On the first day of christmas...

You all know the song... 

On the first day of Christmas my true love gasve to me a artridge in a pear tree..

And so on. For mathematicians everywhere, there are three questions about this song that are just screaming to be asked, and one of those questions can easily be answered.

The second one is a little more difficult, and the third especially so in this day and age.

The first question that tends to get asked is "how many presents does this mean my true love gives me?"

You do need to be careful here, it is not necessarily as easy as people first think (much of maths isn't!). The most common response is to do 1+2+3+ ... +12 = 78, but a little further inspection suggests this may not be the full answer.

Day 1 - A partridge in a pear tree. 1 present

How many presents on day 2? It's not 2...

Day 2 - 2 Turtle Doves and a partridge in a pear tree, That's three presents, so after 2 days you have already been given 4 presents.

What about day three? How many presents on day 3? How many does that make altogether? Now, day 4, day 5, and so on all the way to day 12.

How many presents have you got altogether?

How many of each present (I hope you like gold rings!)

Question 2 is what about the 'n' days of christmas. There is a formula for the total number of presents you get over n (any number of)  days, but it is not a trivial solution.

Question 3 is less maths, and more economics... For the twelve days of christmas, how much would it cost!! Good luck ith that; whilst gold rings may be in the Argos catalogue, or on Amazon, and you may be able to source a pear tree at Whitehall Garden Centre, you may struggle a little more with the French Hens, Turtle Doves, and as for Lords a Leaping, I've no idea where to even start!

Good luck!

Y10 Do the Apprentice

Congratulations to Year 10 for a fabulous Business and Enterprise PSHEE day based on The Apprentice.

As well as learning about about personal and business finance options, Year 10 planned an event, designing tickets, room layout, and catering (including cupcakes!) and  entertainment options.

They came dressed to do business, as you can see from the pictures below.

Best Maths Question... Ever...

Have a look at the link below.

I'm not sure I've worked out the answer!

What do you all think...

http://flowingdata.com/2011/10/28/best-statistics-question-ever/

St Dunstans Visit

Huge thanks to year 6 for letting me visit today, and talk about codes and ciphers.  This is a part of their work on World War 2 at the moment.




We looked at some older ways of hiding codes, including shaving heads, tattooing it, and then letting the hair grow back, wrapping a strip of paper around a stick, and then writing the message, and even writing the message on the inside of a hard boiled egg (sadly this experiment has now failed 3 times, so it is not the most reliable method!!


We moved on to look at Caesar ciphers, pigpen ciphers (font here), and the Sherlock Holmes Dancing men cipher (Font here).  NB. Please ask permission before installing new fonts to your computer.


Eventually we moved on to talk about the magnificent work done by Bletchley PArk code breakers during the second world war.  We found a major flaw in the enigma code by putting loads and loads of 'D's into a virtual enigma, and looking at the output.  Here is the virtual enigma we used - can you spot any flaws!


I want to thank Y6 at St Dunstans again for letting me visit, and making me feel so welcome.  Hopefully many of them will work with us on the National Cipher Challenge when they join us next year

KS4 Parents Forum

We hope you found the KS4 Parents forum useful.

Here are the slideshows from the evening, in case you either missed the evening, or want to recheck any dates.

Y10 Maths

Y10 English

Y11 Maths

Y11 English

Visit to King's Lodge School

Miss Martin and I went to spend an hour with both Y6 classes at King's Lodge school in Chippenham this afternoon.  It was part of their topic on World War 2, and we went to do a bit of maths, and a bit of history about code breaking - in particular code breaking during the war.

We started with a bit of more ancient history - messages wrapped around sticks, shaved heads and tattoos, and even messages written on the inside of a hard boiled egg!

Next we talked a bit about the Caesar Shift - to download your own code wheel click here...

We even had a play with a virtual German Enigma machine.  It has got 15 000 000 000 000 000 000 possible settings!  To play with the settings and encrpyt your own messages you can click here...

To finish students solved a murder mystery, where clues covered a range of different techniques. The key to each of the clues can be found here.

Thankyou to King's Lodge for inviting us in, and a massive well done to Y6 - we were very impressed with how well you engaged with the discussion and the challenges!

National Cipher Challenge 2011

It is back, one of the most fun and eagerly awaited competitions of the year (for me anyway!)

The National Cipher Challenge is a codebreaking competition open to schools across the UK.  Registration opens on Thursday 15th September, with the first challenge on Thursday 29th September at 3:15

We are looking for teams of about 4 students per team willing to take part.

Training will be given in Maths Club time, Tuesdays after school and open to everyone.

For more details, come and see Mr Smy, or just turn up to maths club on Tuesday.

The Competition site is http://www.cipher.maths.soton.ac.uk/.

Good Luck!  As well as the national Leaderboard, we will be posting a John Bentley Leader board here on the blog.

Well Done Y13

Thursday saw The John Bentley School Maths department achieves its best A Level results ever!

In total our students (6 of whom are pictured above) achieved....

1 A*, 8 As, 4 Bs, 1 C and 1 D. These results are not only a significant achievement in themselves, but beat both their personal targets and school targets.

In addition this was the first year group at John Bentley to study for Edexcel AS level in Further Maths, acourse that is rapidly growing in popularity at school.

Results for Further Maths were ...

2 A's, 1 B, 1 C, and 1 D. Students achieved these Further Maths results in just 1 lesson a week, with significant amounts of independant learning and hard work.

One student worked even harder than the rest, and taught himself A2 Level further maths, including the Further Pure 2 & 3 modules! Despite having to do most of the work independantly James managed to not only achieve an A* in maths, but and A in Further maths.

All of our students worked really hard over two years, and deserve the fabulous results above. Despite being involved in many other things both in school and out, such as Duke of Edinburgh awards, many being Head Students, and sporting commitments they never let anything get on the way of their studies.

Well done!

Design a drinks carton

10 M 1 have been designing a drinks carton. The only rule is that the volume must be 330ml, and they need to work out the Surface Area to make sure it does not cost too much to make...

Lydia decided to get creative...

Year 5 Open Evening

Welcome to open evening.

One of the activities we are doing is a data collection exercise, creating live pictograms.

We are also collecting data online, using a Google Form.

Keep refreshing this page (press F5) to update the chart below to the most up to date information.

Year 5 Caeser Shifts...

Congratulations to Y5 for making such fantastic code wheels today, and decrytping such wonderful work.

Don't forget to bring your code wheels with you to open evening.

Feel free to reply to the following message in the comments for this blog...

the only clue I will give you is gT....

ZL SNIBEVGR OVG NOBHG BHE QNL NG WBUA ORAGYRL JNF

Comments will be published once moderated.

See you Thursday!

Year 8 Enigma Challenge Day

10 intrepid year 8 came on a maths trip across to chippenham for a gifted and talented event looking at codes, code breaking and problem solving.

There were 5 sessions, a lecture from a very enthusiastic cambridge profesor, with a real working 2nd world war enigma machine, followed by 4 sessions that covered more code breaking, mystery solving, a celtic knot investigation, and problem solving games and puzzles.

Many thanks to Miss Wenban for organising the trip

Here's what some of the students thought.

---

A group of year 8 travelled to Sheldon School to take part in the Enigma Maths Challenge which consists of puzzles, breaking codes, mysteries and solving problems.

The day started in the hall, we joined the other schools that were already there. A mathematician from Cambridge University came in with an enigma machine which was used in World War 2 to make and break codes. We all got the chance to see how the machine worked and it is the only one that is not in a museum.

The mathematician talked to us about his job and what we would be doing during the day. He talked to us that there are jobs that are just breaking codes and solving problems. Some of the best code breakers were used during the war to solve any codes that the Germans sent. After a while a machine was built so that the English could find out what the message said before the German officers knew what it said.

We learnt a lot about the enigma machine and how it worked at what different things mathematicians do as a job. The talk was very helpful and inspiring.

Kayleigh Roberts

[click here for a virtual enigma machine!]

---

We did a lesson on code breaking with a mathematician from Cambridge University. He showed us lots of different methods to decipher codes for example very famous codes such as the caesar code. He gave us lots of different codes for us to work them out and decipher them. As we went along we got better and could handle more difficult ones so we definately learnt new skills and we will take them back to JBS. Overall the lesson and the whole day was very good and we had a great time!
Caoimhe Kelly

---

Celtic Knots

Practical Puzzles

Year 7 PSHEE Day - Design a theme park

Year 7 have been very busy today, designing their very own theme parks, and seeing who could make the most money.

Hre are some of the facts and figures they were given... (and yes that is me and my family in the first picture!)

Competition was fierce, with students desperately trying to keep within the £500,000 build

budget, and keeping their daily running costs down.

After an early 3 day press viewing to test numbers, designs were tweaked, car parks improved, and rides added. Team also scored each others designs in a trade fair to increase advertising and therefor getting more paying customers through the door.

In the afternoon gates opened at the parks, with the number of visitors dependent on numbers of rides, cost, car park size, and how visually fabulous the designs were!

Congratulations to the following teams for winning in their respective houses...

Kerry B - Pure Adrenelin - £80630

Kerry J - Cheeky Monkeys - £71414

Shelbourne B - Treasure Tower - £80150

Shelbourne J - Awesome Land - £70541

Lansdowne B - A step in time - £83845

Lansdowne J - Spotty Fish 31 - £83577

Fitzmaurice B - MCL - 79894

Fitzmaurice J - CTF 75795

The Winning Design

Kerry B Average - £50426

Kerry J average - £61428

Kerry Overall Average - £55927

Shelbourne B - £57825

Shelbourne J - £61320

Shelbourne Average - £59573

Lansdowne B - £58142

Lansdowne J - £57375

Lansdowne Average - £57758

Fitzmaurice B - £57026

Fitzmaurice J - £58932

Fitzmaurice Average - £57979

The overall winning team was A Step in Time with £83,845 profit over 7 days.

The winning house was Shelbourne with an average profit per team of £59,573

Well done to all who took part, espcially our winning teams.

If you are in Y7 we would love to get feedback - what was the best bit of the day, what did you enjoy the most. Which bit of the day would you change - feel free to leave comments below.

Here are some pics - a random few. We'll add more over the next couple of days.

Year 6 Day - Factor Caterpillars

Corridor Display

Can you spot yours?

Here are some Factor Caterpillars that year 6 made today on their visit to the school.

Max

unknown!

Sophie

Charlotte
Kirsty

Lauren

Millie

Cerys

Ben

Millie

Bethany

Nick

Owain

Connor

Victoria

Y11 Exam (part 2)

Here is a link to the list of topics and what we think may still come up.

https://docs.google.com/document/pub?id=1nQtMRottYtSa9ayaNHr1O1Jv6ZzSGssxWXWHB0lZeRk

It is not a guarenteed list.

See you for maths on Wednesday P1, or through email / twitter.

Otherwise, see you Friday for the exam!

Year 11 Exam

Year 11,

Well done on your exam today. We've worked out what was missing, but are not allowed to share until tomorrow, so best bet is to come into the lesson, or come back to this blog tomorrow.

Hopefully we'll see you in class (Tuesday P1 and Wednesday P1), but failing that 9 o'clock Friday for the CALCULATOR paper.

Opinion polls. Be careful

I did a poll through twitter before the referendum in May 2011.

In it, 72% of the 61 respondants said they would vote 'yes' to av. In the actual referendum only 39% actually responded with a yes vote.

Why the massive discrepency? I asked an almost identical question to the actual referendum, and was very careful to not push my own opinions in tweets I sent out when trying to get responses. If sent a tweet out with a link, I tagged it with either both #tags - #yes2av and #no2av, or with neither tag.

A very similar thing happenned in the 1930's in the USA, on a much larger scale, during a presidential election.
You only need to know that there are two main parties - the Democrats and the Republicans.

A polling company did a MASSIVE phone vote as part of the pre election process. All of these polls showed an overwhelming majority for the Republicans.

When the actual election came around, it turned out to be a Democrat landslide. Why?

A bit of history into 1930's America may help you to find the answer, and then you can try to work out how that relates to my own little poll above.

Answers, comments and ideas are, of course, always welcome.

Maths doesn't have all the answers

Many people (including maths teachers) assume maths has the answer to life the universe and everything. (The answer is 42 - Click here to find out why!).

In particular maths has the answer to "how do i make the most money?". Here is an example.

Drinks companies - Coke, Pepsi, Schweppes etc. - are big business. Their aim is (understandably) to make as much money (profit) as possible.

Therefore - you would think - they would design the cans their drinks come in to be as cheap as possible, to make more money.

To make a can as cheap as possible, you need to use as little metal as possible. This means that for a fixed Volume of 330 ml, you need to reduce the Surface Area to as low a number as possible.

Whilst this sounds complicated, the picture below is the working for this problem, as done in class with Y12 mathematicians.

As you can see, the radius of the can should be 3.74 cm and the height should be 7.48 cm. (NB - the Diameter and the Height are the same, is that coincidence). Compare this to a real can. If the maths says a can should be a certain size why are they not - the company could make more profit (by making cheaper cans).

So - your thoughts please - why do they not make the cans this size? The answer is in work you may do in Tech lessons...

Get the App....

You can now download an app (for Android only at the moment), that makes it easier to view the blog on your Android device.

This app is really just an experiment in app creation, so all comments really are appreciated.

SmartPhone Apps for Learning

Whilst you are (rightly) not allowed your phones out in school, unless your teacher specifically tells you that you can use it, there are a number of apps you can download (free) from the android market place that can help support learning.

Yes, this is android specific, but many of these apps are also available for apple, be it ipad, iPhone or iPod touch.

Evernote is one of the most general purpose. Keep notes, photos, voice memos organised, and tagged. It has the advantage that all notes stay synchronised across all devices. This means my notes are on my phone, my iPod touch, and my school laptop. I can also access than by logging on to their web site from any other computer. Some students have used this to take pictures of exam question s that they struggled with, using the photo as simply writing about a graph question is less effective. The picture is taken from a y11 learning journal, and shows how it can be used (click to enlarge).

Algeo is a graph drawer / calculator. Whilst there is no substitute for your own scientific calculator, if you are plotting or sketching a graph it can be useful to double check the shape. It only draws graphs in radians, so don't forget to double check. For things that don't involve sin / cos / tan, however, it is very simple to use.

Dropbox is also general purpose, and replaces the need for a usb memory stick that is too easy to lose. It's a free online 2Gb storage space. Like Evernote it synchs between web browser, PC download, and Android / Apple download, but instead of notes, it is files of any sort. This means you can work on a document at home, and upload to dropbox when done. You can download to your mobile device if you want to check it, or you can access it through the web at school, or on any pc. It also allows the sharing of files between users, although this is not something I've tried.

Triangle Solver is a simple triangle solver. Type in any three bits of information from the six about any triangle (3 sides, 3 angles) and it calculates the other three using Sine / Cosine rule. It also copes admirably with the case with 2 possible solutions.

Solver, on the other hand, uses the quadratic formula to solve quadratic equations - again, useful for checking answers. Bad news (for most students) if you have an equation that doesn't really have any solutions, you will get a funny complex answer which involves the number i. Sixth form further mathematicians - good news - if you have quadratic with no real solutions, it will give you complex ones!

Wolfram alpha is not a free app, but the mobile website is free. Anyone who has seen it in action knows how powerful it is. If you haven;t then go play! Wolfradroid is a free app, which allows you to speak your entry to W|A!

One last one - Shush! IT allows yuo to put your phone on silent, but decide what time it should become noisy again! Perfect for school. Silent (and in the bottom of your bag) at 08:30, but automatically coming on again at 15:30 for home time. I use it all the time.

So, who has used any of these apps - how have they supported your leaning? What other apps are out there for android that will help your maths, or your learning more generally.

Who uses apple? What ipod touch / iphone apps would you recommend? Who wants to write a blog post on apple apps to support learning? Email the usual address, or come and find me at school.

Published by Mr Smy.

120 Percent

Have a look at this one, as spotted by Miss Martin on her holiday in America.

Clearly 120% of the drink cannot be Vitamin C - that would be silly. What do you think the 120% does actually mean? What else could it mean?

World Maths Day

Yes, its back and bigger than ever.

All students should have their login details from tutors, and its tutor group vs tutor group and year vs year. There is team glory and individual glory to be won.

Go to www.worldmathsday.com, log in and get going.

You can also download the free apps for iPhone, iPod touch or even iPad.

Subscribe to this blog for regular updates.

My Averages Question

My maths teacher mr Smy gave me a maths question, totally made up in his head, and told me to go away and try to work it out.

Question: If I have 5 numbers with Mean=9, mode=10, median=11. What are the numbers?

= 10,10,11,?,?

And i said it won't work because....

• you cant get a higher number than 11 to make 45 because it all ready adds up to 31
• if you add 12 to that it will equal 43 then you would need a 2 and the two can't go in front of the 10 beacuase the median will change.

Luxmi 7BN

Year 9 - Sharing Petrol Costs

What is fair?

9M5 looked at this problem last week...
They looked at different ways that the costs could be shared between the students

Here are their different solutions.


Which do you think is fairest?
Are there any other answers you could suggest that you think are fairer?

QR Codes, what are they?

Do you know what a QR code is?

It's one of those 2-D barcodes you see cropping up all over the place. The QR stands for Quick Response. You may have seen this one around school...

A QR code can be a number of things.

• It can be a link to a website (like the one on the right).
• It could simply be a piece of text with some information on.
• It can write a SMS (text) on your phone, with the number to send it to already there
• It can be a mobile phone contact, ready to save.
• An iTunes link, or an Android Marketplace link.

Go and have a look at http://www.qrstuff.com/ for easy ways to create your own.

There are three main ways to read QR codes like the one above...

1. On an iPhone. Go to the App store, and search for a QR reader.
   
2. On an Android. Again, go to the App market, and search for a QR reader.
3. Using a PC and webcam. You will need software to read the codes. I recommend QuickMark (which is also available for iPhone / Android).
   

Look out; here comes the maths bit.

A QR code is a 2-dimensional array. Each pixel is either black or white. QR codes like the one above are 32 pixels by 32 pixels. How many different QR codes do you think there can be?

Mathematicians would try to make it simpler to work out (at first). What about a 4 x 4 QR code? How many do you think there would be. If you want to practice colouring some there is a blank grid here...

Be careful - even with the smaller grid there are a huge number of possible codes - think systematically.

More bad maths!

Here’s another dodgy deal, spotted by our very own Miss Lee.

Bad Maths

For our first post on our new blog, some Bad Maths (or at the very least bad marketing) spotted by Ryan in Calne. Keep your eyes open, and if you see anymore write your own post - details on the "About this blog" tab above.
If you want to contribute anything mathematical, send it in.