Lesson video

Hello there.

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

And here is the learning outcome for today's lesson.

I can use different strategies to add multiples of 100.

And here is the keyword, only one keyword today.

I'm going to say the keyword, can you repeat it back? 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 adding multiples of 100 up to 1,000.

And in the second part of the lesson, we're going to be adding multiples of a hundred up to 2,000.

Let's get started.

In this lesson you'll meet Sam and Jacob.

And Sam and Jacob are going to be helping you with adding multiples of 100 together today.

And they're going to be asking you some difficult questions as well.

So, make sure you are ready.

What was that Sam? You wanted to say something? We're adding multiples of 100.

This is exactly what we're doing today.

Thank you, Sam.

Jacob finds the next multiple of 100.

Sam says, "What is 100 more than 300?" 400 is 100 more than 300.

What is 100 more than 600? 700 is 100 more than 600.

What is 100 more than 900? What do you think? 1,000 is 100 more than 900.

1,000 is equal to 1,000.

900 at 100 is equal to 1,000 or 1,000.

Sam and Jacob find different ways of making 1,000.

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

If I know five plus five equals 10, then I also know 500 add 500 is equal to 1,000 or 1,000.

And here's that calculation represented using a 10 frame and place value counters.

So, we've got 500s, add 500s and the answer is 1,000 or 1,000.

Jacob says, "If I know four add six equals 10, then I also know 400 add 600 is equal to 1,000 or 1,000." And here is Jacob's calculation represented using place value counters.

We've got their 400s add 600s and that is equal to 1,000 or 1,000.

So, number pairs that total 10 are gonna be really helpful today.

Sam and Jacob look at other strategies they can use.

We can also use our knowledge of doubles to help us add multiples of 100.

I know two plus two equals four.

So, 200 add 200 is equal to 400.

I know three add three equals six.

So, 300 add 300 is equal to 600.

Sam and Jacob also think about using near doubles.

Sam says three plus three is equal to six.

So three add four is equal to seven.

300 add 400 is equal to 700.

So, not only you can use doubles to help you add multiples of 100, you can also use near doubles as well.

Now, wonder what calculations represented using the 10th frame and the place value counts this time.

Jacob says, "Four add four equals eight.

So four add five equals nine.

400 add 500 is equal to 900." Sam and Jacob wonder which symbol they should write between the two expressions.

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

We can jot down the answers to help us work out the correct symbol.

This is a really useful strategy to use when you're trying to work out an answer or solve a problem similar to this one because there's quite a lot you have to hold in your head.

It's really, really helpful, when you've worked out something, jot it down, don't try and keep it all in your head.

So, Sam says, "I know that two add eight equals 10.

So, 200 add 800 is equal to 1,000 or 1,000." So, Sam's going to jot down the answer, very sensible, Sam.

I can use near doubles to work out 500, add 400.

Four add four equals eight.

So, five add four is equal to nine 500 add 400 is equal to 900.

And again, Sam jots down the answer.

Well done Sam.

Can't hold it all in your head, can you? Jacob says, "1,000 is greater than 900." So, it's much easier to compare those numbers now they've been written down as well because 1,000 is greater than 900, equal to use the correct symbol between the two calculations.

So, 200 add 800 is greater than 500 add 400.

Which symbol should we write between the two expressions? What do you think? Use either the greater than, less than or equal symbol.

Jot down the answers to help you work out the correct symbols as Jacob.

Very good advice, Jacob.

To have a good look at those two expressions, what symbol should go in the middle? What symbol should go in between them? Is it greater than, less than, or equals? Pause the video and see if you can work out what the missing symbol is.

And welcome back.

Did you manage to work out the missing symbol? Was it greater than? Was it less than? Was it equals? Let's take a look at what you should have put.

Sam says 500 is 100 more than 400.

So, Sam jots down the answer 500.

Two plus two equals four.

So, three add two is equal to five.

300 add 200 is equal to 500.

The sum of those two numbers is also 500.

So, the symbol, guys, in the middle? 500 is equal to 500.

So, the equal symbol goes in the middle.

Very, very well done if that's what you got as your answer.

Sam and Jacob find different ways to complete the equation.

There are three missing numbers and each of them is going to be a multiple of 100 and they have a sum of 800.

Sam says "800 is the next multiple of 100 after 700, and 700 is the next multiple of 100 after 600.

600 add 100 add 100 is equal to 800." So, one possible answer is 600, add 100, add 100 is equal to 800.

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

So, 400 add 200, add 200 is equal to 800." So another possible answer is this one here, 400 add 200 add 200 is equal to 800.

Find another way to complete the equation.

Now, Sam and Jacob have given you two possible answers already.

Now, without just changing the numbers around, can you come up with a different way to complete the equation? Sam says, "Add together three multiples of 100." I remember you are looking for a sum of 800.

Pause the video and see if you can find another way of completing that equation.

And welcome back.

How did you get on? Did you come up with a different way of completing the equation? Jacob says you could have used doubles to help you.

300 add 300 is equal to 600.

So, 600 add 200 is equal to 800.

So, you may have come up with a calculation 300, add 300, add 200 is equal to 800.

Don't worry if you came up with a different equation as long as the sum was 800 and you used three multiples of 100, well done.

And let's move on to task A.

So, in the first part of task A, you're going to find different ways to make each sum using only multiples of 100.

Can you find a way of making a sum of 700 using three different multiples of 100? And then can you find different ways of making the sum 900 using either two multiples of 100 or three multiples of 100 and I think if you use strategies like doubles and near doubles to help you work out the answers.

And this is part two of task B.

So, use a symbol between each expression.

Use either the greater than, less than, or equal symbol.

And again, very helpful advice from Jacob here, jot down the answers to help you.

So, as you work out an answer, jot it down.

So, that's part two of task A of six different symbols that you need to find.

Pause the video and have a go at task A.

And welcome back.

How did you get on? Did you find lots of different ways of making a sum of 700 and 900? Did you get onto part two of task A? Did you complete part two of task A? Excellent work if you did.

Let's take a look at those answers.

Now here are some possible answers for part one of task A and these are different ways of finding a sum of 700.

So, Jacob says, "Use known facts to help." Six add one is equal to seven, so 600 add 100 is equal to 700.

Five add two is equal to seven, so 500 add 200 is equal to 700.

And there are some different answers as well.

So, you may have had 400, add 300 is equal to 700.

100 add 100, add 500 is equal to 700.

200 add 200 add 300 is equal to 700.

And here are some possible answers for making the sum of 900.

Now, you could work systematically to try and find all of the answers.

So, start by finding an answer using 100, then use 200 and then use 300 that you may have come up with the answer.

100 add 800 is equal to 900, 200 at 700 is equal to 900.

What's gonna come next? 300 add 600 is equal to 900.

And then next 400 add 500 is equal to 900.

There are lots of different ways to make 900 using three multiples of 100.

Here's one of them.

100 add 100 add 700 is equal to 900.

Well done if you came up with lots of different ways of making a sum of 900.

And here are the answers for part two of task A.

So, it really helps to jot down the answers says Jacob.

So, for A, you should have used the equals symbol between the two expressions.

So, 100 add 500 is equal to 300 add 300.

For B, you should have used the greater than symbol, 800 is greater than 700.

So, we need to pause the video to have a good look at those answers.

Please do.

But if not, let's carry on.

Let's move on to the second part of the lesson.

Adding multiples of 100 up to 2,000.

Jacob finds the next multiple of 100.

What is 100 more than 1000? Asked Sam.

Jacob says, "1,100 is 100 more than 1000." What is 100 more than 1,400? 1,500 is 100 more than 1,400.

What is 100 more than 1,900? 2000 is 100 more than 1,900.

Sam thinks about how to add 600 add 600 together.

Sam says, "We can use our knowledge of doubles to help us add multiples of 100.

I know six add six is equal to 12, so 600 add 600 is equal to 1,200.

We could also say 600 add 600 is equal to 1,200.

Jacob thinks of another way to add 600 and 600 together.

We could use number pairs that total 10.

Six add four is equal to 10.

600 add 400 is equal to 1,000.

So, Jacob moves four of the place value counters to fill up that first 10 frame.

1,000 add 200 is equal to 1,200.

Sam says, "That's a very useful strategy, but I think mine was more efficient for adding these numbers." You might be right, Sam, but not everybody finds the same strategy the easiest one or the most efficient one to use.

Jacob might actually find using number pairs the total 10 more helpful than using doubles.

Now, here's what you're going to try on your own.

Find the sum of 700 and 600.

Can you use near doubles to help you? Asked Sam.

Could you use number pairs that total 10? Asked Jacob.

What do you think? Which strategy would be easiest for you to use? Pause the video and see if you can work out how you would out together 700 and 600.

And welcome back.

Did you manage to find the answer? Let's take a look at how Sam and Jacob answered this question.

So, Sam says, "Six add six is equal to 12.

Seven add six is equal to 13.

So, 700 add 600 is equal to 1,300 or 1,300." Jacob says, "I'll partition 600 into 300 and 300.

700 add 300 is equal to 1,000.

1,000 add 300 is equal to 1,300." So, Jacob used number pairs that total 10 to help him work out the answer and partition 600 into 300 and 300 to help him bridge through that 1,000 boundary.

Some use near doubles to help out.

There are different ways of working out the answer and sometimes one method might be easier than another.

Sometimes it just depends on you which method, which strategy you find easiest.

So, very well done if you manage to get the answer 1,300 or 1,300.

Sam and Jacob play a game.

They take turns to choose two cards.

They add the numbers together, they put a counter on the sum.

The winner is the first player to get four in a row.

Sam goes first.

She chooses two cards.

So, 700 and 500.

She adds the numbers together.

I know that seven out three is equal to 10.

I can partition five into three and two.

So, Sam's actually using Jacob's strategy.

Obviously, she quite liked it, really.

She's using Jacob's strategy to try and work out the answer.

She's using number pairs that total 10 to help her bridge through that 1,000 boundary.

Seven add three is equal to 10.

Seven, add three, add two is equal to 12.

So, 700 add 300, add 200 is equal to 1,200.

She puts the counter on the sum.

There's more than one of each number.

So, you have to decide which number you're going to put the counter on.

You have to use a bit of strategy as well.

Jacob goes next.

He chooses two cards, 800 and 900.

He adds the two numbers together.

"I can use near doubles to calculate the sum.

I'll start with a doubles fact." That's interesting.

Jacob's now using near doubles help and work out the answer.

They're almost using each other's strategies, aren't they? Jacob says, "Eight add eight is equal to 16.

Eight add nine is equal to 17.

800 add 900 is equal to 1,700 or 1,700.

Jacob puts the counter on the sum.

Now in fact, on this grid here, there's only one 1,700." So, Jacob has to put his counter here.

Sam has another go.

She chooses two cards, 400 and 600.

Sam adds the two numbers together.

I can see a number pair that totals 10.

Four add six is equal to 10.

400 add 600 is equal to 1,000.

She puts the counter on the sum.

Now, I can see a couple of 1,000s on there.

Sam decides to put it there.

Ah, I think she's already seeing where she could get maybe four in a row.

Jacob goes next.

He chooses two cards, 600 and 800.

He adds the two numbers together.

How do I add the two multiples of 100 together? What do you think? How would you add together 800 and 600? Pause the video and see if you can work out the answer.

And welcome back.

Did you come up with a sum of the two numbers? Let's take a look, see if you've got the correct answer.

So, Jacob says, "I know that eight add two is equal to 10.

I can partition six into two and four.

Eight add two is equal to 10.

Eight, add two, add four is equal to 14.

So, 800 at 200 at 400 is equal to 1,400 or 1,400." So, where would Jacob put his counter? Oh, I can see several 1,400's on the grid.

Jacob puts a counter on the sum, he puts it there.

Oh, Jacob's actually put a counter in between Sam's counters to stop her getting four in a row in that direction.

Oh, very good game play there.

Jacob, well done.

So let's move on to task B.

And in task B, you are going to be playing that game.

You are going to play against a partner.

You are going to take it in turns to choose two cards.

You're going to add the numbers together and then you're going to put a counter on the sum.

So, the winner is the first player to get four in a row.

So, not only have you got to be making sure that you add the numbers together correctly, check your partner's calculation as well, make sure they've added the numbers together correctly.

And then you've gotta think about actually how to win the game as well.

Where are you going to put your count to give you the best chance of winning the game? So, pause the video and have a go.

Play that game against a partner.

And welcome back.

How did you get on? Did you manage to win a game? Doesn't matter if you didn't win because you've actually got much better at adding together those two multiples of 100.

And, actually, you've maybe played against somebody who's really good at this sort of game or maybe is really lucky and that's made you a better player.

Next time, you are more likely to win your game.

Your game may have started like this.

So, you may have chosen number 600 and 900.

Sam says, "I can partition 600 into 100 and 500." Sam could add the numbers together like this.

900 add 100 is equal to 1,000.

900 add 100 and 500 is equal to 1,500.

So, Sam would then put a counter on the 1,500 or one of the 1,500s on the grid.

Your game may have ended like this.

"This is what the game looked like at the end," says Sam.

Can you see who won? So, Sam's playing with the slightly darker counters.

Jacob's playing with the light green counters.

Who won the game? "I won," says Jacob.

"I had a diagonal line of four counters." So, you may have won with a vertical line or horizontal line or a diagonal line.

So, I hope you enjoy playing that game and I hopefully as well, it made you feel much more confident about adding together two multiples of 100 all the way up to 2,000.

Hopefully, today as well, you use different strategies to help you work out the answer.

You may looked really carefully at the numbers involved and thought, "What is the best strategy to use?" Is it using number pairs that total 10? Is it using doubles or near doubles? Is it using a different strategy? Did I just know the fact? Because sometimes they're just facts that you know already aren't they? But very, very well done in today's lesson and I hope you really enjoyed playing the game.

That's a game you could play again some other time, isn't it as well to help you just practise adding together those multiples of 100.

And here is our lesson summary.

So known facts help us to add multiples of 100.

If I know three plus two is equal to five, then I know 300 add 200 is equal to 500.

Adding multiples of 100 can be represented in different ways.