# Lesson video

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Hi everyone, thank you for joining me today, my name is Ms Jeremy, today's math lesson is focused on solving problems involving rounding and place value.

So get yourself sorted with a nice quiet space, free from distractions and once you're ready press play, to begin your lesson.

Let's start by looking at our lesson agenda for today.

So we're going to begin with a warmup which will be a recap of rounding, we'll then participate in a place value battle before looking at rounding in a little bit more depth at the end of the lesson, we will solve some word problems together, and then you'll complete your independent task and quiz.

But today's lesson you will need a pencil, some paper and dice.

If you don't have dice at home, take a moment now to take six more pieces of paper, write the digits one to six on those pieces of paper and turn and face upwards So you can't see the numbers.

Pause the video now get your resources ready and once you're ready, press play to begin the lesson.

Okay, let's begin with our warm up, our rounding riddle.

So let's read this together It says, I'm thinking of a number, when rounded to the nearest 100,000, it is 500,000.

My numbers greater than 460,000, and it's less than 530,000, it is an odd number.

And the question asks us to work out, which of the following options A, B, C, or D could be the correct number according to the clues that we've been given.

So the first thing I'm going to do is spend a bit of time looking back at that riddle and underlining some key information.

Any information that isn't necessary to answer the question i took, I can just leave, but any key information I'm going to underline.

So here, I'm thinking of a number when rounded to the nearest 100,000, it is 500,000.

That's important to know.

My number is greater, than 460,000 and less than 530,000.

It is an odd number.

So lots of clues that help us out, we know that it's going to be rounded to the nearest to 500,000 when rounded to the nearest 100,000.

We know it's greater than 460,000, and it's less than 530,000 and it's got to end in the digit one, or three, or five, or seven, or nine, because it is an odd number.

So take a moment now, pause your video if you'd like to, have a look at those different options.

Which of our options could be the correct number? A, B, C OR D As you're working through, if you don't think a number as possible, see if you can explain why it's not possible.

Take a moment now to have a look at those numbers and see whether you can identify which one is correct.

Okay Let's have a look at some of the options and identify whether they match our riddle or not.

So the first one here and is our number 459,235.

I'm going to go through each of the clues in the riddle and I'll identify if it matches those clues or not.

So first of all, does it round to 500,000? What I can see here, I finds my line on a 100,000 column and have a peak next door, this number would round up to 500,000 because I can see that because my digit in the 10 thousands column is five or above, it would cause our hundred thousands digit to round up to 500,000.

So it does match that, then it says my number is greater than 460,000, but unfortunately this number is not greater than 460,000.

It's less than that.

So already I don't need to look at the rest of the riddle, I know this is not my number.

Let's look at number B now, this is 538,273 Again, I'm going to look and see whether it rounds to the nearest to 500,000 and having a look at my number here, I can see that yes it would round down to 500,000 and let's have a look at the next bit.

Is the number greater than 460,000? It is.

Is it less than 530,000? No it's not.

It's greater than that.

So unfortunately that one doesn't match either.

So we're going to have to look at number C now.

Number C is 492,098, Looking again at the rounding, I can see that it would round up to 500,000, and it is greater than 460,000, it is less than 530,000 however, we've got a problem at the end here, this is an even number because it's got an eight at the end, I know it must be an even number therefore it is not correct.

It doesn't match all of the clues in our riddle.

So by process of trial and error, we've seen that is going to be number D, but we will just double check it using those clues as well.

So looking at again, does it round to 500,000? Yes, I can see straight away it does It is greater than 460,000? It is less than 530,000, and because it ends in a number one, it is an odd number.

So therefore that is my correct answer.

We have to go through all of these options.

What I could have done really quickly is rule out C, if I wanted to straight away, because I can see straight away that is not an odd number.

So I could have crossed that out at the very beginning, if I wanted to be a bit more efficient.

But going through systematically A, B, C, and D that's absolutely fine as well.

Okay, moving on to our next challenge.

So what I'd like you to do is have a look at the numbers on the screen.

We've got three numbers.

Let's say number A together first of all.

It is.

31,420 B is.

142,301 and C is.

824,013 Remember we say that word and, instead of a hundreds there because our hundred column does not have a digit in it.

Now, your task in a moment, I'm going to ask you to pause the video to do this.

Is to identify which of our clues, that we've got on the table here match up to the three numbers that you've been provided with.

So are a pink clue, purple clue, green, and blue clue, identify which of those numbers it matches too? You can see that four clues, but only three numbers.

you might find that there's more than one clue that matches to one of those given numbers, pause the video now to complete your task and resume it once you're finished.

Okay, how did you get on? Let's have a look at some of them together.

So let's look at that pink clue fast.

The pink clue says the digit four has a value of 4,000.

So we've got to identify which of these numbers has a four, that has a value of 4,000.

Let's look at the first one.

Well, I can see here that we do have a four in this number, but this digit four is in the hundreds column.

That's a value of 400 so it's not that one.

Let's look at the next one.

We can see that this number also has a digit four however, the four is in the 10,000 column it has a value of 40,000.

It's not that one either.

So it must be this last one I can see the four that is in the thousands column.

It does have a value of 4,000 So I'm going to match those two up.

Okay, looking at the purple clue now.

The digit three has a value of 30,000.

I'm going to go straight back to A and see whether it matches to that one.

Well I can see, I do have a digit three, and it is in the 10 thousands columns.

So therefore it does have a value of 30,000, that one matches nice and quickly.

The digit two has a value of 20 looking back at it, I can see there is a digit two it does have a value of 20.

This one's got two clues attached to it.

So I'm going to move that one over there.

And the digit one has a value of 1000 so, I'm looking to see all of my options here, and I can see that my digit one here also has a value of 1000.

Interesting, So, interesting that, little bit of a red herring for you B didn't have any of the clues match up to it.

Whereas A had three of them and C had one of them, okay.

It's now time to play a little bit of a game.

We're going to play a place of value battle.

And for this you're going to need your dice.

So if you haven't got a dice at home, you can use bits of paper with the numbers one to six written on just turn them over on your table So you can't see them.

Every time I ask you to roll your dice, instead of rolling a dice pick up the number or a random number from the table, and that is almost like rolling your dice then put it back down face down on your table.

So we're going to play this game to see who can make the greatest number, the number with the greatest value.

We're going to play so that you are playing against me.

I'm going to begin and I'm going to roll my dice.

I'm going to identify what number I get one to six.

And I'm going to decide based on that digit that I get to where to place it on my place value table.

This row here, as you can see, is going to be my row.

And this row here is going to be your row.

I won't be able to see what numbers you get, but you'll be able to all of mine as we go.

You'll have to be pausing the video as we go.

I will remind you when to do that.

Okay.

I'm getting started, I going to roll my dice first.

So, let's see.

Okay.

I've immediately rolled a number one straight away a number one now because that is the smallest number possible, and I want to make the number with the greatest value, I'm writing my one in the column, in the place that has the lowest value.

I going to put it in my ones column.

If I were to put it in my 100,000 column, it would have value, a value of 100,000, but then later if I roll a higher number, a number is greater than one.

I wouldn't have put it in a hundred thousand place.

I'm going to put my one all the way down at the end of my place value table, where it has the lowest impact the lowest value.

Okay now it's your turn in a moment.

Pause the video, roll your dice, and choose where you're going to place your digit, remember you're trying to beat me you want a greater number that I have.

Okay, my turn now, let's have a look while I roll next time.

So, oh no! I've rolled another number one.

You can see I'm.

I'm telling you exactly what I am rolling each time.

So here I am deciding where to put my number one.

Well, I'm not going to try and put it anywhere near my 100,000, my 10,000.

So I'm hoping I might get some sixes later on.

So I'm actually going to put it over here.

This is the lowest value column that I have left because I've already used the ones column.

So I'm going to put it into my tens, putting it at one in the tens column has a value of 10.

Roll your dice and decide where you're going to put your second number.

Okay.

Now it's my turn let's see what I rolled.

Let's hope I don't roll another one.

Ah! thank goodness.

I rolled a number three.

So I'm going to decide where I'm going to put my three.

Now I haven't had a huge amount of luck so far, I've rolled two ones and a three.

So I'm going to hope I get little bit luckier for later on in the game, I'm going to fill my three in my hundreds column, and I'm going to to hope that I roll a four, five, or six next time so I can put them in my thousands, 10 thousands, or 100 thousands.

That's three in hundreds column has a value of 300.

Now it's your turn, roll your dice decide where you're going to put your number and also tell yourself what the value of that digit is when it's placed in that column.

Pause the video now to complete your third number.

Okay now is my time.

Let's see if I get lucky with a four, five or six.

so, oh! I've rolled another three today is obviously a day for double numbers.

So I've rolled another three and I'm going to put it in my 1000 column I don't have a huge number of options left, I going to place it in my thousands column and hope for those greater numbers for my 10,000, and 100,000.

Pause the video, roll your dice, and choose where you're going to put your fourth number.

Okay now it's my turn let's have a look What I rolled hopefully I get a little bit lucky this time round.

Ah, brilliant! I rolled a five, a five.

So thinking to myself, am I going to be cautious, and put my five in my 100,000, in case I roll a four, three, two, or one for my next number, or am I going to be really optimistic and hope that I rolled a six next time? I think I need be a bit prudent.

I going to be a bit cautious.

I think I'm going to put a five in the 100,000 column because my chances are, that I will roll a number that is less than five next time.

That's what the chance is kind of leaning towards my probability leans towards, but we will see.

Roll your dice for the penultimate time and choose where it's going to go on your place value table.

Okay.

Now it's my turn for my last go.

Hopefully I got nice large number We'll see.

Ah! I've rolled another five.

Today is the day for double digits.

Clearly I've wrote two ones, two threes, and two fives.

And I only have one option to where, of where to put my five.

I'm going to put it in my 10 thousands column there.

So the number that I've made is 553,311.

Okay.

How did you get on? I'm not sure what your number is, but you will know both what my number is and what yours is.

Have a look at the two of them who won? Did you manage to create a number that was greater than mine? Or did I win? did I create a number that was greater than yours? And if you can look at both of those numbers together, can you work out in which column was there a difference? Did you have a difference in your 100,000's and 10,000's? In which column did you manage to create your greater number? Spend a bit of time having a look at your number and my number and identifying which of those numbers get greater.

So the next task that you've got is a little bit of an independent task to check your understanding of place value.

The first thing you're going to need to do is to fill in this grid, just here, this place value table, just here.

And you're going to use your dice to roll your.

Roll five different numbers to fill in your place value chart.

So I'm going to to imagine I've rolled a three, I'm going to put that there.

I'm going to imagine I rolled a two, a one, a four and a six.

Wherever you have got a space after you rolled your five numbers, I would like you to put a zero, put a place holder just there.

So you're going to roll your dice five times and place those numbers in to five different spaces before adding a zero into your missing spare space.

After done that, I'd like you to say your number aloud.

So this number is 362,014.

And then you need to write your number using words up here, just write a star.

So you need to write the number is 362,014, but obviously you'll be writing whatever number you wrote.

Then on this section just here, you're going to start writing down the value of some of the digits.

It's your choice which digits you decide to choose to write about.

So I'm going to write about my three, the digit three has a value of what is a hundred thousands.

So it has a value of 300,000.

I'm going to write that the digit one has a value of 10 or represents 10.

And the digit four has a value of four.

There is a place holder in the one in my case, in the hundreds place, so I'm going to write hundreds here.

And then the last thing you're going to do is to partition out the number.

So I'm going to write 362,014 and you can see there are six spaces here for the six parts of your place value table.

So I would need to write 300,000, plus 60,000 which is the six plus 2000 plus zero, there's no hundreds, plus 10, plus four.

That is my partitioned number there and my completed grid.

I'd like you to do the same thing, but using your own rolling of the dice, using your own number.

Pause the video to complete your task and resume it once you're finished.

Okay, let's move on to the next part of our activity.

So we're going to continue to use our dice and this time we're going to use it for rounding activity.

I'm just going to to hide my screen thus you can see the space for the chart properly.

What I'd like you to do with this activity is to roll your dice and create a six digit number using the numbers that you roll in your dice, we then going to have a go rounding the number that we've created to the nearest multiple of 100,000, 10,000, and then 1000.

So, I'll have a go first of all.

I'm going to roll my dice first and pop my number into my place value chart.

I'm going to be moving from left to right So as I roll each number, it's going to, I'm going to start by putting the first digit in the 100,000 and then 10 thousands and go on from there.

So the first digit that I've rolled is a four.

I'm going to place it in my hundred thousands column there.

That's has a value of 400,000, because it's in the hundred thousands column.

I'm rolling the dice again.

Let's have a look on what I get, oh! I've got a three this time a three goes into the ten thousands, rolling the dice again.

I've got a five this time.

I'm placing it in my thousands column.

I'm rolling again and I'm getting a two my hundreds, my tens is a four and my ones is a five again So you can see that I created my number and I filled in the different digits on my place value table.

Let's say this number together the number is, 435,245.

So, now that we've put all of our digits into our place value chart, the next thing we're going to do is to round this number to the nearest multiple of 100,000.

So I'm going to use my shorter method I can use my number line method to help me, my short method is to look at the column and the digit that I am rounding.

So this first one, I'm rounding in the hundred thousands I'm going to underline the digit in the hundred thousands column.

And I'm going to have to identify whether this is rounding down to 400,000 or up to 500,000 in order to do this, in order to have a quick peek at the digit that is in the 10 thousands column.

If that digit it's four or below, then I'm going to be rounding down.

If the digit is five or above, I'm going to be rounding up and in this case, you can see that I'm rounding down.

So I'm rounding this number to 400,000 and that's what I'm adding to the nearest multiple of 100,000.

Now let's have a go at rounding to the nearest multiple of tens.

Of tens thousands.

So rubbing out my marking that underlining my digit in the 10 thousands column, having a peek at the digit in the thousands column.

So in this case, you can see that I'm actually going to be rounding up.

I'm not going to to be rounding down because the digit and thousands column is a five.

That means I need to round up.

So my hundred thousand stays exactly the same.

I'm still dealing with 400,000, but I'm rounding up to the next 10,000, which is a 40,000.

I'm going to to fit in the rest of my number with my place holder that, so when rounded to the nearest multiple 10,000, this number is 440,000.

Okay, last thing I need to do is to do exactly the same thing, but this time I'm rounding to the nearest multiple of 1000.

So underlining the digit in my 1000 thousands column and going to have a look at the digit that's in the hundreds column.

And I can see that I am rounding down because the digit on hundreds is a two, so I'm rounding down.

So my rounded number when rounding to the nearest multiple of 1000 is 435,000.

If you find it easier to use a number line in order to do your rounding, placing your smaller multiple, larger multiple, and halfway point, you can do that for each of these three examples.

You can see there how I've used a slightly quicker method to round this same number in three different ways.

So now it's your turn to have a go.

I'd like you to do exactly the same thing that I did using your dice, or your place value, bits of paper if you need to and create a six digit number, which you were then going around to the nearest multiple of 100,000 to 10,000 and 1000 Pause the video to complete your task and resume it once you're finished.

Okay, now that you've completed that task, we're ready for our final activity for the lesson today.

So we're going to look at some word problems that involve place value and rounding.

Let's have look at the first one together.

It says there are 38,871 people attending a concept approximately how many chairs are needed.

And that word approximately is crucial to this question.

Whenever you see in math, the word approximately what is asking for is a rough estimate or a rounded answer.

So in this case, we are going to try and round our number to either the nearest multiple of 10, 100, 1000 or 10,000.

And it's up to us to decide what we think is the most appropriate way to round.

Now, in my opinion, if we look at the context of this problem, it's asking us for a rough number of chairs that we're going to need for concerts that has 38,871 people coming.

If I were to round to the nearest multiple of 10,000, that would be far too broad, an estimate of the number of chairs without it, I would either get far too many or far too few of the chairs that we needed.

So actually I think we either need to round to the nearest multiple of 10 or the nearest multiple of 100.

In this case, I think I'm going to round to the nearest multiple of 100, and then we're going to have a look at whether we've rounded up or down and identify what the approximate number of chairs that we would need for this particular concert would be.

So let's have a look at how we would do that.

I've got the number 38,871, and I've decided I'm rounding to the nearest multiple of 100 in order to do that, I'm going to do is to have another pick at the digit that is to the right of my number that I'm amounting.

And in this case, it's a seven, So there's a seven in the 10's column.

And because that digit is five or above, I know I'm going to need to round to the greater multiple of 100, I'm going to need to round up.

So in order to round this, I know that my 10,000 is says the same my thousands they're the same, but I'm rounding up to 38,900 instead of a 38,800 in this case.

And so you can see here that we've rounded up.

We would provide this concert venue with more chairs than they needed, but they'd have an approximate value there.

If we wanted to, we could have rounded to the nearest multiple of 10, but in this case, run into scenarios multiple of 100 gave us a specific enough answer and for the context that we were provided with.

Let's look at the next question.

It says, what is the difference between the value of the fours in the number 408,742? So as you can see in this number, the digit four has appeared twice.

We've got four in the tens column and we've got four in the 100 thousands column and a hundred thousand column.

And these fours have very different values because they've been placed in different places, spend about 10 seconds now, working out the value of the four and the 10th column and the four and 100,000 column, You've got 10 seconds.

Okay so we should have seen that the four in the tens column has a value of 40, whereas the four in the hundred thousands column has a value of 400,000.

So even though the same digit has been used twice, the value of those digits, it's very different, depending on the context that we've been, the column that we put each of those digits.

So the question asks us, what is the difference between the values of those fours? What I need to work out is what I would need to multiply 40 by in order to give me 400,000? spend five seconds, having to think about that now think about your place value chart.

How many spaces would we need to move that 40 to the left of our place value chart in order to multiply it so that it got to 400,000.

Okay, so let's have a think.

Well, actually in this case, I can see that multiplying 40 by a number would need to provide us with four extra placeholders or four extra spaces that it would need me to move along.

So my number that I need to multiply 40 by needs to have those four placeholders in it.

So I'm going to put those in one, two, three, four, and I can see that I would need to multiply 40 by 10,000 in order for me to make 400,000.

So therefore I can say that 400,000 is 10,000 times greater than 40.

And that answers the question that we've been provided with there.

You've got five questions to answer.

all of these five questions are based on concepts that we've covered during this lesson, have a go at answering the questions, and then don't forget to come back once you're finished to have a look at the answers together.