Lesson video

Hello, how are you today? My name is Dr.

Shorrock, and I'm very excited to be learning with you today.

I know we're gonna have a lot of fun as we move through the learning together.

Today's lesson is from our unit: Order, compare, and calculate numbers up to eight digits.

This lesson is called Compare Numbers with Up to Eight Digits.

As we move through the learning today, we are going to deepen our understanding of how we compare numbers that have got a different amount or the same amounts of digits, and we're going to build on your prior learning with smaller numbers.

Now, sometimes new learning can be a little bit tricky, but that's okay because I'm here to guide you and I know if we work really hard together then we can be successful.

Let's get started then, shall we? How do we compare numbers with up to eight digits? These are the keywords that we will use throughout our learning today.

We have compare and inequality.

Now it's always good to practise saying words aloud, so let's have a go together.

My turn, compare, your turn.

Nice, my turn, inequality, your turn.

Fantastic.

When we compare numbers we're determining whether a number is smaller than, greater than, or equal to another according to similarities and differences in their values, and an inequality, well, that compares values, and is used to show that one number is not equal to another, and we use those smaller than or greater than signs to show if something is less than or more than each other.

So let's get started with our learning today.

We will start by comparing numbers with a different amount of digits, and we have Aisha and Lucas to help us throughout our learning today.

So Aisha and Lucas are comparing the mass of their favourite animals.

I wonder what your favourite animals are.

Aisha has chosen a polar bear and has done some research and found out that it has a mass of about 650,000 grammes.

Lucas has been doing some researching and found out the mass of his favourite animal, an elephant, and an elephant has a mass of about 5,400,000 grammes.

And when we compare amounts, we use the inequality symbols, the less than or more than, or sometimes if they're exactly the same we would use the equals symbol, and Aisha can never remember which inequality symbol to use.

What about you, do you have a way to help you remember? Ah, Lucas is going to help us.

What's your idea Lucas, how can we remember? "The smaller end, the tip points towards the smaller value." Ah, that's quite a good way to remember, isn't it? "That must mean the larger, opening end points towards the greater value.

Let's look at a simple example.

You can see here, three is greater than two, so looking at that inequality symbol, the large opening of the symbol faces the three, and two is less than three, so the smaller end or the tip of the inequality faces the two.

"And we can read left to right like we would in a book.

and we can say that three is greater than two, but also we could read right to left and say two is less than three." Great advice for us you two, thank you.

Aisha, She can now remember which inequality to use.

I wonder if you can now as well.

So Aisha and Lucas compare the mass of their favourite animals, and Aisha is saying, "The mass of the polar bear is larger at 650,000 grammes," she's saying is larger than 5,400,000 grammes." Why do you think that? Oh, that's because she's saying, "The number starts with a greater digit.

The 6 in 650,000 is greater than that digit 5, isn't it?" What do you think? Do you agree with Aisha? Ah, Lucas is challenging her.

Why might Lucas challenge Aisha do you think? "When we compare numbers, we need to look at the value of the digits." Ah, that's right, not just what the digits are, but their value.

"The value of the digit 6 is 600,000" "But the value of the digit 5 is five million, which is greater than." That's right, 5 million is a greater value than 600,000.

So the mass of the elephant is greater.

So we can use our inequality symbol, remember that tip is pointing towards the smaller valued number, 650,000 is smaller than or is less than 5,400,000.

"The mass of the polar bear is smaller." So let's look at this inequality in more detail.

We could read from left to right like we do in a book.

650,000 is less than 5,400,000, but we could read the other direction and say that 5,400,000 is greater than 650,000.

What do you notice? Is there anything you've noticed about these two numbers? That's right, "The numbers have a different amount of digits." 650,000 has six digits, 5,400,000 has seven digits.

And here, the number with the most digits was larger, wasn't it? The seven-digit number 5,400,000 was larger.

And so that's led Lucas to the conclusion that, "Numbers with more digits are larger." Do you agree with Lucas? "Is that always true or is it just sometimes true?" What do you think? "It's usually true." Why is it only usually true, when might it not be true? When might a number with a smaller amount of digits be greater? Ah, yes, "If we have a decimal fraction number, it might have more digits, but it could have a smaller value." Let's look at an example.

So here, we've got 12,945.

32, well, that's smaller than 37,905.

The fractional number has got more digits, but it is smaller, it has a smaller value, it only has 12 thousands.

The number that's not got a fractional part has got 37 thousands.

Let's check your understanding with this.

Could you fill in the missing symbols, less than, more than, or equal to, for the given numbers? Pause the video while you do this, you might like to compare your answers with a friend, and when you're ready to hear the answers, press play.

How did you get on? Did you say 34,601 is less than 341,670? Did you say 1,456,903 is greater than 945,903? And 13435.

33, well, that's less than 45,370.

And you might have noticed that when we compare numbers, it is important to look at the value of the digits, not just how many digits that number has.

How did you get on with those? Well done.

Let's check your understanding further.

Could you complete the sentences describing this inequality? So reading left to right, and then reading right to left.

Pause the video while you have a go, and when you are ready to go through the answers, press play.

How did you get on? Did you say that 34,601 is less than 341,670? But we could read it the other way and say 341,670 is greater than 34,601.

How did you get on? Brilliant.

It's your turn to practise now, for Question 1, could you fill in the missing inequality symbols for these equations? For Question 2, could you put these numbers in ascending order, so that's smallest to largest? For Question 3, could you look at this set of numbers? And Lucas says, "That 82,804 is the greatest out of them all because it starts with the highest digit." Do you agree, and could you explain your answer? Pause the video while you have a go at those three questions and when you are ready to go through the answers, press play.

How did you get on? Let's have a look.

For Question 1, you were asked to fill in the missing inequality symbols.

6,090,100, well that's greater than 690,100 'cause you've got the 6 million.

589,940, well, that's less than 1,010,222 because you've got that 1 million there.

99,000, well, that's smaller than 600,000 because 99 is smaller than 600.

1,300,610, well, that's greater than 140,017 because you've got that 1 million.

13,450.

6, well, that's smaller than 31,600.

It may have more digits, but we've only got 13 thousands.

The number on the right has 31 thousands, so it is the larger number.

8,000,120, well, that's greater than 999,999 because there are no millions there, so we've got 8 million is the larger number.

214,390.

5, well, that's greater than 141,399 because 214 is greater than 141.

2,150,025, well, that's greater than 225,025 because it's got that 2 million.

Question 2, we're asked to put these numbers in ascending order, so smallest to largest.

We've got 8,304.

99, it's only got 8 thousands.

Then we've got 81,304.

Then we've got 821,304, and finally, we've got 8,102,304.

For Question 3, you were asked to look at this set of numbers, and Lucas says that, "82,804 is the greatest." You might have said that you disagreed and explained that when we compare numbers, we need to look at the value of the digits.

Just because it's got an eight as its first digit in its number, does not mean it's the largest, we have to look at the value of the digits.

The value of the digit 8 in 82,804 is 80,000, whereas the value of the digit 7 in 782,548 is 700,000, and the value of the digit 5 in 5,963,931 is 5 million.

And this means that 82,804 is not the greatest, just because it started with an eight.

How did you get on with those questions? Well done.

Let's move on to the second part of this lesson today, when we're going to start to think about how we compare numbers with the same amount of digits.

So Aisha and Lucas are comparing numbers that they have typed into a calculator.

Aisha has typed in the digit 6352783, and Lucas has typed in 6357283.

What do you notice about their numbers? Ah, okay, so to help us read these numbers, let's pop that separator comma in, and Aisha has noticed something after they've done that, so we've got 6,352,783, and 6,357,283.

Do you notice something? Both these numbers have the same amounts of digits.

That's right, they do, don't they? So how are we going to compare them? "Let's start by looking at a simpler case." That's really important in maths, if something's a little bit tricky, let's take it back and look at a simpler case, and build our understanding first on a smaller number.

We can start at the left and we need to determine which is the largest place value digit that is different.

So you can see, they've both got 4 10 thousands or 40,000.

They've both got five thousands, but can you see that we need to compare then the hundreds digits? "This is the largest place value digit that is different.

The value of the digit 3 is 300, and the value of the digit 2 is 200.

So that means 45,301 is greater than 45,261." And then we can use our inequality with the large opening end at the side of the larger number.

45,301 is greater than or is more than 45,261.

"We can also remember read it the other way round and say that 45,261 is less than 45,301." And we could write the inequality that way around as well to compare the numbers.

So let's revisit our original numbers, now we've done the learning with a simpler case.

Remember, we need to start from the left and look for the largest place value digit that is different, So they've both got six millions, they've both got 300,000, they've both got five in the 10 thousands, ah, so the largest place value digit that is different is the thousands digit.

"The value of the digit 2 is 2,000 and the value of the digit 7 is 7,000." So which number is bigger than, do you think? We can say that 6,352,783 is less than 6,357,283.

But we can also read this inequality the other way around, and say that 6,357,283 is greater than 6,352,783.

So how do we compare those numbers? Well, we had to look for that largest place value digit that was different.

Let's check your understanding with that, true or false? 3,459,230 is that greater than 3,459,324? True or false? Pause the video while you have a think about that, and when you're ready to for answer, press play.

How did you get on? Did you say, well that must be false, but why is it false? Is it because both numbers have the same amount of digits, so we need to compare the largest place value digit that is different.

This is the hundreds place, 3,459,230 is less than 3,459,324.

Or is the reason, both numbers have the same amount of digits, So we need to compare the smallest place value digit that is different? This is the ones place.

So 3,459,230 must be smaller than 3,459,324 because zero is smaller than four.

Pause the video while you think about the reason and when you are ready to hear the answer, press play.

How did you get on? Did you say it's the first answer, A? Both numbers have the same amount of digits, so we need to look for that largest place value digit that is different.

In this case, it was the hundreds place because they both had 3 millions, they both had 400 thousands, they both had 50 thousands, they both had 9 thousands, it was the 100s digit that is the largest place value digit that was different, and 2 is smaller than 3.

How did you get on with that? Well done.

Your turn to practise now, could you for, Question 1, fill in the missing inequality symbols in these equations? For question 2, could you put these numbers in ascending order? So that's smallest to largest.

For Question 3, there's a problem to solve.

Question 4, look at the given digit cards and the inequality.

How many ways can you rearrange the digit cards so that the inequality is true? Pause the video while you have a go at those four questions and when you are ready to go through the answers, press play.

How did you get on? Let's have a look.

For Question 1, you were ask to fill in the missing inequality symbols.

So we've got 7,142,294, it must be more than 7,124,294.

If we look at the place value digits, the first place value digit that is different is the 10 thousands and 4 is greater than 2.

2,140,041, well, that must be less than 2,140,410, but this time, we were looking at the hundreds digit and zero is less than four.

1,104,569 is less than 1,204,569.

Here, we were looking at the hundred thousand digit, and 1 is less than 2.

1,300,610 is less than 1,310,610.

Here, it was the ten thousands place we were looking at and zero is less than one.

2,194,528 is less than 2,194,582, Here, which digit is it that we're looking at? That's right, it's the 10s digit and 2 is less than 8.

3,069,125 is greater than 3, 69,123.

Here, the largest place value digit that was different was actually in the ones column, so we had to look at the 5 and the 3 and 5 is greater than 3 9,999,990 well, that's greater than 9,999,909.

We were looking at the tens digit here and 9 is greater than 0.

3,150,361 is greater than 3,140,361.

And here it was the ten thousands digit that was different, and so 5 is greater than 4.

For question 2, you were asked to put these numbers in ascending order, so smallest to largest.

The smallest had six millions, then we had seven millions, and that number is smaller than the second 7 million number because we've got 7,104,004 and 4 is smaller than 7,105,000, that 5,000 there.

Then we had 7,105,490, that's larger than the previous number because we've got nine tens rather than zero tens, and then we have 8,104,409.

For Question 3, you had to solve a problem about a postman delivering letters.

You might have noticed that both numbers have the same amount of digits and both have 100 thousands.

So we had to compare the largest place value digit that was different, and this is the hundreds digit.

The value of the 3 is 300, and that of the digit zero is zero hundreds.

So 100,312 must be greater than 100,052.

So the postman delivered more letters in the first week.

For Question 4, you had to look at the given digit cards and the inequality, and think of how many ways you could rearrange the digit cards so the inequality was true.

So that 4 million and something was less than something.

So you might worked in a systematic manner, like I did.

I'll show you all the different options that I came up with.

I wonder if you managed to work systematically and find all of those options.

Brilliant, well done.

Fantastic learning today, really proud with the progress that you have made with comparing numbers with up to eight digits.

We know the number of digits can help when ordering numbers, and it's usually the more digits, the greater the number, usually, unless there's fractions involved.

We know when comparing numbers, the greatest value digit that is different determines the greater number, and we can use the stem sentence to help us.

The value of the digit in the mm column is mm, and that supports us to compare numbers.

So really well done today, you should be proud of how hard you have worked.

I look forward to learning with you again soon.