Lesson video

Hello there.

My name is Mr. Goldie and welcome to today's maths lesson.

And here is our learning outcome.

I can use different strategies to subtract multiples of 100.

And here's our keyword for today's lesson.

Just one keyword.

I'm going to say the word, can you repeat it back? The keyword is multiple.

Let's take a look at what that word means.

A multiple is the result of multiplying a number by another whole number.

Multiples of 10 include 10, 20, 50, and 100.

And here is our lesson outline.

In the first part of the lesson, we're going to be subtracting multiples of 100 up to 1,000.

And the second part of the lesson, we're going to be subtracting multiples of 100 up to 2,000.

Let's get started.

In this lesson, you'll meet Sam and Jacob.

What's that, Sam? We're subtracting multiples of 100.

Absolutely right.

That's what today's lesson is focused on.

Jacob finds the previous multiple of 100.

Sam says, "What is 100 less than 300?" Jacob says, "200 is 100 less than 300." What is 100 less than 700? 600 is 100 less than 700.

What is 100 less than 1,000? 900 is 100 less than 1,000.

Sam and Jacob subtract from 1,000.

1,000 is equal to 1,000.

We can use number pairs that total 10 to help us subtract multiples of 100.

If I know 10 subtract three is equal to seven, then I also know 1,000 subtract 300 is equal to 700.

I know 10 subtract six is equal to four.

So 1,000 subtract 600 is equal to 400.

10 hundreds subtract six hundreds is equal to four hundreds.

Sam and Jacob look at other strategies they can use.

I can also use my knowledge of doubles to help me subtract multiples of 100.

So Sam tries to calculate the answer to 600 subtract 300.

Sam says, "I know three add three is equal to six.

Six subtract three is equal to three.

600 subtract 300 is equal to 300.

Here's Jacob's calculation.

He's going to try to work out the answer too.

This time, he's trying to work out 800 subtract 400.

Jacob says, "I know four add four is equal to eight.

I also know eight subtract four is equal to four.

800 subtract 400 is equal to 400.

Sam thinks about how to calculate 900 subtract 800.

"The numbers are very close.

I'll count back from the larger to the smaller number." This is a really useful strategy to use as well.

So if you spot the two numbers are close together, work out the difference between the two numbers.

I can represent the problem using a number line and a part-part-whole model.

100 is the difference between 900 and 800.

They're only 100 apart.

900 subtract 100 is equal to 800.

So 900 subtract 800 is equal to 100.

900 is the whole, 800 and 100 are the parts.

If you subtract any part from the whole, you are left with the other part.

So remember, if you spot two numbers that are close together, it's normally easier, more efficient to calculate the difference between the two numbers by counting from the larger number to the smaller number.

Sam uses a symbol between the two expressions.

We need to use either the greater than, less than or equal symbol.

Jot down the answers to help you work out the correct symbol.

Very, very important advice that, Jacob, well done.

So Sam has a look at that first expression and she says, "I know four subtract two is equal to two." So 400 subtract 200 is equal to 200.

Sam jots down the answer.

And she says, "600 and 700 are very close together.

I can count back from 700 to 600 to find the difference." 700 subtract 100 is equal to 600.

So 700 subtract 600 is equal to 100.

"200 is greater than 100," says Jacob.

So 400 subtract 200 is greater than 700 subtract 600.

Which symbol should we write between these two expressions? We've got 500 subtract 200.

Is that greater than, less than or equal to 400 subtract 100? Sam says, "Use either the greater than, less than or equal symbol." Jacob says, "Jot down the answers to help you work out the correct symbol." So pause the video.

Which symbol would go between those two expressions? And welcome back.

Did you manage to work out the answer? Did you jot down the answers to each expression as you worked them out? Let's take a look to see which symbol you should have used.

So Sam says, "I know five subtract two is equal to three.

So 500 subtract 200 is equal to 300." Sam's making really good use of his number fact that she knows already.

So 500 subtract 200 is equal to 300.

Four subtract one is equal to three.

400 subtract 100 is equal to 300.

So which symbol should be put between those two expressions? 300 is equal to 300.

The missing symbol was the equals symbol.

So very, very well done if you worked out the correct answer.

Sam completes the equation.

We've got a number, subtract another number is equal to 400.

The difference between the two numbers is 400.

Let's use a number line to help us work out what the answer could be.

500 and 100 have a difference of 400.

The two numbers could be 500 and 100.

500 subtract 100 is equal to 400.

600 and 200 also have a difference of 400.

600 subtract 200 is equal to 400.

Now it's your turn.

Complete the equation.

Sam has shown you two numbers that have a difference of 400 and you could use those two numbers.

You could use two different numbers instead.

Find two more numbers that have a difference of 400.

So pause the video and try and work out two numbers that have a difference of 400.

You can use Sam's clue if you want, or you may just want to come up with two different numbers of your own.

And welcome back.

Did you come up with the two different numbers? Let's take a look to see what numbers you may have come up with.

So you could have used 300 and 700.

700 and 300 also have a difference of 400.

The missing numbers could be 700 subtract 300 is equal to 400.

You could have used 800 subtract 400.

You could have used 900 subtract 500.

You could have used 1,000 subtract 600.

Any of those answers would have done.

So very, very well done if you came up with one of those answers.

Let's move on to task A.

So the first part of task A, you're going to use a symbol between each expression.

So use either the greater than, less than or equal symbol.

And don't forget, jot down the answers to help you.

So you've got six different missing symbols there.

Can you work out what all six missing symbols are? And then part two of task A, find different ways to make each equation correct using multiples of 100.

So for A, we've a number, subtraction of the number is equal to 500.

So 500 is the difference between the two numbers.

Can you think of two numbers with a difference of 500? For B, the difference is 600.

So what could the two numbers be? And don't forget to use multiples of 100.

So good luck.

Have a go at completing task A.

And welcome back.

How did you get on? Did you complete part one? Did you get on to part two? Did you complete part two? Very well done if you did.

Let's take a look at the answers.

So here are the answers for part one of task A.

So let's look at A.

So we got there, 500 subtract 100 and 800 subtract 400 are both equal to 400.

Both those expressions have a difference of 400 so you should have used the equals symbol.

For B, 1,000 subtract 700 is greater than 500 subtract 300.

1,000, subtract 700 is equal to 300.

500 subtract 300 is equal to 200.

So the correct symbol should be the greater than symbol in between.

C, both expressions have a difference of 200.

So you should have used the equals symbol in the middle.

For D, 200 is less than 400.

For E, 400 is greater than 300.

And then finally, for F, 700 subtract 400 is equal to 300.

900 subtract 600 is also equal to 300.

So you should have used the equals symbol.

Let's move on to part two of task A.

So the difference between the two numbers is 500.

So you could have used a number line to help you work out the answer here.

So 1,000 and 500 have a difference of 500.

So you could have used 1,000 subtract 500 is equal to 500.

900 subtract 400 is also equal to 500.

Or you could have used 800 subtract 300 is equal to 500.

700 subtract 200 is equal to 500.

600 subtract 100 is equal to 500.

So well done if you got all or some of those different answers.

Here are the answers for 2b.

The difference between the two numbers is 600.

So you could have used 1,000 subtract 400.

And if you got a bit stuck with these ones, you could have used a part-part-whole model to help you work out the answers.

So you know that 600 is one of the parts.

The whole could be 900 and the other part could be 300.

900 subtract 300 is equal to 600.

800 subtract 200 is equal to 600.

And 700 subtract 100 is equal to 600.

Very well done if you got onto part two of task A.

And you tried to find different multiples of 100 that had a difference of 600.

Excellent work.

And let's move on to the second part of the lesson, which is subtracting multiples of 100 up to 2,000.

Jacob finds the previous multiple of 100.

"What is 100 less than 1,100?" says Sam.

"1,000 is 100 less than 1,100," says Jacob.

What is 100 less than 1,600? 1,500 is 100 less than 1,600? "Hmm, what is 100 less than 2,000?" asks Sam? 1,900 is 100 less than 2,000.

You're very good at this, Jacob.

Well done.

Sam and Jacob discuss subtraction strategies.

They are going to sort equations into this table.

So there are three different parts of the table.

The first part says subtract using known facts.

The middle part says subtract using a number line and the last part says count from the larger to the smaller number.

"We can use known facts to help us," says Sam.

"If the numbers are close together, we can count back from the larger to the smaller number," says Jacob.

So you're gonna be thinking about the numbers involved in each calculation and which strategy would you use to try work out the answer? Sam starts with the first equation.

So we've got there 1,500 subtract 200.

And Sam's gotta think about which strategy she would use to answer that calculation.

She says, "The numbers are far apart.

I'll subtract 200 from 1,500." So Sam's going to use a number line to help her work out the answer.

There's 1,500 and she subtracts 200.

She counts back 100 and then another 100.

So the answer would be 1,300.

1,500 subtract 200 is equal to 1,300.

So Sam used the subtract using a number line strategy.

So that's where she puts that calculation.

Jacob tries the next equation.

The next equation is 1,600 subtract 800.

I wonder how you would work that one out.

But Jacob says, "The numbers are far apart.

I'll subtract 800 from 1,600." So Jacob's going to use a number line to help him work out the answer.

He says, "I'll partition 800 into 600 and 200 so that I can bridge 1,000.

So 1,600 subtract 600 is equal to 1,000.

That's 1,600 subtract 600 and that is equal to 1,000.

And then Jacob says, "1,000 subtract 200 is equal to 800." Jacob then takes away 200 more and that is equal to 800.

So all together, Jacob has subtracted 800.

He started at 1,600, he subtracted 600 and then subtracted 200.

That's to help him bridge through that 1,000.

Okay, so Jacob says, "I subtracted using a number line." Sam has a different strategy.

She looks at the same calculation.

"I'd use known facts to find the difference," says Sam.

So Sam's obviously spotted something about those numbers.

I wonder what she's spotted.

She says, "I know eight add eight is equal to 16." So Sam's gonna use doubles to help work out the answer.

So 16 subtract eight is equal to eight.

So 1,600 subtract 800 is equal to 800.

1600 subtract 800 is equal to 800.

Jacob says, "That's a more efficient strategy for this equation." In fact, they're going to move that equation into the subtract using known facts.

Actually, it's quite good they've used two different strategies there to work out the answer because it's a really good way of checking that they have got the right answer.

So nothing wrong with your strategy there, Jacob.

It's just that Sam's saying perhaps for that calculation, her strategy may have been more efficient.

How would you solve the last equation? So the final equation we've got is 1,900 subtract 1,700.

How would you answer that? Which strategy would you use? Could you subtract using known facts? Would you subtract using a number line? Would you count from the larger to the smaller number? Now, how would you work out the answer? Which strategy would you use? Think about the most efficient strategy to give you the correct answer.

Pause the video and think about how you would calculate the answer.

And welcome back.

I wonder whether you got the right answer.

I wonder which strategy you used to give you the correct answer.

Let's take a look, see what Jacob says.

Jacob says, "The numbers are close together.

I'll count back from one number to the other." So Jacob's going to use a number line to help him work out the answer.

Here's 1,900 and 1,700.

The difference between the two numbers is 200.

1,900 subtract 200 is equal to 1,700.

So that means that 1,900 subtract 1,700 is equal to 200.

So the answer is 200.

And Jacob used the strategy of counting from the larger to the smaller number because he spotted that the numbers were close together.

That's probably the easiest way to work out the answer.

You may have used a different strategy to work out the answer, but just ask yourself, did you use the most efficient strategy? Was Jacob's strategy quicker, more efficient than your strategy? But very well done if you got the right answer.

And well done if you used the same strategy as Jacob.

And let's move on to task B.

So in task B, you're going to be sorting the equations into the tables.

It's the same table we've just been looking at.

So would you subtract using known facts? Would you subtract using a number line? Would you count from the larger to the smaller numbers? You got to look really carefully at the numbers involved in the calculation.

Which strategy would you use to work out the answer? Sam says, "What's the most efficient strategy? That's really important.

What's going to be the best strategy to work out the answer? Jacob says, "Find the missing difference each time." So here are the equations you're going to be sorting out.

So there's 12 different equations.

You're looking for the difference between the two numbers and there are some number lines as well to help you work out the answer.

You might want to use those to count back.

You want to use those to count back to find the difference.

Pause the video and have a go at trying to sort those different calculations into the table.

Thinking about the most efficient strategy to use to work out the answer.

And welcome back.

How did you get on? Did you manage to sort some of the calculations into the correct places on the table? Did you manage to sort all the calculations? That's brilliant work if you did.

Now let's take a look at the answers that you may have come up with.

Now, you may have sorted the equations like this.

Now, sometimes you might prefer a different strategy and sometimes it may be that the strategy that you come up with is different to somebody else's.

Now, it doesn't matter as long as it's efficient for you.

What's important is you don't just use the same strategy for every single calculation.

That's really important.

Jacob says, for this first calculation here, he subtracted using known facts.

So 1,400 subtract 700 is equal to 700.

He used known facts.

He says, "I know seven add seven equals 14.

So 14 subtract 7 is equal to 7.

So 1,400 subtract 700 is equal to 700." So he'd used known facts to work out the answer there.

So you probably knew some facts to help you with these equations.

And those equations there you probably put into subtract using known facts.

You may have used a different strategy to work them out, but just have a good look and think, hmm, should I have used known facts to work them out? So just look at those calculations and ask yourself, "Did I use the best method?" These equations here, you probably answered using a number line.

So you subtracted using a number line.

Now, for these, the hundreds digits are far apart.

There's a big difference between 1,900 and 200.

If you're subtracting 200 from 1,900, it's best to start from 1,900 and subtract 200.

But these calculations here, the hundreds digits are close together.

So for those ones, it's easier to count from the larger to the smaller number to work out the difference.

So don't start with 1,500 and subtract 1,200.

It's much more efficient to count from the larger to the smaller number to work out the difference.

So you may not have sorted all the equations in exactly the same way as Sam and Jacob sorted them.

And in fact, you may have come up with the best strategies that you would use.

But it's all about being flexible in your mathematics.

It's all about thinking about the different numbers involved in an equation.

What's the best strategy you should use to work out that particular equation and not always relying on the same strategy each time.

Well done for working so hard today, and hopefully you're feeling much more confident about subtracting multiples of 100, all the way up to 2,000, and you thought carefully about which strategies were most efficient to work out a particular equation.

Well done today.

Very good work indeed.

And let's move on to our lesson summary.

So known facts help us to subtract multiples of 100.

If five subtract three is equal to two, then 500 subtract 300 is equal to 200.

Subtracting multiples of 100 can be represented in different ways.