Lesson video

Hello, I'm Mrs. Hawthorne.

You've made a great choice to be learning math with me today.

I'm really excited to be guiding you through this lesson.

Welcome to our lesson about integer place value, which is part of the Place Value unit.

By the end of the lesson, you'll be able to create integers that meet certain conditions, using your knowledge of place value.

What do you already know about place value? The keywords we'll be learning about today are digit and integer.

We will explore these in more detail in the lesson.

Today's lesson is split into two parts.

We're gonna check that you're familiar with some of the representations and knowledge that will be important for this unit.

So we're gonna start by reviewing integer place value.

And in the second part of the lesson, we're gonna look at using that knowledge to solve some problems around place value, creating integers given certain conditions.

So let's get started with part one.

Let's begin with a question.

What is the same and what is different about these two integers? Pause the video and have a think.

Welcome back.

You may have said things like, "One is larger than the other." You may have said that they both have the same digits or the same numbers.

We call those digits.

So the first number has the digit one, the digit two, and the digit three in that order.

The second number has the digit one, the digit two, and the digit three, but not in the same order.

So you might want to say they have the same digits using one of our keywords from today.

The digits are the symbols we use in our number system.

So in our number system we use the digits zero, one, two, three, four, five, six, seven, eight, nine, and zero.

Let's have a look at these numbers using a representation.

Here's the first number represented using base 10 blocks.

If we read the number out loud, it is the number 123.

You'll notice that in the question I called it an integer.

An integer is a whole number.

So another way of saying the number 123 is saying it's the integer 123.

From the representation you can see it's made up of one 100, two tens, and three ones.

Each digit corresponds to its place value so we can see what each digit is worth in that number.

In the second number on the screen, this is how it would would be represented.

So you can see now that it looks different.

Even though the digits are the same, the number itself looks different.

That's because this time the digit three is now in the hundreds column.

That means it's worth three hundreds which you can see represented at the bottom.

Then you can see two tens, and one one.

This is a number 321.

Let's look at a different way to represent this number.

I'm going to show this integer in a place value chart.

To do that, I'm going to use counters to represent how many hundreds, how many tens, and how many ones this number has.

This number has 100, two tens, and three ones.

So I've drawn one counter in the hundreds column, two counters in the tens column, and three counters in the ones column.

Now it's your turn.

Can you show this integer in a place value chart? Pause the video while you have a go.

Welcome back.

I wonder what you wrote.

Hopefully you wrote that there are three hundreds.

The digit three is now in the hundreds column, so that represents three hundreds.

There should be three counters in that column.

In the tens column there is the digit two.

So we use two counters to represent the two tens.

And finally we have one one which is represented by one counter.

Let's look at larger numbers in the place value chart, we are going to represent the number 32,910,374.

Here we need a much larger place value chart.

We've start at a hundred millions and down to the ones.

Let's represent the number 32,910,374 in this place value chart.

I'm going to start with the 32 million.

I can see where my tens of millions and my millions column is.

So I need three in the tens of millions, that's the 30 million and two in the millions column, that's my 32 million.

Then I need 910,000, so that's 900,000.

So nine in the a hundred thousands column and one 10,000.

So I need one in the ten thousands column.

After that, it says 374.

Now my hundreds column needs three for the 300.

I need seven in my tens column as 70 is seven tens and I need four ones.

Now I have the 374.

So altogether I have my 32,910,374.

When we write this out as an integer in digit form we need to remember that there is a place value column, the thousands column, which has no counters.

That doesn't mean we leave it out when we write our number.

So we write this as 32,910,374.

Remembering to use a zero as a placeholder for the thousands column.

Now it's your turn, which is the correct way to write the integer that is represented in this place value chart? Pause the video while you choose your option.

Welcome back.

Which one did you go for? This is the correct answer.

This is 145,307.

We can see that the zero has been used as a placeholder as there are no counters in the tens column.

You might have thought that c was also a valid option, but we don't use zeros when they don't preserve the place value of other digits.

The zeros in the option c are not needed to read the number correctly.

However, in b, if we didn't include the zero for the tens column, we get a very different integer.

We get the integer 14,537.

That is not the integer that is represented.

It's not the same as 145,307.

So that zero has made a difference and is needed to preserve the place value of the other digits.

Let's look at how we find the value of a digit in an integer.

To find the value of a digit in an integer, you can use a place value chart.

So if we were asked "What is the value of the digit eight in the integer 6,180,254?" We could use a place value chart.

We could place our six in the millions.

We have 180,000.

That's one hundred thousands, eight tens of thousands, and no thousands, and then we have 254.

The digit eight is in the ten thousands place so its value is eight lots of ten thousand, that's 80,000.

Now it's your turn.

What's the value of the digit three in this integer? You can use the place value chart at the top of the screen to help you.

Pause the video while you choose your answer.

Welcome back.

Which one did you go for? If you place this into the place value chart, you would find that the three is in the thousands column.

That means the value of the digit is three lots of a thousand, which is 3,000.

So when we're saying the value of the digit, we don't just say what column it's in, we say how much it's worth.

If you chose a, remember that the value of the digit depends on its place.

If you chose b, remember that we do not just say what column it's in, we need to say what value it has.

Let's look at another representation.

You can partition, which means to break up, an integer using place value to show the value of the digits.

Let's look at how we do this using a part-whole model.

If we take the number 681, we can partition it however we like, but we are interested in place value today.

So we are going to split this number up using the place value of the digits.

So starting with the six, the value of the six, as it's in the hundreds column, think about how you would read it, 681.

So the six is worth 600.

The second digit in the number, eight, is in the tens column, so it's worth 80.

And the third digit is one.

It's in the ones column, so it is just worth one.

Here we have partitioned the number using the place value of each digit.

Let's look at a different number.

Here's the number 95.

This has tens and ones, so we can say how many tens it has by separating out the value of the digit nine, which is 90, and the value of the digit five, which is five.

And you can see that if you add 90 and five, you get 95.

This time we have the number 5,703.

So starting from the left, the digit five has the value 5,000.

It's in the thousands column.

The digit seven has the value 700, it's in the hundreds column and the digit is seven.

Now you might be tempted to put zero next, but for efficiency, we don't need to do that.

We don't need to say that there are zero tens.

So instead we go straight for the next digit, which is three, and the value of that is three as there are three ones.

To check we've done it correctly, we can add 5,703 together and check that we get our integer at the top, 5,703, and we do.

Your turn to have a bit of a think now and see if you've understood what we've just done.

Jacob and Sofia are looking at the integer 107.

So who is correct? Jacob has partitioned 107 like this and Sophia has partitioned 107 like this, who is correct? Pause the video while you have a think.

Welcome back.

Sophia has partitioned it using place value correctly.

If we take Jacob's part-whole model, the one, the zero, and the seven would make eight if we added them together, that is not the integer at the top of the part-whole model.

Jacob has just partitioned the digits.

So the digit one, he's written as one, but we know it has a value of a hundred.

Sofia has also been efficient and not included the zero tens and just shown that that number is made up of 107 ones.

So Sofia has partitioned it using place value correctly.

Now it's time for you to have a go at a task.

In question one, I want you to write down the value of the digit eight in each of those integers.

In question two, I'd like you to write the integer that is shown in words.

And in question three, write the questions using digit form.

You could use a place value chart to help you or you could draw one out.

So in part a you have 516,212 and in part be, 42,093,701.

Pause the video while you have a go at these questions.

Let's have a look at question four.

Question four, give an example of an integer which is greater than 1,000.

In part be, and is less than 2,000.

So it needs to be greater than 1,000 and less than 2,000.

And has the digit five in the tens place.

So in part c, it must be greater than 1,000, less than 2,000, and have a five in the tens place.

And in part d, you need to meet all of the conditions above.

Greater than 1,000, less than 2,000, has a five in the tens place, and your number must contain the digits three and nine.

Pause the video while you have a go.

Now it's time for some feedback.

Question one asks you to write down the value of the digit eight in each integer.

Part a was 285.

The eight is in the tens column so it's worth 80.

In part b, The eight is in the hundreds column, so its value is 800.

In part c, the eight is in the hundred thousands column, so it's worth 800,000.

In part d, the eight is in the ones column, so it is worth eight.

And in part e, the eight is in the thousands column, so it is worth 8,000.

How did you do? I hope you did well.

Question two, you were to write this integer in words.

It's twenty million, eight hundred and five thousand, two hundred and five.

Question three, five hundred and sixteen thousand, two hundred and twelve is written like this, we have 516,212, 12 being one ten and two ones.

In part b, we had forty-two million, ninety-three thousand, seven hundred and one.

Here we need some zeros for placeholders.

Forty-two million, ninety-three thousand, so we have no hundred thousands, and seven hundred and one, meaning we have no tens.

So we write this as shown.

Let's look at question four.

You needed to give an example of an integer, which is greater than 1,000.

I chose 35,678, but you could have had any number you like as long as it was greater than 1,000.

This time it had to to be greater than 1,000 and less than 2,000.

This was a little bit more restricting.

You needed to choose something with a one in the thousands column.

This would mean it'd be greater than 1,000, but it can't have a two in the thousands column or it would not be less than 2,000.

Part c it now must have a five in the tens place.

So I kept my number, but I swapped my digit seven in the tens place for a five.

So I've gone for 1,658.

What did you go for? The important thing is that there is a one in the thousands column and a five in the tens column.

You could have any other digits in the other two places.

In part d, you then have to use the digits three and nine.

We haven't used the digits three and nine so far.

We know that one and five are in the positions of 1,010.

So we know that we can only change the hundreds place and the one's place.

So you could either have 1,359 or 1,953.

Those are the two correct choices.

How did you do? I hope you did well.

It's now time for the second part of today's lesson.

You're going to be using your understanding of place value to create some numbers given certain conditions.

So let's get going.

Where you place a digit in an integer affects its overall value.

Throughout this part of the lesson, we're gonna use digit cards quite a lot.

We're gonna move these digit cards around to make different numbers.

So let's think about a question.

What is the largest two-digit number you can make from these cards? You might want to pause the video and think Welcome back.

Hopefully you said that if you have a two-digit number, the tens place is the highest place value and you want the largest digit there to make the largest number you can.

That means the nine goes in the tens place.

Then we want the next largest digit which is four.

This is the largest two-digit number we can make using those cards only once each.

What about if I'd asked you for the largest two-digit odd integer you can make from these cards? Hm, now we have a restriction.

If I use the nine in the tens place, the only digits I have left are two and four.

This would make our number even.

So the nine has to go in the one's place.

This is the only odd digit we have, and since we know that the last digit must be odd for the integer to be odd, it needs to go there.

Now we still need to make the largest we can with what's left.

So with the four and the two, we choose four as it's larger than two.

So 49 is the largest two-digit odd integer that we can make from those cards.

So we got a different problem.

Here's a different set of digit cards.

We have a seven, a three, a zero, and an eight.

What's the smallest four-digit number you can make from these cards? Pause the video and have a think.

Okay, since we're trying to make the smallest four-digit number possible, you might be tempted to place zero in the first place.

The problem with this is that would create a three-digit number when we read it.

Although zero is a digit, we don't use it if it is not preserving the place value of other digits.

We use it as a placeholder, so it can't go there.

So we place the next smallest digit that we can.

That's the three.

Then we can use the zero.

The zero will then preserve the place value.

It will mean there are no hundreds.

So the larger digits of seven and eight go in the tens and the ones place now.

This will be the smallest four-digit integer we can make from these cards.

Your turn.

Using the digit cards shown on the slide, what is the smallest three-digit integer that you can make? Have a look at the options and pause the video while you make your choice.

Welcome back.

The correct answer is b, 507.

As you saw, although C uses the three digit cards, when you place the zero at the front, the number is red as 57.

That's a two-digit integer.

So we haven't actually made a three-digit integer.

The zero at the front would be ignored when we are reading it.

So 507 is our next best option, which satisfies all the criteria.

We've made a three-digit integer and it's the smallest one that we can make.

Time for some practise.

"Use the digit cards below to create the largest possible five-digit integer, the smallest possible five-digit integer, the five-digit integer that is closest to 90,000, and the smallest possible five-digit even integer." Pause the video while you have a go at those questions.

Question two, "Using these cards, how many different five-digit integers can you create between 50,000 and 70,000?" If you think you found them all, how do you know you found them all? Pause the video while you try this task.

It's time for some feedback.

In question one, we were using the digit cards to create the largest possible five-digit integer.

So we use the largest value digits in the highest place values.

So beginning with the nine, then the eight, then the seven, then the six, and the zero is in the one's place.

So we've got 98,760 as the correct answer.

Part b, we wanted the smallest possible five-digit integer.

Now remember, we can't put the zero at the front of this.

We only have five digits to use, so in order for our number to be a five-digit integer in the end, putting zero at the front will mean we have a four-digit integer and we've been asked for a five-digit integer.

The next smallest digit in our list is six, so we use that in the highest place value.

Then we can place our zero and the other digits in ascending order.

So seven, eight, and nine.

So we have 60,789.

Part c asked for the five-digit integer that is closest to 90,000.

I hope you managed to find 89,760.

You can make numbers that are just over 90,000, but this is closer to 90,000.

It didn't matter whether your number was above or below 90,000.

It should just be the closest one.

And the closest one you can make using those digits is the number 89,760.

In part d, we were asked for the smallest possible five-digit even integer.

You might have used part b to help you.

We know we can't start with a zero.

The next smallest digit is six.

So we use six in the highest place value to start making the smallest integer we can, then the zero, and then we have to be careful about what comes next.

We can't use the same answer as part b as that ends in a digit nine, which is an odd number.

So in order to still make it the smallest, the seven stays in the hundreds place, but the nine and the eight digit will need to swap around.

So it'll be 60,798, meaning that we now have an even integer and it is the smallest one we can make.

Let's look at question two.

Using these cards, how many different five-digit integers did you create between 50,000 and 70,000? Here are all of the integers between 50,000 and 70,000 that you could have made.

There are a lot of them.

I worked systematically to list these numbers.

So I know the only digit I can start with is the six.

That's because there is no digit five to make 50,000 or any number with 50,000 at the start.

I can't use the zero at the front because I won't have a number between 50,000 and 70,000 with only five digits.

So I start with the six and then use the other digits, writing the integers in ascending order.

So I started with the smallest integer I could make.

I knew that that was 60,789, and then I carefully rearranged the digits in ascending order to make sure that I'd got all of the numbers I could.

I hope you found as many as you possibly could and that you enjoyed justifying how you knew you'd got them all.

I hope you did well and I hope that you reviewed your learning of place value.

So to summarise our learning today, digits can have different values depending on their place value.

The place value of a digit affects the overall value of an integer.

I've really enjoyed learning with you today.

You've worked really hard.

I hope to see you in a future lesson.