Lesson video

Hello everybody, and welcome to today's math session.

My name is Miss Hughes.

And today we're going to be learning about comparing numbers within 100 on a number line.

So, let's get going.

For today's lesson, you're going to need a pencil, some paper, and some countable objects to represent tens and ones.

Please pause the video now to go and get these things, if you haven't got them already.

Brilliant, so in our lesson agenda for today, we are going to start off our new learning by understanding numbers on a number line.

Then you are going to have a talk task that focuses on this.

Next, we're going to develop our new learning by comparing three two-digit numbers on a number line, and you'll have an independent task to complete.

Finally, you'll have a quiz to complete, to see how much fantastic maths learning, you have remembered from today's lesson.

I want to begin our lesson today with a bit of a Brain Teaser.

Can you work out the numbers that are hidden behind the smiley faces on this number grid? And when you do that, what patterns do you notice for the numbers behind the blue faces, and the numbers behind the green faces? Pause the video now to give this task a go, and resume the video when you're ready to continue.

Okay, so I know that my numbers on this grid are increasing or going up by one, because I can see here 52, 53, 54, all increased by one each time.

That means that my numbers must be, 51, 55, 57, 59, 63, 67, 69, 71 and finally 75.

So, those are my numbers that were hidden behind my smiley faces.

Remember, there was a second question though.

Did you notice the pattern about the numbers behind the green and blue faces? Hmm.

Well, the parts that I noticed was that my blue numbers both end in the digit seven, and my green numbers, both end in the digit nine.

You might have already also noticed that they line up twos.

So, 57 lines up really neatly with 67 and 59 and 69 also line up.

Now, that our brains are all warmed up from our brain teaser, we're ready to think about numbers on a number line.

Let's count the numbers on our number line, as you can see, my number line is going up in jumps of 10.

So, let's get the count in tens from zero.

Zero, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

When I count up in tens, each number is getting greater by 10.

Let's do the same, but this time counting backwards from 100.

100, 90, 80, 70, 60, 50, 40, 30, 20, 10, zero.

Hmm, that time did you notice that my numbers were getting 10 less than the number before? S0, it seems that when I'm counting this way up my number line, my numbers are increasing, but when I count backwards down my number line, my numbers decrease, they get less and less.

This time let's start at five and we'll count in tens.

Each number will get 10 greater than the one before.

So, let's starts going five 15, 25, 35, 45, 55, 65, 75, 85, 95.

So once again, when I was counting each number, got 10 greater than the one before.

My numbers increased or got greater as I went up my number line.

But if I count backwards from 95 here all the way down in tens, 95, 85, 75, 65, 55, 45, 35, 25, 15, five.

Hmm, when I count this way, in tens, my number gets 10 less than the one before.

So, when I count up my number line, my numbers are increasing in value.

They're getting greater, but when I count backwards down my number line, my numbers are decreasing in value.

They're getting less.

Here, my numbers are getting 10 less than the number before.

Probably the further a number is from zero, if I was to count my number and up this way, and get further and further away from zero, the greater my numbers get.

So, the further numbers from zero, the greater its value.

However, when I'm counting backwards towards zero, the closer a number is to zero, the less its value.

So, the numbers that are closer to zero, are much smaller in value, have a lesser value.

Then my numbers that are further away from zero.

Now that we know this important rule, we can use it to help us compare two numbers on a number line.

For example, which number is greater, 31 or 13.

I'm going to start by marking each number on the number line.

I know that 13 must go here on my number line, because 13 is made up of one jump of 10 and three ones.

So, 10, 11, 12, 13.

So, 13 belongs here.

31 would go here on my number line, because it's made up of three tens, 10, 20, 30, and one, one, 31.

Now, that I've marked my numbers on my number line, I can see clearly which number is furthest away from zero.

31 is furthest away from zero.

Therefore, its value is greater than 13, because 13 is closer to zero than 31, the value of 13 is less.

Therefore, 31 is greater than 13.

I've made both of my numbers, 13 and 31 on bead strings.

Just to help us compare our two numbers.

It's important when we've got beads string representations, just to count on numbers to make sure they're correct.

So, let's quickly count that now.

10, 11, 12, 13.

So, this bead string represents 13, 10, 20, 30, one.

So, this beads string represents 31.

Just from looking at my bead strings, we can see from the representations that 31 is much greater than 13, because it's got more beads.

You can see that it is longer as well.

So, we can tell that it has the greater value.

So, 31 is greater than 13, Let's have a look at another one, which number is greater, 47 or 42.

So, I'm going to start by marking each number on the number line, because remember the further a number is from zero, the greater its value, and the closer a number is to zero the less it's value.

So, by putting my numbers on a number line, I can see how far away it is, compared to the other number to zero.

So, I know that 42 has to go here on my number line, because it's made up of four tens.

So that's 10, 20, 30, 40, and two ones, 41, 42.

47 which go here on my number line, because it's made up of four tens again and seven ones, one, two, three, four, five, six, seven.

So, I've put my two numbers on one number line.

And now I can see very clearly, which number is the furthest away from zero.

These numbers are really close together on the number line.

However, 47 is further away from zero.

Therefore, it's value is greater than 42.

Because 42 is closer to zero than 47, the value of 42 is less than 47.

Therefore, 47 is greater than 42.

42 is less than 47.

Here I've my bead string representation that we can use to double check.

So, let's just count them quickly.

10, 20, 30, 40, 41, 42.

So, this bead string represents 42, and this bottom one let's count them.

10 20, 30, 40, 41, 42, 43, 44, 45, 46, 47.

I can see from my two bead string representations that this one, the one that represents 47, is longer and has more beads.

Therefore, we know that its value is greater than 42, which has less beads.

So, 47 is greater than 42.

We're going to have a go at just one more now.

So, which number is greater, 23 or 73.

And I've got my rule here to remind me.

So, remember I start off by marking my numbers on the number line.

So, 23 goes here and 73 goes all the way over here.

So, now that I've marked my numbers on a number line, I can see clearly which one is further away from zero and therefore greater.

23 is closest to zero, that means that the value is less.

73 is furthest away from zero, and that means it's value is greater than 23.

Here are my bead strings, just to double check.

I've got my bead string here that represents 23.

And my bead string here that represents 73.

You can see very clearly that 73 has many more beads and is therefore greater in value.

So, 73 is greater than 23.

In today's talk task, you are going to be comparing two, two-digit numbers like these ones, 82 and 22 that you can see on the board.

And you're going to follow these four steps to help you to compare them and decide which one has the greater value and why.

The very first two things that you need to do for this talk task is make these two numbers.

So, I'm going to make a representation of 82 and 22.

Now on our new learning, we did this on a number line.

So you could if you have a number line at home, make the numbers by finding them, where they fit on the number line.

I also made numbers on a bead string.

So, if you have a beat string, you can do that too.

If you have neither of these, that's okay.

In this particular talk task, I'm going to use countable objects in a place value chart, to represent my digits.

So, let's do 82 first.

82 has eight tens.

So, I'm going to put eight tens in there and two ones.

Now, I'm going to make 22.

It has two tens and two ones.

So, now I've represented my two numbers.

I can start to think about comparing them.

To do that, I'm going to use some sentence structures, which I would like you to do when you come to do your task.

So, the first one is 82 is greater than 22.

In my representation, 82 has eight tens, but 22 only has two tens and eight is greater than two.

82 is further away from zero than 22.

22 is less than 82.

In my representation 22 has only two tens, but 82 has eight tens and two is less than eight.

22 is closer to zero than 82.

Therefore, 22 is less.

Okay, so you are going to compare each of these pairs of numbers now, following these steps like I have done, and using these sentence structures to help you explain which number is greater and why, and which number is less and why.

So, pause the video now to have a go at this task, and press play when you're ready to continue.

Okay, welcome back, team.

Let's go through some of these answers then.

So, the first two numbers that you've got are 17 and 71.

71 is greater than 17, because 71 has seven tens, but 17 only has one ten.

And seven tens is greater than one ten 71 is farther away from zero than 17.

17 is less than 71, because 17 has only one ten whereas 82 has, sorry, 71 has seven tens.

And one is less than seven.

17 is closer to zero than 71.

Okay, so that was my explanation for those two, I'm going to quickly find through these ones now.

39 is greater than 32, 32 is less than 39.

And I can see this because they've got the same number of tens.

If we look at the ones, nine is greater than two.

So, 39 is the greater number.

97 is greater than 47, 47 is less than 97.

And I can see that because we're looking at the tens column.

Four tens is much less than nine tens, nine tens has a greater value.

54 and 45, I can see that 54 is the greater number, and five is less because 54 has five tens, which is more than four tens, which 45 has.

In our Develop Learning session of our lesson, team.

We're going to have go at comparing three, two-digit numbers to help us solve problems. So, our problem is on the board here.

It says Antonio, Bella and Carlos empty their piggy banks.

Antonio has 27 pence, Bella has 72 pence, and Carlos has 49 Pence.

Who has the most money and who has the least money.

So, what we are trying to work out is, who has the greatest amount of money, and who has the smallest amount of money.

And we want to think about of these three numbers, what strategies we could use to compare them, to help us solve this problem? Hmm, I know we could make our numbers by representing them in tens and ones.

Like we did in our talk task.

Oh, we could mark the numbers on a number line and see which one is further from zero.

Just like we did in our new learning.

Let's try finding our numbers on a number line first.

Remember when comparing numbers on a number line, the further number is from zero, the greater its value.

The closer the number is to zero the less it's value.

Let's think about the information we already know that's going to help us solve this problem then.

So, I've underlined the important information in our question.

We know that Antonio has 27 pence.

Bella has 72 pence and Carlos has 49 pence.

So, these are my three numbers that I am going to compare.

So, let's find our numbers on the number line then.

27 is going to go here.

72 goes over here on the number line, and 49 belongs here on the number line.

Great, so now that we found our numbers on our number line, we can see which is the greatest and which is the smallest, by looking at how far away it is from zero.

I can see that 72 is furthest away from zero, than all of the numbers.

So, that means it's the greatest.

Remember, Bella had 72 pence.

So, it's Bella that has the greatest or the most money.

27 is closest to zero.

So, that means that it is the least, or it's value is less.

Antonio is the person that had 27 pence.

So, he's the person that has the least amount of money.

That's how we go about solving another one.

In this one, the three little pigs are comparing how many sticks and bricks they have, who has the most sticks or bricks.

That's what we want to figure out.

So, we want to find out which little pig has the greatest number of sticks or bricks.

From the picture, I can see that the pigs have organised very neatly their sticks and bricks in groups of tens and ones.

So, they're going to be quite easy to count.

Let's count how many they've got altogether.

And then we can start to compare, the numbers of sticks and bricks.

So, 10, 20, 30, 40, 41, 42, 43, 44, 45, 46.

So, this little pig that has 46 bricks, 10, 20, 30, 31, 32, 33, 34, 35.

This little pig has 35 sticks, and 10, 20, 30, 31, 32, 33, 34, 35.

Oh, this little pig has 35 bricks.

Brilliant, so now that I found out how much, or how many bricks and sticks each pig has got, and I've got my three different numbers now to compare, I can think about comparing them.

I'm going to mark these numbers on a number line so that I can see which one is further away from zero.

Remember, the number that is furthest away from zero, is the one with the greatest value.

And we're looking for that number, because we want to know who has the most.

So, we're looking for the greatest value.

So, our first pig has 46 bricks, which is here on my number line.

The pig in blue trousers has 35 sticks, which goes here on my number line.

So, 10, 20, 30, 31 32, 33, 34, 35.

And the pig in purple trousers has 35 bricks, which goes 10, 20, 30, 31, 32, 33, 34, 35.

Oh, it will go in exactly the same place as the number of all this pig's sticks because 35 and 35 are the same.

But I can see they have the same number of sticks and bricks.

Hmm, now we found our numbers on our number line, we can start to compare them.

I can see that 46 is the furthest away from zero.

Therefore, the first pig in red trousers has the most sticks or bricks.

35 is closest to zero, so the other two pigs have the least number of sticks and bricks.

In fact, the pig with blue trousers has 35 sticks and the pig with purple trousers has 35 bricks.

So, therefore the number of sticks is equal to the number of bricks.

Their amount of items is exactly the same.

Let's have a look at this in more detail.

So, this number of sticks, that one of the pigs had, is equal to this, oh sorry, this number of sticks is equal to the number of bricks, that another of the pigs had.

In other words, the number 35 is equal to the number 35.

This is how we would write it as an equation.

35 is equal to 35, using our equal sign to show that they are the same.

They mean the same thing.

Neither is greater or less than the other, because they are equal.

Right, team, it's time for our independent task now.

In this task, you are going to solve the problems, by marking numbers on a number line and comparing them to decide which one is greater, and which one is less.

For this first independent task, you're going to need to count the numbers of items each person has and write them in each blank, because then you will have an amount that you can compare.

Just like we did with our three pigs example.

Then to each mark the three numbers on the number line to help you decide who has the most or least of the given items. Check your answers on a bead string or by making each number of tens and ones, by making the smallest number, then the middle value and finally the greatest value.

And this is helpful to see in our representations, which number is greater.

Once you've completed that task, the second independent task you're going to do exactly the same, except this time, you're going to tick the true statements.

So, tick the statements here that tells true.

Finally, in this third task, I would like you to use the digit cards that you can see on the screen, to create the smallest two-digit number that you can.

And the greatest two-digit number that you can.

Can you also try and make a number that is less than 50, or a number that is less than 30? That's your challenge for today? Right guys, so pause the video now to complete your three independent tasks.

And resume the video, once you're finished and you're ready to continue.

Welcome back team, an excellent job in your independent tasks.

Let's go through the answers.

So, in this first task, you had to compare the different amounts of bricks.

So, if you counted Alan, you would have noticed had 55 bricks, Bert has 25 bricks, and Charlie has 35 bricks.

So, now that we found out how many bricks each person has, we can compare them on the number line.

So, 25 should go here.

35 should go here.

And 55 should have gone here.

I can see that 55 is the greatest value, because it's furthest away from zero.

Therefore the person who has the most bricks is Alan, because Alan has 55 bricks.

The person who had the fewest bricks is Bert, because Bert only had 25 bricks.

And we can see from our number line, the 25 is closest to zero.

So, therefore it has the smallest value.

Okay, in this next example, Daniel has 12 sticks, Eleni has 12 sticks and Faris has 52 sticks.

So, what I should've done was find those on my number line, which I have done here.

And you'll notice that 12 and 12 go in exactly the same place because they are equal.

Now, that we found our two numbers on our number line, we can tick some true statements.

So, let's read them.

Eleni has fewer sticks than anyone else, hmm.

Well, Eleni does have fewer sticks and Faris because she's got 12 sticks and that's closer to zero.

So, it's got a smaller value.

However, Daniel has the same amount, he has 12 sticks.

So, she's not got fewer than Daniel, because they have the same amount.

So, that is not true.

Faris has the most sticks, that's true.

So, I'm going to tick that box.

Faris has 52 sticks, which we saw on our number line is furthest from zero.

So, it has the greater value.

Daniel has an equal number of sticks to Eleni.

Is true as well.

So she'd take that because they both have 12 sticks, and they are equal.

Finally, your third and final task, you're asked to create the smallest two-digit number and the greatest two-digit number out of these number cards.

So, the smallest number you could have had was 13.

That was the smallest number that you could possibly make out of these digit cards.

The largest number that you could have made was 97.

And then you were asked to make numbers greater than, sorry, make a number greater than 50, or make a number less than 30.

So, these were all of the numbers that were less than 30.

I've realised that I've what I've done is put all of the numbers that are less than 50.

However, some of the numbers you could have had that were greater than 50 were, 61, 63, 67, 69, 71, 73, 76, 79, 70, sorry, 91, 93, 96, 97.

And those are the numbers that you could have had that were greater than 50.

Team, that's the end of our lesson for today.

I'm really impressed with the way that you persevered with comparing two-digit numbers.

So, great job.

And I look forward to seeing you on another math session, very soon, bye bye.

Okay guys, you know what to do, so, when the video has ended, don't forget to go and complete the quiz, just to remind yourself everything you've learned in today's lesson, and recap your learning, good luck.

If you'd like to, please ask your parents or carer to share your work on Instagram, Facebook, or Twitter, tagging @OakNational and #LearnwithOak.