# Lesson video

In progress...

Hello, my name is Mrs. Behan and for this lesson, I will be your teacher.

In this lesson, we are going to use all of the addition strategies that we know and the subtraction strategies that we know, to work out the points scored in a game.

Let's begin by looking at the lesson agenda.

We're going to review familiar calculation strategies.

We're going to add and subtract in the context of a game.

We're then going to include some multiplication strategies.

And at the end of the lesson, there'll be an independent task for you to have a go at.

I know you'll be keen to find out how you got on so don't worry, I will go through the answers with you.

There are a few things that will help you in this lesson.

You'll need something to write with, a pencil or a pen.

Something to write on.

And it might be good if you could find some dice.

If you don't have those things to hand, just pause the video now, whilst you go and get them.

Remember, try to work somewhere quiet where you won't be disturbed.

We're going to apply our knowledge of addition and subtraction strategies into a game this lesson.

We will need to draw on everything that we already know and we're going to be selecting the most efficient strategies.

We're going to be adding and subtracting in the context of a game of darts.

Have you ever heard of darts before? Have you ever seen a game of darts being played? Well, it involves a lot of mental addition and subtraction.

Here is a reminder of some strategies that you will be familiar with.

Partitioning.

Partitioning tens and ones in a number and recombining once you've added the two separately.

Using known facts.

So I know that three plus three is equal to six, that will help me if I need to calculate 30 plus 30.

I could work out that it is 60.

I might have a number and I need to add 47 to it.

Well, why don't I round up 47 to 50 to make it easier.

Doubling and halving.

You should be able to recall your doubles and halves really, really quickly to help you with any mental calculations.

Finding the difference.

So the difference means the gap between the numbers.

So what is the difference between one number and another? It's that gap.

And counting on or back.

It's a very efficient strategy to use.

We need to be thinking about efficiency and using efficient strategies.

Dart players need to do some maths pretty quickly.

So they will need efficient strategies to use.

Let's have a look at the game of darts.

This is a dartboard.

And to play, you have three turns.

You have three turns of throwing one of these.

Now this is called a dart.

You throw three darts into the dartboard and then you add the scores that you land on to give you your total.

So if my dart lands here, I will score three points.

If my dart lands here, I will score four points.

If my dart lands over here, how many points will I score? That's right, I will score 11.

You get the idea.

So I played darts and on my throw number one, my first throw, I scored 20.

My dart landed at three for my second throw.

And my third throw, I scored 14.

So, can you do that mental calculation for me and add up my three numbers? That's right, my total is 37.

So I added third, sorry, 20 plus 14 to make 34 and three more is 37.

So that's how I calculated it.

Did you use a different strategy? Was it faster or did it take longer to work out than mine? So, what is my total here? Throw number one, I scored 13.

Throw number two, I scored seven.

And on my final throw my dart landed in number 12.

So can you add up my score for me? My total is 32.

How did you do it? Well, I looked for a number bond that I could see.

I noticed that 13 plus seven is equal to 20.

20 plus 12 is equal to 32.

Darts is actually a game for two players.

Now, the way it works is that each player starts with 501 points.

Every turn that player deducts their score from their total number of points.

So looking at my previous example, where I won 37 points, I would start at 501 and I would have to subtract my 37 from that.

And the winner basically is the person who's closest to zero.

So, my starting amount is 501.

We're pretending now that we've started a brand new game.

So have a look at the scores that I have won.

I scored 20, 14 and three.

So my total is 37.

So I need to subtract 37 from 501.

So you can see we're using addition strategies and subtraction strategies now.

At any point, if you feel like you need some time to think, just pause the video and then join in when you're ready.

So, I'm going to use a number line for this one.

So 501, I'm going to take away one first, because that gets me to 500, which is a nice, easy number to work with.

Multiple of 10, multiple of 100.

And then we'll subtract 30.

You can see I'm starting to partition 37 into different numbers.

A one, a 30, so what else have I got left to take away? So I actually need to take away six more.

So 470 or 470 subtract six is equal to 464.

So my total paints now is 464.

It's not the only way of calculating 501 subtract 37.

Now, there are other ways as well.

So I could round and adjust.

I can round 37 to 40 by adding three.

Then I can subtract 40 from 500, which is 460.

And then I'll add one back on.

Now that's because I didn't subtract from 501, I only subtracted from 500.

So I needed to add the one back up there to make the difference the same.

So 501 subtract 40 is equal to 461.

461 plus that extra three I took off when I rounded is 464.

So again, that's just another way of calculating.

I'd like you to pause here now whilst you fill in these grey boxes.

What might be hiding under the grey boxes? You have enough information on the screen to help you.

Pause here whilst you figure it out.

Then when you're ready, come back to me.

Did you work out at the score? Okay, let's go through it together.

I scored 18, 10 and 19.

What is the total? My total is 47.

So now I need to subtract 47 from 464.

I don't start again from 501, I'm going to subtract from 464.

So, this is how I did it.

I can round 47 to 50.

So I do 464 subtract 50 is equal to 414.

Now I need to take away, sorry, now I add the extra three I took away.

When I subtracted 50, I took away too many points because I only needed to take away 47.

So the gap between 47 and 50 is three.

So I need to add to that back on.

So 414 plus three is equal to 417.

Another way of working it out was to draw the dienes out.

So you can see I had 464 and then I subtracted 50 and then I added the three back on.

So that's how I rounded and adjusted to find the difference.

417 is my new score.

So if you have someone to play with and some dice available, you and your friend can play.

Instead of starting at 501, why not start at 201.

And this is how you do it with dice rather than darts and the dartboard.

You roll the dice two times to make two, two digit numbers.

So I will roll a dice twice and I might make 33 and I'll roll it two more times and I'll get 15.

Then you roll one dice to make a one digit number.

So for example, six.

You need to have two, two digit numbers and one, one digit number.

Then you're going to add up your three scores like I've done here.

So example 33 plus 15 plus six is equal to 54.

And you can use whichever strategy you like, but remember the fastest one and the quickest is the most efficient.

That's the best strategy to use.

Not one that's going to take your ages.

So 201 subtract 54 is equal to 147.

And then it's your friends go.

So your friend will repeat steps one to three.

And you carry on playing until you end up with zero points.

Whoever gets to zero first, wins the game.

Okay, there are some more rules in a game of darts.

If you land on the inside ring, can you see how it's got red and green tabs on it? Well, if you land on that inside ring, 'cause sometimes the dart can go in that very small space.

You triple the number of points you had.

You triple the points, that means multiply by three.

If you land on this outer ring of red and green tabs, you double your points.

Doubling is the same as multiplying by, that's right two.

So you double the number of points.

For example, if you land on 10 on this outer ring.

So that would be this point here, if you land there on that red tab, you get to double your points.

So you get 20 points.

If you land on the red part in the middle of this bit here, that's called the bullseye and that's worth 50 points.

Everybody loves to get the bullseye, you get the most points there.

And if you hit the green area around the bullseye, you earn 25 points.

But those are in the centre of the dart board, so those are worth more.

So can you calculate my total? On my first throw, I landed here.

So it's on the outside ring so I get to double my score.

So 20 multiply by two is equal to 40.

On my second throw, I got triple 10.

I landed on the inner ring here.

So my calculation is 10 multiplied by three, and I've worked out, it is 30.

My final throw, I landed in this segment here.

So the score was 11.

So now work I'll work out the total.

So 40 plus 30 plus 11 equals 81.

Those are quite easy to add up because I've got two multiples of 10 there.

So I know that's 70.

70 plus 11 is easy to calculate, it's 81.

But now I need to deduct it from 417.

That's a little bit trickier.

So you could use any strategy that you like.

Well 417 subtract 81 is equal to 336.

I actually adjusted this and I did 416 subtract 80, which was 336.

You are ready now to have a go at the independent task.

So here is a dartboard and I've listed the points that I earned when I took my turns.

So I started with 501 points as a new game normally does.

On the first turn I scored 20, 30, and 16.

So you need to add up that to find out what I got as a total for turn one, then you will subtract it from 501.

You then look at turn number two, I Scored 14, nine, and 15.

You need to add those three numbers together to find out the total of what I scored for turn number two.

Then you subtract it from whatever I have left after turn one.

And you keep going in that way.

I also scored some triple numbers and some bullseyes as well.

So don't forget a bullseye is worth 50 points.

If you triple it, you multiply the number by three.

And if I scored a double, you multiply the number by two.

So I want to know how many points do I have left at the end of my sixth turn.

When you ready come back to me and we will go through the answers together.

Okay, then.

So we start with 501 points and then turn number one, I scored in total, this adds up to 39.

So I subtract that from 501 and I have 462 points left.

On the second turn, this totals 38.

So 462 subtract 38 is equal to 424 points.

On turn number three, I add all these three points, these three scores together and it's 41.

424 subtract 41 is equal to 383.

On my fourth turn I scored triples and a bullseye.

Remember a bullseye is worth 50.

So altogether the value of my fourth turn was 70 points.

383 subtract 70 is 313.

On turn number five, I scored this many points, which totaled up to 94.

313 subtract 94 is equal to 219.

And on my sixth go, I had double 15, 16, and nine, and the total was 55 points.

So 219 subtract 55 points is equal to 164.

So how many points do I have left? I have 164 points left.