a few moments to let you know how you've got on.

Welcome back, let's have a look at what you put and what we've got.

Here's an example of the equation you might have written.

920 subtract 770 equals 150.

There is another possibility here though.

Some of you may well have put something along the lines of, 920 subtract 150 equals 770.

You could see that this number line represents that too.

Okay, are you ready to move on? Let's go for it.

Lucas and Laura both spin again.

They discuss the numbers they get.

Lucas has got 180 and 760, and Laura's got 290 and 930.

Lucas says, "The numbers are much further apart." "It makes it trickier to find the difference efficiently." "Should we spin again?" says Lucas.

"Let's just re-roll the 100s column on the second number." "The numbers have to be closer together to use the find the difference strategy." "Okay, so my second number is 360." "My second is 430, that gives a difference of 10 plus 100 plus 30.

That's 140, so I win." Wow, Laura did that really well in her head straight away.

Lucas and Laura have another go.

You can see Lucas has drawn 330 and 580, and Laura's got 750 and 970.

Lucas says, "I think you've won again." Laura says, "Let's find the difference and see." They find the difference between their numbers, starting with Lucas.

He writes it out as a subtraction equation.

Then, what Lucas does is he partitions it in his head.

He starts on 580 and takes away 80 at first to get to 500.

Then he takes away another 100 to get to 400, and then he takes away 70 to get to 330, which was of course, one of his numbers.

Then what he does is he adds together the bits that he subtracted whilst he was counting back, 80 plus 100 plus 70, but he realises that that's a tricky addition.

He says, "I'll combine the tens first." So he takes 70 and 80 and adds them together, giving him 150, added to the 100 that's already there, he gets 250 and says, "My score was 250." Now it's time to do Laura's.

Laura starts with a subtraction equation again, but notice that she decides to count on instead of counting back, so she starts on 750, adds 50 to it to get to 800, adds another 100 to get to 900, and then adds 70 to get to 970, the minuend of her two numbers.

She then adds together 50, 100, and 70, because they were the steps that she took to go from one number to the other.

She says, "I'll combine the tens first as well," which she does, 50 and 70 are 120, then she adds on the 100 that is already there.

"My score was only 220, well done Lucas." Okay, let's check your understanding.

Lucas and Laura both spin again.

Find the difference for Laura and Lucas, who won? Pause the video here, have a go, and then come back in a moment for some feedback.

Welcome back, let's have a look at what the answers were.

So for Lucas, you might have done something like this.

610 subtract 10, subtract 100, subtract 20 gives 480, so we're starting on the minuend and counting back until we get to the subtrahend.

Altogether, we counted back 130, so his score was 130.

Now let's have a look at Laura's.

We know that Laura likes to count on.

She's starting on her subtrahend and counting on until she gets to her minuend.

She counts on in three steps of 10, 100, and 50, which altogether gives her a score of 160.

Looks like Laura won again.

Okay, it's time for you to have a practise now.

You are gonna play a similar game using the spinner.

Have three rounds and use the scorecard below.

The 100s digit has already been chosen for you.

So you can see, we've got player one and player two, and in each of those sections there's a column for the minuend, the subtrahend, and the difference.

You can see that there are placeholders in all of the 1s columns and there's some different digits in the 100s columns.

So your job is to spin the spinner once and fill in those blank digits.

Then you've got to calculate the difference and see who it is that's got the greatest difference and is therefore the winner.

And lastly, what do you notice when you've got your full scorecard in front of you? Number two is requiring you to look at this question.

It says, below are six different three digit numbers.

Arrange them into the table below to match the clue.

We've got 910, 940, 860, 890, 750, 790, 930, and 800.

You've got to arrange them into these columns, the minuend and the subtrahend, and they've got to match the clue on the right hand side.

The clues are, this pair has the smallest difference, or, this pair has the greatest difference, or, this pair has a difference of 100, or, this pair has a difference less than 100, but greater than 50.

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

Enjoy the game, enjoy working out the clues, good luck.

Welcome back, it's time for some feedback.

Here's the game having been played by Lucas and Laura.

You can see how they've managed to fill it in.

The winner was Laura.

Well done Laura.

She said that, "We noticed that all the 100s were two apart.

This meant we only had to calculate the tens difference and then add 100." That's a good spot, Laura, well done.

Okay, let's look at number two.

We had our clues and our numbers.

Let's reveal them gradually.

940 and 930, that pair gave the smallest difference.

910 and 750, that pair had the greatest difference.

890 and 790, that pair had a difference of 100.

And 860 and 800, this pair had a difference less than 100, but greater than 50.

Okay, I hope you enjoyed doing that.

Here's a summary of what we've been learning about today.

When the minuend and subtrahend are close together, the difference can be found efficiently.

The difference can be found by counting or adding on from the subtrahend to the minuend.

The difference can be found by counting back or subtracting from the minuend to the subtrahend.

Finding the difference can be used efficiently with three digit multiples of 10, provided they aren't too far apart.

All right, I've really enjoyed today's lesson, I hope you have and I hope you found it really useful and you can put into use all of the things you've learned when you come across three digit multiples of 10.

Thanks very much.

I hope to see you again soon in another maths lesson.