Lesson video

I have been.

I've been working on this for about four months.

It was a gift from a friend for my birthday and this is the nothing that gives me a headache and leave me feeling really, really tense.

I'm going to put it down.

I'm going to take some deep breaths.

And I'm going to focus, so I'm ready to teach this Maths lesson.

Have you got anything around you that could steal your attention? If you do, can you move away from it? Find a quiet space where you can settle down for this maths lesson for the next 20 minutes or so.

Press pause while you get yourself sorted, then come back when you're ready to start.

In this lesson, we will be exploring efficient mental strategies for division.

We're going to start off with a place value activity, then I will go through the options for you when it comes to mental division, give you a chance to practise and finish up with your independent task.

Things that you're going to need, fairly simple, pen or pencil, some paper and a ruler.

Press pause if you need to collect anything, come back and we'll start.

So here's our activity.

You can see there seven numbers.

Some of those digits are black, some are red.

The red digit, what can you tell me about the value of the red digit? Can you identify its value? Before you press pause, let me show you what I mean.

In the number 31,925, the two has a value of two tens, the two is in the tens column.

The two represents 20.

Now press pause and have a go at saying or writing those sentences for the other numbers.

Come back when you're ready.

Are you ready? Okay, let's see, shall we? I will say a sentence, you tell me the number I'm describing.

The two has a value of two hundredths, 12.

72.

Good.

The nine is in the hundreds place.

Oh, we've got some options.

Okay, then I'll also tell you there's a one in the thousands place.

Good.

Last one, the three represents 30,000.

Good, say that number again.

Excellent.

Okay, let's take a look at this problem.

Can we read it together? After visiting Russia, Antony had some money left in Russian Rubles, so in Russian currency, and he went to change them back into pounds, into British currency.

The approximate exchange rate is one pound, one of the British currency to 80 of the Russian.

Approximately how much in pounds did he get for 4800 of the Russian currency? Press pause and have a go at answering those questions.

What do you know? What do you not know? And what skills or knowledge could you bring and use to help solve the problem? So what do you know? Tell me.

Tell me something else you know? And what do you not know? Okay, great.

So I'm going to highlight that now.

So we know the exchange rate, one British Pound is worth 80 of the Russian currency.

We also know that he's got 4800 of the Russian currency.

We don't know how much in pounds he would get for the 4800 of the Russian currency.

This next part, now, I didn't ask you about the third question, what knowledge or skills do you have? Because often that gets revealed in the next part, when you use a bar model to represent the maths within the problem.

Can you press pause, go and draw a bar model to represent what you know from the problem, what you don't know from the problem.

And then hopefully, you'll see the skills and knowledge connected to the problem that you'll need to use to solve it.

Press pause, come back, and we'll compare bar models.

Let's take a look.

Hold your bar models up, let me see.

Looking good, well done.

Compare to mine now, please.

So what do we know? We know that he's got 4800 of the Russian currency.

And we know that 80 of them, a group of 80 of them is worth one pound.

Does this help to reveal the maths that we need? What what maths do you think is going to help? Oh, someone said subtraction.

Tell me more.

Subtract, subtract 180 at a time, an eighty, another eighty, another 80.

More efficient than that, division.

Division is repeated subtraction.

So what will our division expression be? 4800 divided by 80.

That's going to help us find how many equal parts of 80 there are in 4800.

So here's where the mental strategies come in.

For solving this equation, for finding the unknown quotient, which strategies could you use? Press pause and note down some ideas for how you might go about solving this problem.

Don't finish solving it, just think about how you would do it.

Come back when you're ready to compare.

Now, I'm going to show you the names of three strategies.

These names might not be what you've written down, but as we go through each of them, you might then see some connections to what you've noted.

So we're going to think about how we can solve a division using factors, using multiples, and using an equivalent division.

Division using factors.

This is really, really useful when you're dividing by a number, which is a times table that you're not that confident in.

So for example, here we are dividing by 80.

But dividing by eight is going to help us.

And if your eight times table is a little shaky, you're really going to like this approach.

This is where we look at 80.

And instead of dividing by 80, we change 80 into two factors of 80.

We could divide it into more than two factors, but in this example, we'll stick to two.

I'll show you what I mean.

We've changed 80 into 40 and two.

What's the connection between 40, 2 and 80? 40 multiplied by two is 80, 40 and 2 are factors of 80.

We can divide 4800 by 40, and then by two, and the result will be the same as dividing by 80.

Really powerful.

So have a look 4800 divided by 40, Fours in 48? 12.

40s in 4800? 120.

120 divided by two, twos in 12? Six.

Twos in 120? 60.

The quotient is 60, 4800 divided by 80 is 60.

And we've solved it by dividing by factors of 80.

There are other factors of 80.

Two factors of 80 different to 40 and two? Tell me good.

Good.

So we could use 20 and four, 20 times four is 80.

We can divide by 20, twos and 48.

So 20s in 4,800? Pretty it.

And now divide 240 by four, fours in 24.

So 40s in 240? Brilliant, this calling out participation is perfect.

Keep it going, well done.

Are there any other factors or two factors that we could turn, split 80 into? Yeah, we could have 10 and eight.

10 times eight is 80.

So they are factors of 80.

We can divide 4800 by each of them.

Divide it by 10, make it 10 times smaller? Tell me, louder.

480.

And then we can divide this by eight.

Eights in 48? Six.

Eights in 480? 60.

Three ways there of solving the missing quotient by not dividing by 80, but by factors of 80.

Perfect for when there's a times table that you're not so good with, that you haven't yet got ready just to recall at the click of a finger.

Next, division using multiples.

Now I bet this is one you were thinking of, perhaps you just weren't thinking of this title.

So here's where we're thinking about 80, and multiples of, groups of 80 multiplied by 10, 800.

So I know in the 800 of 4800, there are 10 80s.

Now I'm thinking about the 4000.

And I'm making connections.

I'm thinking about fours and eights, fives.

80 times five is equal to? Let's work it out.

Eight times five is 40, 8 times 50 is 400, 80 times 50, 4000.

So I've got 10 lots of 80, 50 lots of 80, I've got 60 lots of 80 in 4800.

So I've divided here by making connections and using multiples of my divisor.

Last one, equivalent division.

4800 divided by 80.

I can change both of those two numbers, reduce them, make them both 10 times smaller and have another division that's equivalent.

480 divided by eight, the quotient would be the same as it would be for 4800 divided by 80.

So what is the quotient? 480 divided by eight, eights in 48? Six.

So eights in 480? 60 of course, 60 is the same division that we've been looking at over the last few pages.

But why? Why will that quotient be equal to 4800 divided by 80? Here's where, there's a really lovely connection to fractions.

84800 hundredths, and eight 480 eightieths are equivalent.

We can divide the numerator by 10, and the denominator by 10.

We can multiply the numerator by 10 and the denominator by 10.

The fractions are equivalent.

Importantly, if I described that as a horizontal relationship, there's a vertical relationship too.

4800 divided by 60 is 80.

And 80 multiplied by 60 is 4800.

And it's the same for eight and 480.

There's the same relationship of multiplying it, dividing by 60.

So because of that, the horizontal relationship around 10 and the vertical relationship around 60, those fractions are equivalent.

So the divisions are equivalent.

It means that we're able to solve a larger division mentally with an equivalent division, where those relationships exist.

Really, really nice mental strategy.

So coming back to the original problem, of course, we've looked at three different ways of solving 4800 divided by 80, solution was 60.

So what does that mean? What does the 60 mean? It's the part we didn't know, it's how much money in British pounds he'll get for 4800 of the Russian currency.

60 Rubles.

Gosh, he had 4800 of the Russian currency and it's only worth 60 of the British pounds! Wow.

So think now about these three strategies.

Look back at the notes you made at the beginning, did those notes that you made match any of these titles? Having worked through each of these strategies, which are most confident in using? Which of them would you need some more practise with? Have a quick think, have some reflection, and in a moment, I'll give you a chance to practise.

Okay, so let's have a go now at using those.

I've got three divisions for you.

And I would like you to use these strategies for solving them.

I've got an extra one here now, which one was not on the previous page? Division using related facts.

So for some of these divisions, you might notice a nice connection to perhaps a multiplication fact, or another division fact that you can use to solve the division that you've been given.

So we've got four, four different approaches here to have a go at using.

Press pause, work through the divisions, try using the different strategies and come back when you're ready to share.

Let's take a look.

First of all, hold up your paper.

Let me see if I can see any signs of your mathematical thinking.

Okay, good.

Yes, I can for some of you.

For some, all I can see is the quotient, the solution, so I have no idea how you solved it.

Pay attention as I go through the each of these.

I'll shown you the quotients, but I will also show you my thinking and how I approached it.

So 2400 divided by six, what is the quotient? It's 400.

We've got that out of the way.

How I can solve that using related facts, or I can spot 24 divided by six is four, I know that.

If I make it 10 times bigger, and another 10 times bigger, 24.

100 times bigger, 2400, four 100 times bigger, 400.

I've used a related fact and placed my new skills to find the quotient.

Division using factors, same problem, but maybe using factors instead of using related facts.

Divided by six, if the six is and not your strongest table, then we can find factors of six and divide by those instead.

Two and three, two three is a six.

So I can divide by two.

I know that there are 12 twos in 24, so there are 1200s in 2400s.

Then I'm dividing 1200 by three, which is 400.

And again, I can use 12 divided by three is four to help me With that, if I need to.

750 divided by three, first of all using multiples, getting the solution, the quotient out of the way.

250.

Brilliant, but how do we get that? We can think about three lots of 100 is 300.

Another three lots of 100 is 300.

So I've got 600 there now.

I've got 200 lots of three, 50 lots of three, 150, half of 300.

So I've got 250 lots of three is 750.

I've used multiples to help me solve 750 divided by three.

In terms of using related facts, 250, yeah we know that's the quotient.

We can think of three lots of 25 is 75.

So, three lots of 250 is 750.

Last one, using related facts, okay, related facts.

300 is the quotient.

Fantastic, but how do we solve it? 75 divided by 25 is three, 750 divided by 25 is 30.

So 7500 divided by 25 is 300.

I've used a related fact, I've increased it in size to match my original calculation.

And I've got the missing quotient.

Using factors, you already had a sneak preview.

Factors of 25, five and five? Five, five is 25.

So I can divide by five, 1500 using how many fives are in 75, 15 to help me.

I then need to divide that by five, 1500 divided by five it's 300.

It is the quotient.

And maybe we could use how many fives are in 15 to help us.

I'd like you to pause now to have a go at your activity where you'll get the chance to use each of those strategies for some mental division.

If there's one that you weren't feeling as confident in or haven't used as much before, give it a good go in this activity, and we'll review it afterwards.

Press pause, come back when you're ready.

How did you get on? Hold your paper up, let me have a look.

Even better, fantastic.

Earlier, there were so many of you just giving me quotients, now I can see mathematical thinking.

I can see the mental strategies you've been using.

Perfect, well done.

Let me show you the mental strategies I used.

It may be different to yours, and that's fine as long as our quotients are the same.

First one, what is the quotient? Good, 300.

So I approached that using 2400 divided by two is 1200, 1200 divided by four is 300.

Can you spot the approach I've used? I've used division using factors, good.

Eight is two times four.

So I can divide by two, divide by four, it's the same as dividing by eight.

Second one, what's the quotient? Brilliant, 400.

How did I approach it? Let me show you, see if you can give its name, its strategy.

So I used 12 divided by three is four, which I used to say what 1200 divided by three is, 400.

What approach? Good, I used related facts, and of course some place value skills in there as well.

Question three, what's the quotient? Good, it's three.

How did I get it? So I used 24 divided by eight is three.

What approach have I used? Equivalent division.

I've made 240 10 times smaller, 80 10 times smaller.

So the quotient is going to be the same.

I've reserved, preserved, conserved the proportion, the relationship between 80 and 240, and eight and 24.

So equivalent division.

And question four, what's the quotient? Good.

How have I solved it? 2400 divide by two, then divided by 10.

How have I done it? Division using factors.

I wonder how that compared to yours.

Did you use the same strategy for all of them? Did you use different strategies as you moved through? And did you really push yourself out of your comfort zone and try the ones you weren't so confident with? Question five, a word problem.

Some maths was hiding in there.

Did you find the expression 7200 divided by six? And what was the quotient? Good.

I solved it with 72 divided by six is 12.

So what have I used here? Good, I've made connections back and back, 12 made 10 times bigger, another 10 times bigger.

So from 12 to 1200, 100 times bigger using my place value skills and related facts.

Another busy lesson, you must have so much work in front of you that you could share if you wanted to.

If you do, please ask a parent or carer to share your work on Twitter, tagging @OakNational, and #LearnwithOak.

Thank you so much for joining me for this Maths lesson.

You've worked really hard and I'm so, so proud of you.

Thanks for participating, for holding things up and calling things at me through the screen.

You've given your learning such a good go, and I'm really, really impressed.

Now time for a break in between lessons if you've got some more lined up for the day.

I'm tempted to continue having a go at this but perhaps I'm better off walking away from it.

Thanks for joining me.

See you again soon, bye.