Lesson video

Hello there, my name is Mr. Goldie and welcome to today's maths lesson.

I'm sure you're going to have lots and lots of fun.

Here is the outcome for today's lesson.

I can partition three digit numbers into two and three parts.

Let's look at the keyword for today.

So just one keyword today, the word is partition.

So repeat after me, partition.

Excellent.

Partition means splitting an object or value down into smaller parts.

Six could be partitioned into three and three, or it could be partitioned into four and two.

And here's our lesson outline.

The first part of today's lesson is partitioning three digit numbers using base 10 blocks.

And the second part of today's lesson is partitioning three digit numbers using bar models.

Let's get started.

So in this lesson you will meet Sophia and Andeep.

Andeep represents a number using base 10 blocks.

"I've represented the number 375," says Andeep.

"How many different ways can I partition 375?" How many different ways can Andeep split 375 into different parts? "There's only one way to partition 375," says Sophia.

"You can partition 375 into hundreds, tens and ones." There's our hundreds, there's our tens and our ones.

300 add 70, add five equals 375.

Is Sophia, correct? No.

She is not.

There are many ways to partition 375.

Andeep starts by partitioning 375 into two parts.

So 375 can be partitioned into 370 and five.

There's 375, so we could split it up into 370 and five.

370 add five equals 375.

Sophia thinks of another way.

375 can also be partitioned into 375.

So there's 375 and this time we can split it into hundreds and 10s of ones.

300 add 75 equals 375.

Are there any other ways to partition 375 into two parts? "375 can be partitioned into 200 and 175," says Andeep.

"200 add 175 equals 375.

375 can also be partitioned into 100 and 275," says Sophia.

That 100 add 275 equals 375.

Andeep and Sophia find other ways to partition 375 into two parts.

There are still lots of ways left.

I can rearrange the base 10 blocks.

So here's the base 10 blocks.

Andeep's gonna mix them up and rearrange them.

So 375 can also be partitioned into 220 and 155.

220 add 155 equals 375.

"375 can also be partitioned into 120 and 255," says Sophia.

Sophia is getting more confident at partitioning 375.

So she comes up with 120 add 255 equals 375.

Sophia thinks that they have now found all the ways to partition 375 into two parts.

"There are still lots of ways left," says Andeep.

375 can also be partitioned into 250 and 125.

250 add 125 also equals 375.

Sophia has a bit of a think.

375 can also be partitioned into 150 and 225.

So 150 add 225 also equals 375.

Sophia partitions 375 into two parts.

"How have I partitioned 375?" asks Sophia.

Pause the video and see if you can work out what two numbers Sophia has partitioned 375 into.

And welcome back.

Did you manage to work out what the two numbers were? You should have said they are 240 add 135.

240 add 135 equals 375.

Well done if you got that correct.

Andeep and Sophia, think about ways to partition 375 into three parts.

"375 can be partitioned into 200 and 175," says Andeep.

200 add 100, add 75 equals 375.

"375 can also be partitioned into 100 add 100 and 175," says Sophia.

100 add 100, add 175 equals 375.

Andeep and Sophia, think of other ways to partition 375 into three parts.

"375 can be partitioned into 120 and 120 and 135," says Andeep.

So Andeep's rearrange the base 10 blocks to make three different numbers.

120 add 120, add 135 equals 375.

"375 can also be partitioned into 130 and 130 and 115," says Sophia.

130 add 130 add 115 also equals 375.

Andeep partitions 375 into three parts.

"How have I partition 375?" Asks Andeep.

What do you think? Can you complete the calculation? What three parts has Andeep partition 375 into? Pause the video and see if you can work it out.

And welcome back.

Did you manage to work out the answer? So hopefully you said 110, add 110, add 155 equals 375.

Very well done if you've got the right answer.

Sophia partitions 375 into two parts.

One of the numbers is 105.

"What is the other number?" asks Sophia.

I wonder how you'd word that out? 105 adds something equals 375.

Andeep says "I'm going to rearrange the base 10 blocks to find the other number." That Andeep's going to rearrange the base 10 blocks.

He's going to make 105 and that will give him the other number.

So there's 105.

The other number is 270.

105 add 270 equals 375.

Andeep partitions 375 into three parts.

Two of the numbers are 125 and 240.

What is the other number? So 125 add 240 add what other number equals 375.

Sophia says "I'm going to rearrange the base 10 blocks to find the other number." So she's going to rearrange the base 10 blocks to make 125 and 240.

And that should give her the other number.

There's 125 and 240 and she's left with 10.

So the missing number was 10.

Very well done Sophia.

Andeep partitions 375 into three parts.

Two of the numbers are 260.

What is the other number? Is it A, 115? Is it B, 125? Or is it C, 215? Pause the video and see if you can work out which number it is.

And welcome back.

Did you manage to get the right answer? Let's find out.

The answer was 115.

Very well done if you said 115.

And let's go on to our task.

So task A.

The first part of task A, use base 10 blocks to represent the number 340, and then complete the calculations by finding the missing part.

A is 300 at what number equals 340.

So you can rearrange that based 10 blocks and see if you can mark out the missing numbers.

And then part two of task A, use base 10 blocks to represent the number 450.

Complete the calculations by finding the missing part.

And this time there are three parts.

So you've gotta work out one of the missing parts.

And then part three of task A.

Use base 10 blocks to represent the number 395.

How many ways can you complete the calculation? So one of the parts is 110.

What could the other two parts be? Pause the video and have a go at task A.

And welcome back.

Let's have a look at some of those answers.

So for part one of task A, you had to complete the calculations by finding the missing part.

So the answer to A was 300 add 40 equals 340.

Let's look at the answers for part two.

So this time you were given two of the parts and you had to find the missing part.

So the answer to A was 300, add 100, add 50 equals 450.

But I dunno if you got one to part two and you answered some of those questions.

And then the answers to part three, here are some possible answers and there are lots and lots of different answers you could have come up with.

So one of the possible answers was 110, add 45, add 240 equals 395.

So lots and lots of different answers to that one.

So very well done, if you've got onto to part three and you managed to find some different answers.

And let's move on to part two of our lesson.

So part two of our lesson is partitioning three digit numbers using bar models.

Sophia uses a bar model to partition 550.

"I'm going to partition 550 into three parts," says Sophia.

So she's going to use base 10 blocks and she's gonna partition the base 10 blocks into three different parts.

The parts are 200.

So one of the parts of the bar model is 200.

Add another 200.

So another part is also 200.

Add 150.

So the last part is 150.

200 add 200, add 150 equals 550.

Andeep uses a bar model to partition 550.

"I'm going to partition 550 into three parts," says Andeep.

Andeep partitions 550 slightly differently.

So one of the parts is 300, another part is 220 and the final part is 30.

300 add 220, add 30 also equals 550.

Andeep finds another way to partition 550 using the bar model.

"I'm going to find a different way to partition 550 into three parts," says Andeep.

So again there's 550 and Andeep has rearranged the base 10 blocks to find three different parts.

One of the parts is 330.

Another part is 110 and another party's 110.

So 330 add 110, add 110 also equals 550.

Sophia partitions 550 into three parts.

"How would you complete the bar model to show how I partitioned 550?" Asks Sophia.

So it's 550, how would you complete the bar model? Pause the video and see if you can work out how Sophia has partitioned 550.

And welcome back.

Let's see how you got on.

Let's see what answer you came up with.

So you should have said 210, add 210, add 130 equals 550.

Very well done.

If you managed to work out how Sophia had partitioned 550.

Andeep uses a bar model to partition 550.

"I've partitioned 550 into three parts," says Andeep, "I'm going to calculate the missing part," says Sophia.

Sophia uses base 10 blocks to try and find out the missing part.

She knows that two of the parts are 100.

So we've got their 100, add 100 add the missing part and that equals 550.

So we've got their 100 add 100.

The missing part is made from 305 10s.

So the missing part is 350.

Add 100, add 100, add 350 equals 550.

Sophia uses a bar model to partition 550.

"I've partitioned 550 into three parts," says Sophia, and there's 550 represented in base 10 blocks.

"I'm going to rearrange the base 10 blocks to find the missing part," says Andeep.

So Andeep rearranges the blocks.

And he's got there 220, add 210.

And the final part is 120.

220 add 210, add 120 equals 550.

Very well done Andeep for working out the missing part.

Andeep uses a bar model to partition 550.

"I partitioned 550 into three parts," says Andeep.

Calculate the missing part.

So to help you, there are the base 10 blocks.

Can you try to work out the missing part and you can use the base 10 blocks to help you.

Pause the video and see if you can work out the missing part to the bar model.

And welcome back.

Let's see whether you managed to find the answer.

So we actually don't need to rearrange the blocks, although they're in a slightly different order to the bar model.

So the first part is 200.

The last part here is 150.

And then what's left over gives us the missing part from the bar model.

So the missing part is 200.

200, add 200, add 150 equals 550.

So the missing part of the bar model was 200.

Very well done if you've got the right answer.

Sophia uses a bar model to partition 550.

One of the parts is 140.

What could the other parts be? I'm going to remove 140 to help me calculate the other two parts.

So there's 550 altogether.

Andeep is going to remove 140.

He's going to take away 140 and that will leave him with a total of the other two parts.

The other two parts could be 410.

So Andeep could partition the 410 that is left into 410.

The answers could be 410.

Because 140 add 400, add 10 also equals 550.

Can you find a different answer? What could the two other numbers be? Pause the video and see if you can mark out the answer.

And welcome back.

How did you get on? Did you manage to find an answer? And there are lots and lots of different answers you could have come up with.

But here's the one that Andeep came up with.

So the numbers could be 200 and 210, but there are several other answers.

So there's several different ways of doing that one.

So you could have partitioned the 410 into 200 and 210.

And let's move on to task B.

So the first part of task B is find four different ways to partition the number 470.

You may use base 10 blocks to help you.

So the easiest way of doing that is to make 470 using base 10 blocks and rearrange them in different ways to make different numbers.

So can you find four different ways of partitioning 470? And for each of your answers, you should have three different parts.

Part two of task B, find the missing number.

This time, the whole of each of the bar models is 490 and you're given two of the parts.

What could the other part be? And again, you might find it really helpful to use base 10 blocks to help you find the answer.

Actually make 490 outta the base 10 blocks, make those two parts and see what is left over.

And finally, part three of task B.

So how many different ways can you complete the bar model? So the whole on the bar model is 435 and you've got one of the parts.

One of the parts is 105.

What could the other two parts B? And how many different ways can you complete the bar model? How many different answers can you find? And again, you may want to use base 10 blocks to help you.

So pause the video and have a go at task B.

And welcome back.

And let's take a look at those answers.

So for part one of task B, here are some possible answers.

Here are some ways you could have partitioned 470 into three parts.

So you could have had 110, 110 and 250.

You could have had 210, 220 and 40.

And you may have come up with lots and lots of different answers of your own as well.

Here are the answers for part two.

So in part two you are looking for a particular answer and you're looking for the missing part.

So the whole of each of the bar models is 490.

If the parts were 110 and 110, the missing part was 270.

Very well done if you got onto to part two and you managed to find the missing answers.

And finally, here are some possible answers for part three.

And again, there are lots and lots of different ways of finding the answers.

The two parts that are missing add up to equal 330.

So as long as your two parts equal 330, you've got the right answer.

So you could have had 105, add 300, add 30 that equals 435.

You could have had 105, add 320, add 10, that also equals 435.

So very well done if you got onto part three and you managed to find some of those answers.

And excellent work today.

And I hope you're feeling much more confident about partitioning three digit numbers into different parts.

And finally, let's look at our lesson summary.

So three digit numbers can be partitioned into two or three parts in many different ways.

Partitioning of three digit numbers can be represented using base 10 blocks or bar models.