Business: Tips for students studying AQA Unit 3: Strategies for Success

AQA Unit 3: ‘Strategies for Success’ requires A-Level students to have a full understanding of strategy in terms of finance, marketing, operations and human resources. Typically the case will be based upon a strategic decision that the business might take. The theory behind the exam is extensive; however, the following are a few key areas that from my experience need to be pushed heavily with students.

1. Making effective use of the case study is paramount. I would expect no student to even attempt the questions before understanding the real underlying issues from the case study. The use of well-placed selective arguments focused on the question means that students should spend around 10-15 minutes really understanding the case study before attempting to answer even the first question. Students need this time to plan and become more selective in identifying their key points. The use of a SWOT analysis has been particularly effective in previous years. I have often asked students to place an ‘S’ next to case evidence where a competitive advantage can be seen, an ‘W’ next to internal factors of weakness that may provide them with a competitive disadvantage, an ‘O’ next to external opportunities and a ‘T’ next to those threats that are outside of the control of the business. The need to be really selective is vital. What are the main issues that really jump out at you? Students will need to only select a few points here for deeper analysis. Often I have asked my group to break the question down and catalogue the elements of the case study in list format in terms of importance that most precisely provide the examiner with what they are looking for.

2. Often a case will ask you whether to adopt a plan or not. Possibly as with many past papers, a new management team has been installed in the business to provide a new strategic focus. Students must be able to assess the likelihood of that particular plan becoming a success. Drill down into areas of the case looking at liquidity, cash flow, Ansoffs matrix, profitability, efficiency, management capability, and competitive offering amongst other areas. With my groups previously, I have asked them to ‘reverse engineer’ the question, by simply asking them ‘What should you not include in the answer?’ By asking my business students this question it allows for a discussion within the group as to what are the most important aspects of the case, by breaking down those elements that are of least importance.

3. When completing Ratios or Investment Appraisal, students must take account of the case study and its qualitative theory and not just the quantative data that is produced from completing a formula. Of course it is vital that students can quickly and efficiently calculate ARR, Payback and NPV and provide understanding of theory behind the methods. However, their work must always be supported with the written case. For example, a student may say an organisation with above 50% gearing is overly leveraged with debt, but have they truly considered the main aims and objectives of the firm. What type of organisation are they? Many firms are able to work with high levels of gearing and this can even provide benefits for shareholders.

4. The impact of external market forces will run through the exam like a stick of rock as the case study will focus on attractiveness of the market. Students will need to have a real understanding of the influence of such forces. Accordingly, as students prepare their revision it is vital that they focus on the role of Porter’s five forces model and bring in the underlying economic drivers that will shape the market within the case study. There are plenty of great materials online for students to develop their understanding of Michael Porter; in particular the following video from Harvard Business is an excellent resource: http://www.youtube.com/watch?v=mYF2_FBCvXw

5. Often I have found that those middle learners who are prone to use generality and unstructured responses need to be shown how to retain focus in their answers. In particular, these students must be required to plan all of their answers before getting stuck in. This often allows them to keep their responses in the context of the case study. In particular, with the final question students must not ‘sit on the fence’. Recommendations are often the most difficult for these students as occasionally they lack the confidence here to deliver a final decision. A lesson spent on the final question only is often a lesson well spent.

Daniel Baker

Secondary Maths - Visualising the Mean

I was working recently with Mr Davaasuren. He had written some teaching material about averages and we were looking together at what he had done. We discussed some of the issues involved in helping students to understand about mode, median, mean and range.

The next morning we met again and he asked if I would like to see the model he had made the night before. You can see it in the photograph

It consists of six transparent vertical tubes with a scale next to each one. The tubes are all connected via a further horizontal tube at the bottom. 

The tubes can be filled with coloured water and there is a stopper to go in the top of each one. Mr Davaasuren carved the stoppers from erasers.

This is how it works. Suppose you have the six numbers, say 16, 18, 12, 7, 16 and 9.

First fill the tubes to the level of the lowest number, in this case 7. Since they are all connected they will all fill to the same level.

Put a stopper in the fourth tube. The level of this will stay at 7. Add liquid to bring the rest up to 9. Stopper the sixth tube. Continue in this way until the levels in each tube are the six numbers in order and there is a stopper in each tube.

First we can demonstrate the range. It is simply the difference between the highest and lowest levels.

Next the mode. There are two tubes at the same level, so that is the mode.

Next the median. Find the highest and the lowest (18 and 7) and “discard” those. That leaves 16, 12, 9 and 16. Now discard the highest and lowest of those (one of the 16s and 9). That leaves the 12 and a 16. The median is halfway between the two. We can find this by removing the stoppers from those two tubes. The levels will even up so that they are both on 14.

Finally the mean. Remove all the stoppers and the liquid in every tube will adjust to the same level – 13 – and this is the mean.

Isn’t that brilliant? Range, mode, median and mean all demonstrated at the same time. Along the way it shows why the mode might not be a good choice of average and the fact that the median for an even set of numbers if the mean of the two middle numbers.

You could also use it to discuss what happens if you change the scales. Suppose, for example, you add 10 to every number on each scale. How does that affect the range, mode, median and mean? What if you add a different number? What happens if you multiply every number by 2? Or some other number?

Mr Davaasuren intends to make a video of his Mean Machine in action and put it on a website so that teachers will be able to show it in their classrooms. Unfortunately the website is in Mongolian and unless you have a working knowledge of that language you will have difficulty using it. On the other hand, if you have some plastic tubing laying around in your garage you might be able to make your own Mean Machine.

Students often find it hard to understand why the mean is defined in the way it is. I think this visualisation of evening out the different levels is a superb way to visualise it. It made me wonder if there are other tricky mathematical topics which could be explained easily if we just had the right visual aid. Any suggestions anybody?

Chris Pearce

Law - Using Forums to Build Students’ Analytical Skills

For this activity you will need:

• Access to an VLE such as Moodle
• A group of willing students.
• The 'carrot' in the activity is the idea that whatever comes out of the forums will form the basis for the students own individual essays or assessments which follow on form the Forum.

When opening any Forum for use in an educational context it is wise to set ground rules.

My Own Ground Rules for Working In Forums

• The forum is to be time-limited. After the allocated time it will be made available as an archive but not for on-going contributions. This gives a sense of urgency to the task.
• All students must participate and make at least (three) postings. You can tell students that part of the overall assessment grade will depend on their contribution in the forum.
• A posting can be an original idea or a development of another students posting.
• All postings, being public, must show a certain level of respect and be generally supportive. Any criticism must not be personalised or sarcastic, etc.

Example Task

Often it works best to take students into a computer room for the initial launch of the forum. This will definitely speed things up and hopefully create the  initial ‘buzz’ needed for students to return to the forum in their own time.

Teacher ‘seeds’ the forum with some initial comments and questions.

From my own subject - law - on a topic of reforming the law or murder I might ask:

• How satisfactory is it that we are relying on an ancient definition of such a serious crime?
• What issues are there arising from the definition?
• Is the Mens Rea for murder clear?
• What about recent cases about assisting a loved one to die or euthanasia – how satisfactory is the law?
• How might we consider reforming the law?

And so on...

Each prompt forms a thread within the Forum and students join in as many threads are they are willing and able to join.

Advantages of this Technique

• It leaves a permanent record of a discussion.
• It allows students to construct their own knowledge according to their own interest.
• It allows students across several groups to collaborate when they would normally be limited to the class group.
• It allows students to add in comments at any time.

The technique allows students to work collaboratively for a limited period of time and then use the resource to build an Individual piece of work. It works.

Nigel Briggs

Prose poetry: comparing texts

On the blog this week is a very modern exemplar of that unusual genre of literature, the prose poem. The term originates from the famous French poet, Baudelaire, who described his 1869 publication, ‘Paris Spleen’, as ‘Little Poems in Prose’.

The Encyclopaedia Britannica defines a prose poem as: "a work in prose that has some of the technical or literary qualities of a poem (such as regular rhythm, definitely patterned structure, or emotional or imaginative heightening) but that is set on a page as prose."

‘Chessiderata’ opens with a deliberate parody of Max Ehrmann’s famous prose poem, 'Desiderata'. Both pieces are overtly philosophical but whereas ‘Desiderata’ offers an unashamedly optimistic perspective on the Universe, ‘Chessiderata’ explores the darker side of life through the medium of the ancient war game of chess.

You might wish to read both of these texts with your students and then ask them to:

1. Analyse the ways in which ‘Chessiderata’ conforms to the prose poem genre.
2. Explain how the title, ‘Chessiderata’, and the accompanying picture are effective and how they link to the text.
3. Explain some of the thoughts and feelings that the author of ‘Chessiderata’ expresses about life.
4. Compare ‘Chessiderata’ with ‘Desiderata’ in terms of attitudes, use of language and structure.
5. Write a prose poem of your own in which you reflect upon an aspect of life which is of fundamental importance to you.

Copyright Brian Mitchell

This activity can be used to introduce students at KS3 to different types of literature and extend their abilities as critical readers. It is also suitable as preparation for the comparative and analytical components of GCSE.

Download: Chessiderata

Read: Desiderata

Peter Morrisson

Peter Morrisson is a teacher, author and director of animated films. He currently lectures at the Isle of Man College of Further and Higher Education. 

Notes from the history of Maths: Size matters...

On January 25th 2013, in Orlando, Florida, a computer running as part of the Great Internet Mersenne Prime Search (GIMPS) discovered the latest, largest known prime number.

They are called Mersenne primes after Marin Mersenne (1588-1648), a French monk. He acted as a communication hub for mathematicians and scientists of the day, sharing ideas between the likes of Descartes, Fermat, Pascal, Huygens and Galileo. Born to a working class family he went to the same school as Descartes. Eventually he joined “The Order of Minims”, who considered themselves the least (minimi) of all religions on earth and lived a very simple life.

One of his works was “L'harmonie universelle”, where he was the first to publish the laws relating to the vibrating string: its frequency being proportional to the square root of the tension, and inversely proportional to the length.

At the time, many mathematicians were obsessed with finding a pattern in prime numbers. Marcus du Sautoy, in “The Music of the Primes”, suggests that his interest in music may have given him insight into the formula for Mersenne primes: 2ⁿ-1. If you double the frequency of a note, you go up an octave, creating harmonic notes. A shift of 1 might be expected to create a very dissonant note, not compatible with any previous frequency – a ‘prime’ note. However, the formula could also have been a result of the search for perfect numbers. A perfect number, such as 28, is the sum of its factors other than itself (1,2,4,7,14).

It was Euclid that showed that whenever the sum of powers of 2 is a prime number, then you can create a perfect number by multiplying the sum by the highest double added. Since the sum of powers of two is 2ⁿ – 1 (sum of a Geometric Series), in modern notation, Euclid showed that:
Whenever 2ⁿ – 1 is prime, then (2ⁿ – 1) x 2ⁿ-1 is perfect.

For example, 1 + 2 + 4 = 7 is prime, so 7 x 4 = 28 is perfect. However, 1 + 2 + 4 + 8 = 15 is not prime, so no perfect number can be generated. The next sum works (31) and this generates a perfect number (31 x 16 = 496).

So, the hunt for perfect numbers - which were felt to have religious significance -  became a search for when 2ⁿ – 1 was prime. In 1644, Mersenne conjectured that this was the case when n = 2, 3, 5, 7, 13, 19, 31, 67, 127 and 257. It was quite a feat, at the time, to have found that 2047 (2¹¹-1) is not prime as 2047 = 23 x 89. No one knows how Mersenne came up with the list and it was only in 1876 that Edouard Lucas devised a method for checking Mersenne numbers.

He found 2⁶⁷-1 was not prime but 2⁶¹-1 was. Some have suggested this was a misprint in the original publication! It was also found that some numbers not on the list do produce primes (89 and 107). It was found that n=127 works and this remained the largest Mersenne prime until computers were invented. Only in 1952 was it found that 2⁵⁷ did not work. Whilst the Lucas method can show whether a Mersenne number is a prime or not, it doesn’t show how non-primes can be factorised. In 1903, Frank Cole gave a talk at the American Mathematical Society. Without saying a word he wrote:

2⁶⁷ – 1 = 193,707,721 x 761,838,257,287.

He got a standing ovation.

It is very difficult to factorise large numbers with large prime factors. This is why the hunt for ever bigger prime numbers is important. Prime numbers are used in on-line purchases. Credit card numbers are encoded by using numbers that can only be factorised into two primes of, at least, 60 digits each.

As e-commerce has grown, so has the need for bigger primes. The latest 2^57,885,161-1 has 17,425,170 digits.There is prize money available for large primes and the Electronic Frontier Foundation (www.eff.org) is now offering $150,000 for the first prime over 100 million digits and $250,000 for one over a billion digits. You can help the search by downloading the GIMPS software (www.mersenne.org). They will award you $3,000 for a new prime with less than 100 million digits. Happy prime hunting!

Don Hoyle

Mathematics Matters

Maths Madness in March

There’s so much happening in March there just aren't enough school days in the month to cover it all!

Here’s a selection of some of the most important and exciting events happening this month:

1st: St David’s Day
4th – 10th: Climate Week
5th: World Literacy Day (part of World Education Games)
6th: World Maths Day (part of World Education Games)
7th: World Science Day (part of World Education Games)
7th: World Book Day
8th: International Women’s Day
10th: Mother’s Day
11th: Commonwealth Day
13th: No Smoking Day
14th: Pi Day
15th: Comic Relief: Red Nose Day
15th – 24th: National Science and Engineering Week
17th: St Patrick’s Day
20th: Spring Equinox
21st: International Day for the Elimination of Racial Discrimination
21st: World Poetry Day
22nd: World Water Day
23rd: Earth Hour
24th: Palm Sunday
26th – 1st April: Passover
27th: Holi
29th: Good Friday
31st: Easter Sunday & British Summer Time begins (possibly the best day in March!)

Here are just three activities to try this month.

Key Stage 1
22nd March: World Water Day
International World Water Day focuses attention on the importance of freshwater and advocates for the sustainable management of freshwater resources.
– How much water do you use?
Ask the children to investigate how much water they use in a day.
Ensure they have access to the following information:

Lower Key Stage 2
23rd March: Earth Hour
Earth Hour is a worldwide event that aims to raise awareness about the need to take action on climate change by encouraging homes and businesses to turn off their non-essential lights for one hour. Earth Hour 2013 will be held on Saturday 23 March between 8.30 p.m. and 9.30 p.m.
– Energy audit
Undertake an energy audit in your school.

• Ask the children to work in groups to make a list of all the different electrical appliances in the school – perhaps assigning different groups to different areas of the school. Encourage groups to collect the data in a table, detailing the type and number of each appliance.
• Provide children with the information in the table below. If there are appliances in the school that are not on the list, ask them to find out the average yearly running costs for these appliances.
• What about the cost of heating?
• Bring groups together to pool and present the results.
• Discuss the results – What conclusions can you draw? Where does most of the school’s energy consumption occur? How could the school reduce its energy consumption?

Children could undertake their own energy audit at home.

Upper Key Stage 2
14th March: Pi Day
Pi Day commemorates the mathematical constant  π (pi). Pi Day is observed on March 14 (3/14 in month/day date format), since 3, 1 and 4 are the first three digits of pi in decimal form.
– Discovering Pi
Begin by discussing the terms ‘circumference’, ‘diameter’ and ‘radius’ with the children.

Gather together a collection of at least 6 circular objects, all different sizes. For example, plates of different sizes, waste paper basket, analogue clock, geometric circular shape.
Ask the children to:

• use a tape measure to measure the diameter and circumference of each of the objects
• record their measurements
• find the average of all of the answers they have just calculated

Discuss the results with the children. Explain to the children that mathematicians have calculated that the circumference of a circle is about 3.14 or 31/7 (22/7) times the diameter and that this number is called pi (after a letter in the Greek alphabet) and it is written: π.

Find more activities related to Pi in Collins New Primary Maths – Enriching Maths Resource Pack 6

Peter Clarke
Series editor, Collins New Primary Maths

Chess … it’s not just for squares!

In today’s high-tech schools, with their Wi-Fi networks and electronic registration systems, it would be easy to dismiss the ancient art of chess as, well – just that … ancient! Admittedly, the origins of chess can be traced back at least 1500 years but this eloquent metaphor for life is certainly not, nor is ever likely to be, past its sell-by date.  In fact, in a world which can often spin hopelessly out of control at a moment’s notice, chess offers an enticing alternative – a world that can be controlled … but only if you are sufficiently adept.  Perhaps this is what accounts for chess’s enduring appeal.

Of course, thanks to the Internet, chess has evolved and now has its own high-tech platform on websites such as:

www.chess.com

On Chess.com, there are usually 10,000 or more active participants at any one time and so it is possible to play 24/7 with members from right across the globe.   As a result of the Elo rating system, you will always be matched with a suitable adversary for your ability level. Even more amazing, there is no admission fee!

Websites like Chess.com provide all the thrills and spills of many other, much more perilous web-based entertainment services.   Personally, I imagine on-line chess to be rather like on-line gambling but, unlike the latter, no matter how bruised and battered you might feel at the end of a disastrous campaign, all you have staked is your Elo, and all you have lost is your pride!

Undoubtedly, the benefits to schools are many.  Playing chess may well raise IQ scores, enhance problem solving skills, improve concentration and memory, and encourage lateral thinking. It is also a pastime which transcends the barriers of age, class, religion, nationality, language and culture.  In Armenia, chess has actually become part of the curriculum.  This small country of some three million, which has had its fair share of warfare and tragedy in recent years, now encourages its children to experience the thrill of combat without any of the carnage.

Furthermore, chess is an incredibly inexpensive activity to run.  With an enthusiastic instructor at the helm, one who is able to pass on the flame by igniting young imaginations with a true sense of the wonder of this timeless pursuit, chess club might never be the same again!


Peter Morrisson

Peter Morrisson is a teacher, author and director of animated films. He currently lectures at the Isle of Man College of Further and Higher Education.