Lesson video

Hello there.

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

I'm sure you're going to enjoy it.

And here is the outcome for today's lesson.

I can represent a three-digit number up to 199.

And here are our key words.

So three key words today.

I'm going to say the word, can you repeat it back to me please? The first word is represent.

Can you say that, represent.

Three-digit number.

Can you say three-digit number? And the last keywords are place value.

Can you say place value? Wonderful.

So represent means showing something or standing for something.

The number 10 can be represented as the digits 10, or 10 in a 10s frame, or as a base 10 block.

A three-digit number represents a number of hundreds, tens, and ones.

127 is a three-digit number.

Place value means how much a digit is worth in a number.

In 127, the digit two has a value of two 10s, or 20.

And here is our lesson outline.

So in the first part of the lesson, we're going to be representing three-digit numbers using base 10 blocks.

And in the second part of the lesson, we're going to be looking at three-digit numbers represented on number lines.

Let's get started.

In this lesson, you will meet Jacob and Aisha, and Jacob and Aisha are going to be asking lots of questions and helping you today.

Aisha represents a three-digit number using base 10 blocks.

She uses one 100, so she uses 100.

She uses three 10s.

Three 10s equals 30.

She uses four ones.

Four ones equals four.

"What number have I made?" says Aisha.

"What is 100, add 30, add 4?" says Jacob.

100, add 30, add 4 equals 134.

So Aisha has represented the number 134.

Aisha represents another three-digit number.

She uses one 100, so she uses a hundred.

She uses five 10s.

Five 10s equals 50.

She uses three ones.

Three ones equals three.

"What number have I made?" says Aisha.

Here's Jacob and Jacob saying, "What is 100 add 50, add 3?" 100, add 50, add 3 equals 153.

So this time, Aisha has represented the number 153.

Aisha represents another three-digit number.

She uses one 100.

She uses four 10s.

Four 10s equals 40.

She uses six ones.

Six ones equals six.

"What number have I made?" asks Aisha.

What do you think? What number has Aisha represented this time? What is 100 add 40, add 6? 100, add 40, add 6 equals 146.

Now, here's a problem for you to think about.

Jacob represents a three-digit number.

So he's using base 10 and he's created this number here.

"I've made the number 124," says Jacob.

Is Jacob correct? Has Jacob made the number 124? Pause the video and have a think.

Okay, welcome back.

What do you think? Has Jacob represented the number 124? No, Jacob is not correct.

Jacob has represented that 100 and 40 and 2.

So he's represented the number 142.

"124 would be represented like this," says Aisha.

So we've got that 100 and a 20 and a 4.

120 and 4 equals 124.

Place value grids can also represent three-digit numbers.

So a different way of representing three-digit numbers.

We've got the place value grid.

This is the number of hundreds.

So in that column,, we would put the number of hundreds.

So in this case, there is 100.

This is the number of 10s.

And this example, there are two 10s.

Two 10s equals 20.

And this is the number of ones.

So in this example, there are four ones.

So the number represented there is 124.

So we've got 124 represented with base 10 blocks.

And on a place value grid two Aisha represents a three-digit number.

She uses one 100, she uses seven 10s, she uses five ones.

"How would I complete the place value grid?" says Aisha.

There's our place value grid.

So how many hundreds are? There's 100.

How many 10s? Seven 10s.

How many ones? Five.

So 100 add 70, add 5 equals 175.

Jacob represents a three-digit number.

He uses one 100, he uses two 10s, he uses eight ones.

"How would I complete the place value grid?" asked Jacob.

So how many hundreds are there? How many 10s? How many ones? There's one 100, there are two 10s, there are eight ones.

100 add 20, add 8 equals 128.

So we've got there 128 represented as base 10 blocks and on place value grid as well.

Match the blocks to the correct place value grid.

We've got there representations of base 10 blocks and place value grids.

Can you match up the correct place value grid with the right representation of base 10 blocks? Pause the video and have a think about it.

And welcome back.

Did you manage to connect them up correctly? Let's have a look, see if you are right.

So our first representation is 131 and that should be linked to the place value grid in the middle.

We've got there 131 represented in base 10 blocks and 131 represented on the place value grid.

In the middle, we've got 113 representative base 10 blocks and that should be connected to that place value grid, 113.

And the last one is 133.

Well done if you connected them up correctly.

Aisha represents a three-digit number.

She uses one 100, she uses zero 10s, she uses two ones.

"How would I complete the place value grid?" says Aisha.

How many hundreds are there? There's 100.

How many 10s are there? There are zero.

We put a zero in there as a place value holder.

And how many ones are there? There were two ones.

So what number has Aisha represented? 100 add 2 equals 102.

Jacob represents a three-digit number.

He uses one 100, he uses eight 10s, he uses zero ones.

"How would I complete the place value grid?" says Jacob.

How many hundreds have we got? There's 100.

There are eight 10s.

And how many ones were there? Zero.

So what number has Jacob represented? 100 add 80 equals 180.

Aisha represents a three-digit number.

She uses zero hundreds, she uses no hundreds, she uses six 10s, she uses seven ones.

"How would I complete the place value grid?" says Aisha.

How many hundreds did she use? She used zero.

She uses six 10s, she uses seven ones.

What number has she represented there? 60 add 7 equals 67.

Complete the place value grids.

So we've got there two representations using base 10 blocks.

How would you complete the place value grids using those? Pause the video and have a go.

How did you get on? Did you get the right answer? Let's have a look at that first one.

In that first representation of base 10 blocks, we've got 105 10s and no ones and we would complete the place value grid like this.

There is one 100, there are five 10s, there are zero ones, and that number there is 150.

In the second representation, we've got 100 and 7 ones.

So we complete the place value grid like this.

There is 100, there are zero 10s, there are seven ones.

That number is 107.

Very well done if you've got those correct.

And let's move on to our task.

So in your first part of task A, you're going to use base 10 blocks to represent the number shown on the place value grids.

So use some base 10 blocks and can you actually create those numbers.

So that first one we've got 100, three 10s and two ones.

And see if you can actually say the number as well.

What would the number be? What three digit number is represented? Circle the correct answer.

So there are three representations there of numbers using base 10 blocks.

Can you work out what number is represented? Pause the video and have a go at your first tasks.

And welcome back.

How did you get on? Did you manage to complete all of the tasks? Excellent work if you did.

So for part one, your answers should have looked like this.

For the first, number 132, you should have represented it as 100, three 10s and two ones.

And here are the next three answers.

So for the first one, we've got 161, and you should have represented that as 100, six 10s and one one.

Very well done if you've got those correct.

And the second part of task A, what number is represented? The first number represented using base 10 blocks is 120.

The one in the middle was 115, not 151, and the last one was 143.

Very well done if you got into that task and managed to complete that.

And let's move on to the second part of the lesson.

So the second part of the lesson is three-digit numbers represented on number lines.

Jacob represents numbers on a number line.

We've got there a number line from 0 to 100.

This number line shows the 10s numbers, 10 10s is equal to 100.

This number line shows the 10s numbers from 100 to 200.

So it's still going up in 10s, still counting up in 10s, but this time the numbers represented on the number line go from 100 all the way up to 200.

Jacob represents numbers on a number line.

What number is represented by the base 10 blocks? So there is a representation of a number using base 10 blocks.

What number is represented? The base 10 blocks represent 140.

Where would 140 be shown on the number line? So not all the numbers are marked on the number line, not all the numbers are shown on the number line.

Can you work out where 140 would be? Well, it should be just before 150.

150 is marked in the number line.

140 is the 10 that comes before it.

So 140 would be there.

Jacob represents numbers on a number line.

What numbers are shown by the arrows? Count on or back from the numbers that are given.

So there's our first arrow.

What number is the arrow showing? We've got some of our 10s numbers.

We've got 0 and 50 marked on there.

So we could count up from 0: 0, 10, 20, 30, or we could count back from 50: 50, 40, 30.

So the number represented is 30.

What number is represented by that arrow? Well, 50 is marked.

Can we count up from 50? So it'd be 50, 60, 70.

So that number is 70.

What about that number there? What number is represented? 100 is marked.

What 10s number comes after 100? Would be 110.

What number is represented this time? We've got 110 marked on the number line now, 120 will come next, and then it will be 130.

And our last arrow, we've got a 200 marked at the end.

There's 200.

What's the 10s number that comes before 200? It would be 190.

If you went too short about that, you could have count it up instead from 150.

Jacob represents numbers on a number line.

"5 is halfway between 0 and 10," says Jacob.

So the number shown there is number five, is halfway between 0 and 10.

The number halfway between 70 and 80 also has five for a one's digit.

So what number do you think would be halfway between 70 and 80? Answer would be 75.

Can you work out what the other numbers are? So you've gotta look carefully at those 10s numbers and think about what number would be halfway between the two 10s numbers.

So what number would go there? What number is shown by the arrow? The number is 115.

What number is halfway between 140 and 150? The answer would be 145.

And our last one, what number is halfway between 170 and 180? The answer would be 175.

Jacob represents numbers on a number line.

"The digits of each number add up to equal 14," says Jacob.

So here we've got the number 167.

The digits of 167 add up to equal 14.

1 add 6, add 7 equals 14.

So what number is represented by the arrow? Remember the digits have got to add up to make 14.

Well, the number is between 50 and 60, so it's got to be a fifties number and the digits add up to make 14.

And this number is much nearer 60 than it is to 50.

The answer would be 59.

9 and 5 equals 14.

What numbers are represented this time? So this time the number is in between 80 and 90 and it's slightly nearer 90.

It's not quite halfway, the number, is it? Slightly nearer 90.

86 is represented.

8 add 6 equals 14.

Let's try another one.

So this time the number is in between 140 and 150 and it's much nearer 150.

So it's 140 something.

The number is quite near 150.

So the answer would be 149.

1 add 4, add 9 equals 14.

You might have spotted there number pairs to ten.

9 add 1 equals 10, add 4 equals 14.

And our last number is this one here.

So this time the number is in between 190 and 200 and slightly near 190.

It's not quite halfway, is it? So it's slightly less than 195.

So the answer would be 194.

And again, 1 add 9 or 9 add 1 equals 10, add 4 equals 14.

Jacob represents numbers on a number line.

"The digits of each number add up to equal nine," says Jacob.

Can you work out what numbers are represented? So there are four arrows pointing at numbers on the number line.

Can you work out what they are? Pause the video and have a go.

See if you work out what they are, remembering the digits of each of the numbers adds up to equal nine.

Welcome back.

Did you manage to work out what the answers are? Let's see if you were right.

So the first number was in between 80 and 90 and it's definitely nearer 80, isn't it? So the answer should be 81.

8 add 1 equals 9.

The next one was in between 110 and 120 and it's nearer 120.

And remember, of course, the digits that got to add up to make nine.

The answer should be 117.

The next number was in between 140 and 150 and it's slightly nearer 140.

So the answer would be 144.

Four add four equals eight, add one equals nine.

And our last number is a number in between 160 and 170.

And it's quite a lot near 160.

The number is 162.

Very well done if you've got those correct.

Number lines can also be used to measure volume.

So here we've got two measuring jugs with an amount of liquid inside them.

The scale counts up in 10s and you can see there the 50, 100, 150, and 200 are marked on the scale.

The volume of the first jug is 110 millilitres.

The volume of the second jug is halfway between 80 millilitres and 90 millilitres.

And halfway between 80 and 90 is 85.

So the volume of that second jug is 85 millilitres.

What is the volume of each jug? So how much liquid is in each jug? So that first jug, there's more than 150, less than 200.

We can count in 10s to work out how many millilitres of liquid there are in the jug.

So we've got 150, 160, 170, 180.

So that first jug, we've got 180 millilitres.

The second jug, well, it's between 100 and 150.

So this time we can count up from 100.

So 100, 110, 120.

So the second jug is 120 millilitres of liquid inside it.

The third jug, a little bit trickier this one because the liquid isn't on one of the 10s numbers, it's actually in between two of them.

So you could start from 100 and count up, or you might know, of course, that 140 is 10 less than 150.

The amount of liquid is halfway between 140 and 150.

So the amount of liquid in the jug would be 145, 145 millilitres.

Here's one to try on your own.

Which jug contains 105 millilitres of liquid? Pause the video and work out the answer.

And welcome back.

Let's see if you were right.

Was it A, was it B, was it C? Which one do you think it was? It was B.

B has 105 millilitres of liquid inside it.

Number lines can also work as scales to measure mass.

We've got a panda sitting on the scales and this time, we're measuring mass in kilogrammes.

The circular scale counts up in 10s.

This represents 30 kilogrammes.

This represents 140 kilogrammes.

This represents 190 kilogrammes.

What is the mass of the giant panda? The mass of the giant panda is 90 kilogrammes.

Number lines work as scales to measure mass.

What is the mass of the giant pandas? So the first giant panda, you can see there that the mass is greater than 150 and in fact, it's the next 10s number after 150.

The answer would be 160, 160 kilogrammes.

The second giant panda, the arrow is also indicating, is also pointing to a 10s number.

So the mass of the second giant panda is 130 kilogrammes.

Number lines worker scales to measure mass.

This time the arrow is showing a number halfway between two 10s numbers.

So this time, can you work out the mass of the giant pandas.

So our first giant panda, the mass is 85 kilogrammes.

The number there is halfway between the 80 and 90.

Our second giant panda, the mass would be 135 kilogrammes.

The mass would be halfway between 130 and 140.

What is the mass of the giant panda? You've got there four options.

Is the mass of the giant panda 115 kilogrammes, 125 kilogrammes, 105 kilogrammes or 120 kilogrammes? Pause the video.

What do you think the answer is? And welcome back.

Did you manage to get the answer? Which one do you think it was? Let's see if you were right.

The answer is 115 kilogrammes.

Let's move on to task B.

So the first part of task B, label the arrows on the number lines.

The digits of each number below add up to equal 13.

Each of the numbers shown on the number line, the digits of the number add up to equal 13.

And the second part of task B, how much liquid is in each jug? So for each jug, can you work out the amount of liquid inside it by using the scale and try and be as accurate as you can be.

The third part of task B, work out the mass of each giant panda.

The digits of each panda's mass adds up to equal 10.

So when you work out the mass from the scale, the digits of the mass have got to add up to equal 10.

And then part four links to part three.

So using those same four pandas, you have to work out which panda is which.

They've all got names of the pandas.

Can you work out which one is which? Write their names underneath their mass.

So Piper is heavier than Pablo, Percy is lighter than Polly and Polly is lighter than Pablo.

Can you work out the names of the pandas? So pause the video and have a go at task B.

And welcome back.

And let's see how you got on with those tasks.

The digits of each of the numbers had to add up to equal 13, so you should have got the answers 49.

9 add 4 equals 13.

85, 8 and 5 equals 13.

139, 157 and 184.

Very well done if you've got those correct.

Part two now is a bit tricky, this one.

So your answers may not have been exactly the same as these, but they should have been very, very close.

So the first one you can see it's halfway between 60 and 70.

The answer should be 65 millilitres.

And then the next one would be 175 millilitres.

Next one was a bit tricky, but it was definitely near 100 than it was to 110 and it certainly wasn't halfway.

So you should have got about 102 millilitres.

And the last one, so 188 would've been a very good answer for that one.

And here are the answers for part three and four of task B.

So there are the pandas' masses and their names as well.

So Pablo was 118 kilogrammes, Polly was 109 kilogrammes, Percy was 82 kilogrammes and Piper was 136 kilogrammes.

So well done if you got onto part three and four and you managed to work out the masses of the giant pandas and their names as well.

And excellent work today.

Very well done indeed, and I hope you're feeling a lot more confident at representing numbers on number lines and using base 10 blocks to represent numbers as well.

And let's look at our lesson summary.

So place value tells you the worth of each digit.

Three-digit numbers can be represented using base 10 blocks.

Number lines can also represent three-digit numbers.

Use the 10s intervals and the halfway points as the five numbers.

So for example, 135, 165, to help estimate other numbers.

Number lines can also be used for measurements.

For example, you can use 'em to work out capacity and mass.