Lesson video

Hi.

It was my birthday recently and my friend gave me this as a gift.

I don't really know if I can call them my friend anymore.

This has left me feeling so frustrated.

I just cannot find any way of getting all the colours back to the same face.

You know I think I'm going to put it down so that I can focus on this Math lesson.

And I'd like you to do the same.

So if you've got anything close by that is distracting you, put it aside, find yourself a space where you can focus on your Math learning for the next 20 minutes and come back when you are ready.

Press pause, I'll see you in a moment.

In this lesson, we are using our learning from previous lessons, rounding decimals to the nearest whole number to help us solve problems. Our agenda for the lesson, we'll start off with a recap on rounding whole numbers before also recapping rounding numbers with one decimal.

Then we will use that learning and those skills to solve some problems together, setting you up for the Independent Task.

Things that you'll need; pen, pencil, something to write on, a ruler if you have one, press pause, go and collect what you need, come back and we'll get going with the lesson.

Let's start off with some counting.

Counting in multiples of hundred, 100.

My turn, your turn, back and forth in multiples of 100.

Are you ready? 100, 300, 500, 700, 900, 1,100, 1,300, and stop, well done.

Let's do that again, except we'll count in multiples thousand and we will start with you.

Are you ready? Your turn.

2000, 4000, 6000, 8000, 10000, 12000, 14000 and stop, well done.

So we've been counting in multiples there of hundred and thousand.

That is an important skill to recap every now and then, particularly with activities like this in mind.

Similar to previous lesson but with numbers, all of these numbers, all four of these on the left, you need to round to the nearest 10, then that same number to the nearest hundred and that same starting number to the nearest thousand.

Press pause, come back when you're ready and we will review.

How did you get on? Hold up anything that you were writing on so I can have a little look.

Good, well done.

Let's have a look at them together, shall we? So rounded to the nearest 10, notice the colours for some of the digits now, drawing our attention to parts of those numbers to look at.

For example 475 to the nearest 10, is it nearer to 470 or 480? Well, in this case, it's halfway between the two.

So we know we round to the next multiple of 10, 480.

Interesting, 4,500 did not change, why did it not change? It's already a multiple of 10.

Let me start the sentence.

And can you finish it for what we've just looked at here.

When rounding to the nearest 10.

Good, well done.

Rounding to the nearest hundred now, notice the colours change.

Our attention is being drawn to different parts of the number when we round to the nearest hundred.

For example, 1,563, is it nearer to 1,500 or 1,600? Maybe you're visualising a number line in your mind to notice it's closer to 1,600.

There are your other solutions as well.

And again, 4,500 has not changed.

Why has it not changed? It's already a multiple of, in this case one hundred where we're rounding to the nearest hundred.

It's already a multiple of 100.

Will it change with the last example? Before we get there, this time, can you start the sentence and I will finish it.

This sentence is all about rounding to the nearest hundred.

You start it, one, two, three.

You need to consider, which is the closest multiple of hundred to that number.

Good.

Here we go then.

Rounding to the nearest thousand.

Notice the colours change once more.

Drawing our attention to different parts.

For example, 89 is that going to be closest to zero or 1000? Zero, same for 475 and finally 4,500 did change halfway between 4,000 to 5,000.

So we round to the next multiple of thousand, 5,000.

Sentence, let's say this one together, one, two, three.

When rounding to the nearest thousand, you need to consider which is the closest multiple of thousand to that number.

Okay, rounding to the nearest whole number.

We've recapped rounding to the nearest 10, 100, 1,000.

Let's recap rounding to the nearest whole number 0.

4 rounded to the nearest whole number is, are you visualising in your working memory a number line? Are you thinking, which is the previous and next whole number to 0.

4? And then are you thinking, where does 0.

4 sit? Perhaps you're drawing a number line and you're representing on paper what hopefully soon you'll see in your working memory.

Either way it's supporting us.

0.

4 rounded to the nearest whole number is zero, it's closer to zero.

How about this one? So the number line there all work visually, press pause if you need to.

9.

7 rounded to the nearest whole number, press pause.

Are you ready to share? Tell me what it's closest to.

10, and now we explain why it's closest to 10.

or why we round to 10.

Because if we plot on a number line nine and 10, 9.

7 is closer to 10, it's further from nine.

We round it to 10 as the nearest whole number.

Here is another one, press pause if you need to.

Are you ready to share? Tell me, how did you go about solving this problem? How did you find out which whole number is closest? Good, we're thinking, which is the previous whole number? Which is the next? 423, 424, then we can think more, which is 423.

3 closest to.

And we can see it there on our number line.

We may have seen it visually in our mind is closest to 423.

So it rounds to that number.

Okay.

Let's start using our skills in rounding to the nearest whole number to solve a problem.

You might recognise this problem from the ready for a challenge in a previous lesson.

Let me give it a read.

I think of a number with one decimal place.

It is rounded to the nearest whole number.

The answer is 74.

What is the highest possible number I could have thought of? What is the smallest possible number I could have thought of at the beginning of that problem, where it says, "I think of a number." That number, what's the highest and smallest or lowest it could have been? Press pause, have a go see how you get on.

Come back when you're ready to take a look together.

Are you ready? So what did you get? The highest possible number? Tell me again.

Okay, and the smallest or lowest? Aha, okay let me share with you how I approached it.

So I thought about, if the answer is 74, I know when it comes to rounding, there will be a choice between two numbers.

And in this case, the choice between two whole numbers.

If the answer is 74, or it could have been 73, depending on what that number was that I was thinking of to start off with.

And I know that, I know that the solution is okay, it's going to round to 74.

So therefore the highest it could have been is 73.

9 and the smallest is 73.

5.

Both of those would round to 74.

But, when you told me, when you called out your solutions, some of you had a different, higher number.

And that's made me really realise, although the choice could have been between 73 and 74, it could also have been between 74 and 75.

There could have been a number bigger than 74 that would still be closer to 74 if rounded.

So I wonder here, is this then the highest it could have been? What number is that arrow pointing to now? 74.

5, 74.

5 would round to 75.

Okay, so how about here? Is that the highest it could have been? 74.

4.

Yes and that would round to 74.

So that one leaves us 73.

5 is the smallest, 74.

4 is the highest, both would round to 74.

Okay, we had a look in detail there at that problem.

So similar problem again, I changed the number.

Press pause, have a go at solving it, come back and share your highest and smallest numbers when you're ready.

Ready? Okay.

Now help me out.

I may have made a similar mistake or not thought deeply enough as with the last question.

So again, I'm thinking there are two possible answers.

that the number I'm thinking of could round to.

There's the previous and the next whole number 323 or 324.

So the highest 323.

9, the smallest 323.

5.

No, of course.

I need to think about it being between 324 and 325 as well.

Not going to make that mistake again.

I know it can't be 324.

5.

So that is the highest it could be.

Tell me what the highest it could be is and the smallest.

Fantastic.

So we've used our skills in rounding to solve problems. Here's another one.

This is going to link to your Independent Task.

I roll two dice, a six and a three.

I use those dice to make two numbers.

Each of the numbers has one decimal place.

So I could make 6.

3 or 3.

6.

Now 6.

3 rounded to the nearest whole number is six and 3.

6 rounded to the nearest whole number is four.

My challenge for you is with two dice, maybe you've got some board games you could collect them from, if not, don't worry.

Ask a parent or carer to help you find some virtual dice online.

Once you've got your dice, my challenge, by rolling them twice to make two decimal numbers like I've done, can you find two decimal numbers that would actually round to the same whole number? My two decimals did not round to the same whole number.

The challenge is to find two decimals that would.

Now I've got a table for you on the next page that could help you to structure your, your findings.

So as you can see, I've got my three and my six.

They were my rolls.

These are the decimals that I wrote, 3.

6, 6.

3.

And next to each of them, the rounded whole number.

If I rolled a two and a three, I could make this decimal.

And this decimal here are the rounded whole numbers and they are not the same.

They're still different.

The challenge is to find two decimals that would round to the same whole number.

Two and six, 2.

6, 6.

2.

No, hasn't rounded to the same whole number.

Will it be possible? If you are successful and you are ready for a challenge, make up a rule.

When you have found all the possibilities, can you make up a rule to explain when both of the decimal numbers will round to the same whole.

Press pause, go and complete your activity, then come back and share what you found.

How did you get on? Quite challenging.

I was rolling, rolling, rolling, and not in a very systematic way, just at random.

And I wasn't getting very far.

So I stopped and I thought more efficiently, more systematically.

I started to work in an order.

Before I tell you about that order, let me see your work, hold up your paper, hold up your tables.

Let me see what you have found.

Good work everyone.

I can really see there how you've recorded your findings, really clearly well done.

So, as I said, I was working randomly and then I made a change.

So I started by thinking right, if I rolled a one with one dice, which numbers could I roll with the other dice? I could run another one, a two, three, four, five, or six.

When I drew attention, when my attention was drawn to rolling two ones, I thought, well, the decimals I could make are 1.

1 and 1.

1.

Which of course would be round to one.

And I recorded that in my table.

With one as one of the numbers and two, three, four or five or six as the others, the decimals I made to that, none of them rounded to the same whole.

So I repeated the process but with two, what could I roll with it? The second dice.

I could write a one, two, three, four, five or six.

Again I noticed, what if I roll a two and a two, I can make 2.

2, I can make 2.

2, both would round to two.

And that pattern continued.

When I rolled two numbers that are the same, the two decimals I make will both round to the same whole.

However, I also noticed and did you, when I rolled a four and a five, I made 4.

5 and 5.

4, which both round to five.

So it was possible with two different numbers as well.

Fantastic work everyone.

If you would like to share that work with Oak National, please ask your parents or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Well done everyone, I'm really pleased with how you have used your rounding skills.

Rounding numbers with one decimal place to the nearest whole number.

You've used those skills to solve some problems today.

And one of those problems was from the ready for a challenge in the previous lesson.

And you've managed that today.

Look out for the ready for a challenge in future independent tasks and push yourself to have a go at those.

Lesson five done, lesson six, ready to continue our decimals learning.

See you again.

Bye.