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Darts and Maths!

Key Stage 2 Maths

 

 

 

Video Synopsis

When Philip New, the head of Year 6 at Woodland Middle School, set up a darts club, he noticed a significant change in their attitude to maths and their ability to do it. In this programme, Philip explores darts as a vehicle for teaching different areas of KS2 maths.

First, he gives his pupils a breakdown of the dartboard followed by quick-fire questions to develop their mental calculation skills.

From this, Philip moves to the interactive whiteboard and asks the children to calculate his scores and share how they do their calculations.

He also develops a range of other activities based on collecting and recording data and adapts the dartboard to tailor lessons according to objectives, abilities and the time available.

Celebrity darts player, Bobby George, shares a few tips with the pupils and demonstrates his own mental arithmetic skills.

Phil feels that using darts has brought a new dimension to his maths teaching and is pleased to see the children smiling and enjoying what they're doing.

This programme resources and support materials were available via Teachers TV website but as from 29th April 2011, the website was disbanded. For anyone wanting further information regarding any of the 3,500 15min videos that Teacher TV broadcast please visit the UK Department of Education website. click here. My thanks for Teachers TV for their permission to continue broadcasting this video.

If you wish to download the interactive checkout the teacher uses plus supporting material you can from here Primary Games.Since first writing, this page the Primary Games websites has been updated. So if you can’t initially find what you are looking for I suggest you send them an email.

Updated December 2018

 

The Dartboard

If you are new to darts you may have wondered why the numbers are arranged in this fashion. Well, the numbering system used in the modern day dartboard is accredited to Brian Gamlin a carpenter from Bury in Lancashire. However, this cannot categorically be proved and a more plausible person is also suggested (Read the History of Darts)

The numbering system on a standard dartboard is designed in such a way as to reduce ‘lucky shots’ and reduce the element of chance. For further details about the board click here.

 

Know the Dartboard

So now you know the board is arranged in a way that reduces lucky shots and punishes bad shots. Just look at what is either side of the 20; 5 and 1 so if you miss the 20 you are likely to hit a 5 or a 1. Many social players, therefore, throw most of their scoring darts towards the left-hand side of the board from the 12 down to the 19 because they believe they have a higher percentage of hitting a higher score than throwing for the twenty / treble twenty and in many cases they would be correct. Regular players and the professionals you may have seen on TV never adopt this strategy/method of play. They will throw for the higher scoring trebles and regularly hit them this is purely down to Practice. If you want to be good at the game not only do you need to Practice and set yourself goals and targets to achieve. You also need to learn dart maths!

 

Dartboard Segment Values

 

Darts Maths!

‘I hate maths’ I hear you say. Well, we use maths every day in a number of forms and you probably have never given it a second thought. Every time you look at a clock you are using maths: Ever heard someone ask for the time and a reply coming back quarter past one? Similarly well you may know that is the same as 15 minutes past one and dart maths can be as easy as this.

Depending on your age you may have heard of the following:

1. Addition +

2. Subtraction  -

3. Multiplication x

4. Division -:-

5. Percentages %

6. Averages Ave

Well, the first four of these are used in every game of darts and the last two are used to judge how good a dart thrower is at scoring and hitting checkouts.

A basic game of darts starts with each thrower starting from a number ending in ’01 such as 501, 301 etc. The reason why the start numbers end in ’01 is so that a dart thrower must hit at least one odd number to enable him or her to finish the game on a double. Each player throws three darts in turn and the sum of the score they hit is subtracted from the starting or the remaining total. The game must be finished by hitting a double equalling the amount they have left i.e. If a player is on 20 and they hit a double 10 (2x 10 =20) then they win the game. If their score more than the 20 say they hit a double 15 (2x 15 =30) they bust and go back to the score they were on before they took their throwing turn.

For the purpose of this game, we are going to play 301.

 

How to score

Each player throws three darts into the board and the total number is added together then subtracted from the starting number or remaining total

Example

First throw: Dart thrower A hits 16, 3, 17 giving a total of?

16 + 3 + 17 = 36

Now can you take the total scored (36) from the starting number 301?

301 - 36 = 265

This now leaves you now 265 to score, but before I go any further I will explain how to add and subtract, you may already know but if you don’t here is how to do it.

Let's take the three dart scores again 16, 3, & 17 by aligning them up under each other it makes adding them together easy. We align them up in HUNDREDS (H), TENS (T) & UNITS (U) and in this case, we have do not have any HUNDREDS

e.g.

1. First of all, we arrange the numbers under as follows: Fig 1

2. We then add together then UNITS column 6 + 3 +7 = 16. We place the 6 under the === sign and carry the 10 or 1 TEN over to the TEN’s Column: Fig 2

3. We now add the TEN’s Column including the carried 10 TEN 1+1+1 = 3 Fig 3

Maths image 1

4. Now how to subtract this 36 score from the starting score of 301. Remember how we added numbers together, well we subtract these in a similar fashion. First, we arrange the two numbers in the same HUNDREDS (H), TENS (T) & UNITS (U) fashion but we put the number we are want to subtract from first followed by the number we wish to subtract. Fig 4

5. So here we subtract the units first but 6 from 1 leaves a negative number and therefore we need to borrow a TEN to complete the calculation but as you can see we have a 0 in the TEN’s column, therefore, we need we need to borrow a ten from the HUNDRED column. Fig 5

6. Now you can see the HUNDRED’s column has reduced from 3 to 2 because we have taken Ten from it and now the Ten’s Column reads 10 not 0. We can now borrow a Ten from the TEN’s Column to place into the UNIT’s so we can subtract 6 Fig 6

6.1 Now the UNIT’s Column reads 11, the TEN’s Column reads 9 and the HUNDREDS column reads 2. We now proceed to subtract the 6 from 11 = 5 Fig 6

Maths image 2

This is basic mathematics and I know arithmetic is now taught differently in school however this was how it was taught back in the 1970s! It works!  if you are an adult and find this hard to follow, please.

Now back to the game!

After throwing 36 in his first throw player A is left to score 265. In the next three throws, his dart throwing accuracy improves and he starts to hit a few doubles and trebles which helps reduce his score quiet fast. Here is what he scored with his next three darts:

Double 20, Single 18 and a treble 13 so what has he scored?

Double 20 = (2 x 20 = 40) or (20 + 20 = 40)

Single 18 = (1 x 18 = 18) or ( = 18)

Treble 13 = (3 x 13 = 39) or (13+13+13 = 39)

We add the totals of each dart together to as before:

Maths image 3

In his next throw, player A scores the following :

Double 19, Treble 15 and Double 17 Can you work this one out?

Here is his total score of 117 but I will leave it to you to work out how I got there. Now subtract this from player A’s remaining total of 168 = 51. I will again leave you to work this one out.

Now the game of darts must be won by hitting a double that equals your remaining score. A bull’s eye (50 points) counts as a double outer bull (25). Therefore player A may wish to throw for a number 1 to leave 50 and if he hits the bull he wins the game, but there are many ways he can finish. Can you work them out?

Here are a couple of ways to get you started.

The player could hit a single 10 and a single 1 to leave 40 which is double 20 i.e. (2 x 20) He could hit a treble 15 (45) to leave 6 which is (2 x 3)

There are many more ways and for a bit of fun see if you can record them all using only 3 darts!

 

Times Table

We have only touched on two other maths problems here so far. When we come to higher scoring, Multiplication and Division come into play. You may have heard the words ‘Times Table’ before in a maths lesson at school or may have built your own ‘Times Table’ sheets which may have looked something like this:

I found this a handy device to help me learn and memorise basic Multiplication. So if I wanted to know what 5 x 9 totalled I would move down to the 5 and across to the 9’s column and before long I didn’t need the sheets at all. In darts, you only need to know up to your 3 Times table up 20 and of course, know that 2 outer bulls (2 x 25 = 50)

Free to use for schools, colleges, students and teachers I have now added a free downloadable Times Table Sheet 25 x 25.

 

Times Table Chart

Times Table Chart

Times Table Sheet

Here are all the scoring numbers on a dartboard.

Darts times table

Bullseye =  50  Outer Bullseye  =  25

Ok so, you know how to add up, subtract, multiply and divide. Any decent player would not use a calculator or use H T U to add up and subtract fast. A decent dart player can work out basic maths and know how to throw for high checkouts faster than many maths teachers! It is a question of learning. If you have ever watched a professional darts player on TV, when he or she is looking to win the game they know what to hit to checkout high scores

 

Example:

143

This can be achieved a number of ways but because most dart players Practice throwing for the treble 20 most of the time if a combination shot can be achieved using a treble 20 more often than not they will use it. Therefore 143 = Treble 20 (60) Treble 17 (51) Double 16 (32) to win. But are there other ways to go? The answer yes, but I will leave you to work them out using the above table to help you if you need to.

In the sport of darts, there are a number of three dart finishes that can be hit, the highest being 170. This can be achieved by hitting Treble 20 (60) Treble 20 (60) and the bullseye 50 (which is counted as a double outer bullseye). But you can not checkout 169, 168, 166,165, 163,162 & 159 with three darts! These are commonly known as bogey numbers because you can checkout higher numbers but there is no way of checking out these in three darts. All good dart players will know this and they will try to avoid leaving these numbers if possible.

I mentioned earlier that a basic game of darts uses addition, subtraction, multiplication and division in all games but to see how good a dart thrower is we refer to statistics! ‘What is that!?’ I hear you say, another boring maths lesson! Well, yes, but many adults find the statistics hard but for this purpose, I will keep it very basic.

The two most commonly used statistics used in darts are dart averages and percentage doubles hit. We will start with the latter first.

What is a percentage? Well, a percentage is a term that can be described as a rate, number or amount in each 100. If your teacher says you have got 98 questions correct out of a 100 then this can be described as you achieved 98% of the questions correct and to work a percentage out we just need to divide one number into another and multiply the answer by 100. Here are some examples

Again you are set 10 questions you answer 8 questions correctly so what is this as a percentage:

Well if we divide 8 / 10 = 0.8 if we now multiply this by 100 it now equals 80, therefore, we can say you have achieved 80%

Here is another you score 4 out of 8 attempts at goal when you play football so what is your percentage success rate? Well let’s see:

4 / 8 = 0.5 and if we multiply this by 100 we get 50, therefore, your success rate is 50%

But now back to darts, sometimes we see some statistics showing the frequency a player hits a target he is aiming for and the most common in darts is the doubles percentage hit.

To calculate this we basically look at how many darts are thrown for a double and how many are hit therefore if a player throws 1 dart and hits the double first time he or she is said to have a success rate of hitting a double 100% of the time (remember 1/ 1 x 100 = 100 or in this case 100%)

But if he takes 2 darts to hit the double then he or she has hit 1 out of 2 and expressed as a percentage = 1 / 2 = 0.5 x 100 = 50 or 50%

So during a course of a match, the player has to win several games or in dart terms 'legs' to win a match. So he or she may have thrown 20 darts at double and hit a total of 7 this works out as 7 / 20 = 0.35 x 100 = 35%. So it can be said the success rate of the dart player hitting his or her doubles is 35%.

Darts Checkouts and Average Calculators Click here...

 

Dart Averages

It is one of the most referred to statistics in the game of darts. It gives a good indication of good a dart thrower when compared to others even if they don’t play against each other. Here is how you work out dart averages.

Basically, you just divide the number of darts thrown into the score achieved. Therefore if a player wins a game of 301 and he or she has taken 12 darts to do this then their dart average is 301 /12 = 25.08 this sometimes can be expressed as a throw and therefore this number is then multiplied by 3 (3 darts in a throw) = 75.24. This is very simple but what if you didn’t win the game what is your average?

Well, let’s look at the losing player. He/she also threw 12 darts but only achieved 255 points so again we divide 255 / 12 = 21.25 or 63.75 per throw.

Averages are usually a sum of a number of games not just one but the same principle applies: you divide the total amount scored by the number of darts thrown. Generally speaking a dart thrower with a higher average is likely to win more games but this is not always the case because whoever throws first has an advantage and also a player may play a very bad game followed by several good ones.

There are a number ways you can use darts to help your maths and in turn, this helps your darts. Being confident about your maths will give you an edge over players that struggle with arithmetic.

Here are a few questions you can test yourself on but please don’t email your answers or ask for the answers as I am not your maths teacher!

1.How many ways can you score 26 with 3 scoring darts

2. How many ways can you checkout 100 finishing on a double but not using more than 3 darts?

3. What is the highest score you can hit using three scoring darts?

4. What is the highest checkout you can hit with 3 darts?

5. What is the lowest checkout you can do using all three scoring darts?

6. Hitting three different green segments of a darts board what is the highest number you can achieve in three darts?

7. Hitting three different only red segments and not counting the bull what is the lowest number you can hit?

8. If a player plays a game of 501 and he averages 60 points per throw with his 3 darts how many darts will it take him to finish the game? (whole number only)

9. Give two examples of checking out 82 with two darts. You must finish on a double!

10. What is the sum or total of all the scoring segments on a dartboard?

 

Useful links:

Another great resource site for helping you understand or teach maths can be found at the 'Interactive Resources Site.' click here

Have Fun!

If you are an adult and would like help with your maths then don’t be shy contact The Department of Education.

 

 

 

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