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. 

Why is learning a language important?

Recently we had the opportunity to meet Naomi who was at Collins on a work experience placement. Whilst she was here we discovered  she is passionate about languages and plans to study French and Italian at university, and so we asked her why she thought learning a language is so important...

Language is our most complex yet fundamental communication tool. It is at once a separating and unifying force; both alienating and a source of comfort and place.  Discovering a new way of speaking is possibly one of the most liberating of human achievements.

For most of my life I’ve been fascinated by languages and I’m looking forward to starting university this September to study French and Italian. Next month, though, I’m lucky enough to be going to Paris for an 8 week ‘term’ at the Sorbonne University. Having spent a year and a half out of education I can’t wait to resume my studies and where better to do so than this iconic capital?

I’ve always enjoyed the logical interplay between languages and French and English share so much common-ground. [Note George Bush’s ‘faux-pas’ (ironically) at complaining for there being “no French word for ‘entrepreneur’”] Yet, the relative failing of our language-education in this country is slightly embarrassing- as a Nation we tend to fall back on the excuse that ‘everyone else speaks English’, which may be largely the case- but finding that you can begin to understand a language in context is immensely satisfying.

The most effective way to learn and maintain a language is to completely immerse your self in it, but for many that is not a feasible option. However there are now so many great language guides out there that lend themselves to independent study. I’ve used the Collins French Verbs and Practice book which has a clear and engaging lay-out to drum in conjugations and key grammatical points, without being dull and monotonous. It provides great revision too and helps to make the grammar sections of exams a lot easier.

In preparation for A-levels my teachers suggested that we read French newspapers; highlighting and looking up unfamiliar words, which proved to be a quick and effective method for expanding vocabulary. With the Collins Robert French dictionary I found up-to-date definitions as well as a section for “language in use”, to gauge a more fluent usage of words and phrases.

New ways of speaking offer the possibility of accessing new ways of thinking too, which is surely an immensely exciting prospect with which to incite people to adopt a new language. Not to mention new scientific research which has shown how language-learning is actually beneficial to our health; it develops new neural pathways in the brain, consequently staving off the threat of dementia and Alzheimer’s! In short, we should all be avidly swatting up on our French grammar.

In an increasingly globalised world, where many ancient native languages and dialects are gradually becoming extinct, it is more important than ever that we cherish and embrace our linguistic diversity. What a dull world would it be if we all spoke in a common tongue?

Business News Quiz 15.02.2013

1. Which high-street bank has said it will cut 3,700 jobs following a strategic review, as it aims to reduce costs by £1.7bn.
Natwest ( ) Barclay’s ( ) HSBC ( ) Lloyd’s TSB ( )

2. What 2 airlines are planning to merge to form one of the world's biggest airlines, according to media and newswire sources? 
KLM & Delta ( ) Lufthansa & Qatar ( ) British Airways & Virgin Atlantic ( ) American Airlines & US Airways ( )

3. Which supermarket’s Value Spaghetti Bolognese contains 60% horsemeat, DNA tests by the retailer have found?
Tesco ( ) ASDA ( ) Waitrose ( ) Sainsbury ( )

4. The rate of UK consumer price inflation remained unchanged at what level, for the fourth consecutive month in January, official data has shown?
3.5% ( ) 2.7% ( ) 4.5% ( ) 3.7% ( )

5. Luxury smartphone maker Vertu has launched its first Android-operated handset. The Vertu Ti costs how much? And is made at the firm's headquarters in Church Crookham, Hampshire? £8,994 ( ) £16,994 ( ) £18,994 ( ) £6,994 ( )

6. Which Leeds-based high street retailer, which has around 120 stores and employs some 2,500 staff, has entered administration?
Republic ( ) ASDA ( ) ARK ( ) Northern Foods ( )

7. Which carmaker has reported a net loss of 5bn euros ($6.7bn; £4.3bn) for 2012, compared with a 588m euro profit a year earlier? 
Vauxhall ( ) Peugeot Citroen ( ) Ford ( ) BMW( )

8. Who is trialling a new TV and film streaming service called Clubcard TV. The free on-demand service will allow the supermarket's 15 million loyalty card holders to access TV shows and films online?
Staples ( ) Tesco ( ) Boots ( ) Sainsbury ( )

9. Apple’s boss has called a lawsuit brought by activist shareholder David Einhorn a "silly sideshow". But he said the board is discussing Mr Einhorn's proposal to help shareholders get a better return on their investment despite so much of the computing giant's money sitting idle in cash. Who is Apple’s boss?
Tim Ford ( ) Tim Cook ( ) Steve Jobs ( ) Steve Wozniack ( )

10. Global sales of which technology product fell in 2012 compared with the previous year, according to a report from research company Gartner? 
Computer games ( ) Tablet’s ( ) Mobile phones ( ) Laptops ( )

Answers –
1 – http://www.bbc.co.uk/news/business-21423691
2–  http://www.bbc.co.uk/news/business-21454925
3 – http://www.bbc.co.uk/news/uk-21418342
4 – http://www.bbc.co.uk/news/business-21425939
5 – http://www.bbc.co.uk/news/technology-21387371
6 – http://www.bbc.co.uk/news/business-21431753
7 – http://www.bbc.co.uk/news/business-21439941
8 – http://www.bbc.co.uk/news/technology-21429675
9 – http://www.bbc.co.uk/news/business-21442296
10 – http://www.bbc.co.uk/news/technology-21441953

Donna Jestin

Maths Activities – The 25th Anniversary of Comic Relief

You’ll have a red nose soon and it won’t be just because of the cold – it’ll soon be Red Nose Day, aka Comic Relief and the numbers will be crunching telling us how well we've been doing raising money to help children around the world.

This year is very special for it’s the 25th Red Nose Day and the celebrations and fund raising drives are going to be keener than ever. Usually schools take their feet off the pedals a little to allow children to enjoy the fun or to carry out fund raising activities of their own. If you want to get a little work done in the maths lesson that day but still involve Comic Relief, try these activities and the English activities that accompany them.


Activity One – Allocating Money
Year 3 to Year 6

This activity enables children think about how a number can be split using fractions or percentages and allows them to make decisions based on their concerns for others.

LO:
Be able to use fractions and percentages to divide up a sum of money and allocate it based on personal beliefs.
Be able to calculate sums involving large numbers using a calculator

Talking Point:
Each year Comic Relief raises tens of millions of pounds, all of which is spent on helping children around the world. Expenses are paid by sponsors from the interest earned on money in the bank waiting to be used.

Ask the children to say what kind of children are helped by donations to Comic Relief and can they suggest any others.

Should all the money be given to one type of need or should it be spread around, one country or region or several. There is often controversy over the amount that is spent in foreign countries instead of on suffering children in the UK. What are their views on that?

Activity:
In 2011, almost £75m was pledged or donated during the day of Comic Relief and over £100m in total. Using the total figure of £100m ask the children to decide which of the following causes would be most deserving of receiving some of the money.

How many children in each category could be helped if the money was spent purely on them?

Talking Point:

Ask them whether this is a fair way of spending the money. How else would they apportion it and ask on what basis they are making their decisions.

Ask them to calculate how much they would spend as a fraction or percentage of the £100m on each cause and calculate how many children would be helped in each scenario. How many children would be helped overall? They should write notes for each justifying their decisions.

Talking Point:

Should the decision be made just on how many can be helped or are there other criteria that can be used? Ask them to reconsider their decisions and calculations based on the class discussion.

At Home:

Get the children to research projects that have been funded by Comic Relief in the past. How much was spent, what was it spent on, and how successful was it in terms of numbers helped?

Activity Two – Scale: How Many Times?

Year 3 to Year 6

In their daily lives children often encounter large numbers that seem abstract in isolation. This activity enables the children to compare large numbers by scale. E.g. England is ten times bigger than…, there are a hundred times more starving people in Africa than… etc.

LO:

Use ‘times bigger’ to compare the size of numbers, measures etc.

Use pictures to compare size.

Talking Point:

Ask the children to say how many times taller they think their teacher is than them. How many times heavier is the teacher than they are?

Activity:

Start off writing pairs of numbers on the board e.g. 4 and 32. Ask the children to say how much bigger 32 is than 4. You are likely to get the answers either 28 (difference) or 8 times (multiplier). Use further pairs of numbers and ask the same question. Ask the children which they think gives them the better idea of comparable size.

Use the worksheet that accompanies this activity and ask the children to measure the differences in length, width or height of the first few examples then calculate the number of times greater each measurement is (to the nearest whole number). Does ‘five times bigger’, give a more accurate comparison than say ‘4cm bigger’?

Back to Comic Relief now and the accompanying sheet gives children practice on calculating how many times bigger numbers are using the receipts from Comic Relief over the last 25 years.

At Home:

Ask the children to compare things such as size of food packages, length of gardens, speed limits etc. by using ‘times bigger’

Dave Lewis, Primary Teacher

You can find ideas on how to celebrate Red Nose Day in your literacy lessons here...

How many degrees in a U turn?

I had the luxury last week of watching the ministerial announcement on education live on TV.  The big question seemed to be how much of a ‘U turn’ this actually was.  In terms of a change of direction, how much of a change?

Well, certainly there are some bodies floating in the water.  There will no longer be a move towards having a single Awarding Organisation commissioned to accredit a particular subject.  I know that there’s been some debate over this but I think a choice is likely to keep the AOs customer focused.  The name GCSE will be retained, instead of being replaced by ‘English Baccalaureate Certificate’ which means that students currently in Years 8 and above won’t be following courses that are being demolished to make way for a shinier replacement.

However a number of developments are still being actively followed up and this is a longer list.

For a start, the timescale: reformed GCSEs in sciences are supposed to be ready for first teaching in 2015 and first examination in 2017.  However Ofqual has since raised concerns over this and remember that they are key players in this.  As expected, assessment will be linear and we can expect fewer questions in exam papers with more marks on each.  Science will be expected to have a greater focus upon quantitative problem-solving.

Controlled Assessments may or may not survive; there’s a case to be made, though I suspect it’s not a done deal that they stay.  However there is an acceptance that different subjects may need to be assessed in different ways.

Expect an end to the tiering of papers, the possible use of a ‘core + extension’ model and continued emphasis upon extended writing.  Don’t assume that new specifications will replace old on a ‘one for one’ basis.  The ‘core + additional’ model may not survive, for example; a two year double award course would only have exams at the end.

What also emerged, though with far less skirmishing, were the draft revised programmes of study for all subjects in KS1-3. The proposed KS3 programme for science bears close reading.  Running to 11 pages, there is significant detail in terms of content; astronomy and geology are out and there is extended coverage of human biology and classical physics.  ‘How science works’ is replaced by ‘Working scientifically’, which is to be delivered through the content.  There are, of course, no level descriptors.

There is also significance in the proposed timescale.  It is suggested that the current programme be disapplied from September 2013 and the new programme applied from September 2014, thus allowing for a phased transfer.  Furthermore it is proposed that the implementation is simultaneous for all years in a key stage, as opposed to being introduced on a rolling programme.  Key documentation is at
https://www.education.gov.uk/schools/teachingandlearning/curriculum/nationalcurriculum2014/b00220600/consultation-national-curriculum-pos and the consultation period is open until April 16^th.

Is it a U-turn?  Well, it’s a change.  I think the upset last summer showed what can happen if too many factors in an assessment system are changed at once.  We don’t want to go there again.  However there are other features which can be seen as a continuing trend.  Bit of a dodgem car moment perhaps.

Ed Walsh

Ed Walsh is Science adviser for Cornwall Learning. In the past, he has worked extensively with teachers, schools, local authorities and national agencies in relation to science education

Primary Maths Activities for the 40th Anniverary of the UK joining the EU

One of the main changes Britain encountered when joining the EU was the use of metric measurements in our daily lives. Still not completely integrated to the European system of weights and measures, does the dual system actually cause confusion or can children cope better than adults at mixing and matching imperial and metric measures? Using money abroad has got a lot easier with the adoption of the Euro by many of the holiday destinations that the children may visit.

Activity One – Measuring and Weighing
Year 2 to Year 6

This activity enables children to work on weighing and measuring using imperial and metric measures, estimating and using different scales and finally decide which system is easier or better.

LO:
Be able to use metric and imperial scales to measure mass, length and capacity.
Be able to estimate length, mass and capacity in the different scales based on previous knowledge.      

Talking Point: Ask the class to tell you how tall they are and how heavy they are (sensitivity is likely to be needed here!)

Compile a chart of the children’s names with height and weight on it. If they give answers in stones and pounds or feet and inches, mark them on the chart in red, if they use metric measures, use blue. At the end of the exercise compare how many used each type of measure and ask a selection why they did. Which do the children find easier to use to compare against others and why that is so.

Activity: Ask the children to bring in scales, rulers and tape measures from home with a combination of imperial and metric measures on them and spend some time discussing the breakdown of units into m, cm and mm or feet and inches etc.

Set out a selection of objects and ask the children to estimate their lengths and masses in whichever unit they prefer to use, then measure them accurately. Give them rough equivalents for the conversion from metric to imperial and vice versa and ask them to convert them.

Talking Point: You can play a little game to check their understanding of the units of measurement. Hold up a book and ask ‘Does this book have a mass of 200g?’ or ‘Is this book eleven inches long?’ By repeating the questions with different standards of measure you’ll get an idea of their preference and understanding.

At Home:
Get the children to ask their parents and grandparents which units of measurement they would use for driving distance, weight, height, capacity etc. and compare answers. In class, you can collate the information and do a Carroll Diagram showing age ranges against metric/imperial usage. Discuss the results which are likely to show a large number using imperial measurements.

Activity Two – Shopping European Style!
Year 3 to Year 6

This introduces children to the operation of ratios for exchange rates, which whilst not obviously in ratio form, operate as, for example, one pound = 1.2 euros so, 1: 1.2

LO:
Use ratios to answer questions based on exchange rates
Use multiplication to answer questions based on exchange rates

Talking Point:
Ask the children to put up their hands to tell you which foreign countries they have been to on holiday or to visit friends. Ask them what the name is of the money that is used in the country they have visited. If they can remember, ask them if they think they can buy as much with a dollar, a euro, a rupee or a zloty as they could with a pound. Tell them that the way to work out if something is cheaper or more expensive in another country is to use exchange rates so that prices can be compared in the same currency.

Activity:
Show an exchange rate in a calculation table such as this:

Ask them if they can predict how many euros would be the same as 3, 4 or 5 euros etc.

You can do this simply by adding 1.20 onto the euro column figure each time you add one to the pound column but there is another way. Ask if anyone can tell you how many euros equal £10 and if they give you the correct answer ask how they calculated it. It’s likely that some will continue adding 1.20, ten times but some may have worked out that you can use 1.20 x 10 and get the answer.

If you have completed work on simple decimals such as 0.5, you can extend this activity to calculating how many euros are the same as £1.50 or £2.50 etc.

Activity 2:
Use the accompanying worksheet for children to calculate the equivalent costs of items in a toy shop. You can amend the prices to suit the level of challenge you want to present. You can also amend the currency if you wish.

Extension:
You can use the reverse exchange rate to get the children to calculate how much an item priced in a foreign currency might cost in pounds.

At Home: Ask the children to find the tourist exchange rate table from a newspaper and calculate the currency equivalent of £5 and £10 in perhaps ten of the world’s currencies.

Dave Lewis

Primary Teacher

Secondary English - It's good to talk

"I could put you in the movies,” he leered whilst leaning across towards the attractive young woman who sat opposite. 

“Really?” She sounded unconvinced.

“Really!”

He placed an over-sized palm on her knee and smugly flashed a gold tooth in what he must have imagined to be a debonair fashion.  She flinched, as if about to be devoured whole by a snake.  It may not have been the reaction he was looking for, but it didn’t seem to deter him.

“I could make you a ssstar!” he announced emphatically.

She squirmed again.  It sounded uncomfortably like a hiss.

Imagine that you are sitting on a busy commuter train on your way home after another hectic day in the classroom, and you suddenly hear the above snatch of conversation. What do you do?

Roundly chastise yourself with, “I’m a teacher, and teachers don’t eavesdrop!”, then virtuously change seats and continue with your marking?

Or, if feeling somewhat heroic, do you take off the bifocals and charge in with, “Excuse me, madam, is this rather large, intimidating-looking man bothering you!?”

Or perhaps you take a mid-course, stay where you are, put on a convincing display of conscientious coursework correction and surreptitiously cast sly, sideways glances whenever you can?

If your reaction is the latter, then the above piece of dialogue has succeeded because it has clearly caught your undivided attention. And this is a good rule of thumb for writing effective direct speech – it should be interesting enough to captivate a casual passer-by!

As your students will be writing about 800 words for their GCSE creative writing assignment, they will only need a limited amount of speech.  The majority of the story will be narrative with some description.  However, good dialogue does undoubtedly allow characters to step right out of the page and burst into life.  It also enables the writing to become more multi-sensory and vivid, whilst simultaneously casting the reader in the undeniably tantalizing role of voyeur.  So, with all this in mind, the following tips might be of use to your students.

1. Effective dialogue should enhance the interest level of the story, e.g. by creating conflict, tension, suspense or humour.

2. Effective dialogue should convey new information to the reader and, therefore, it has to be vital and fresh.

3. Effective dialogue should reveal the personalities of your characters and, thus, the more interesting and varied your characters are, the more interesting your dialogue will be.

4. Effective dialogue should be short, sharp and to the point, so avoid wordiness.

5. When using dialogue, it is important to ensure that the reader always knows who is speaking. Beginning a new paragraph for each new speaker is helpful but you will also need to tag certain lines, e.g. he said, she replied.

6. But only tag when absolutely necessary so as to avoid needless repetition.

7. Tags should not be intrusive. Some authors say that you should avoid alternatives such as he retorted, she queried, he growled, and so on. In the hands of a good writer, he said and she said, if used sparingly, can become invisible.

8. However, others authors believe that these tags should be diverse. Instead of Lucy said, you could substitute Lucy remarked ironically.

9. Perhaps the answer is to explore what your favourite novelists actually do and then experiment in your own writing. Occasionally, you might use such variations as exclaimed, declared, whispered, stated, roared, etc. But, as a general rule, you might stick to a mainstay of said, replied and asked, and only use the others when they are most effective. Remember, tags should remain invisible and so should only be used when required.

10. This is what happens when you over-use them:

“Just stick with me," he confidently asserted.
"Are you certain?" she asked.
"Dead certain," he replied reassuringly.
"I'm not," she retorted, nervously laughing.
“I can make you a star!” he repeated.

11. One very effective trick is to intersperse brief flashes of narrative with dialogue in order to reveal what your characters are thinking and feeling, and in order to show what they are doing. This will help you to hide your tags. Or you can use beats. This is when you put in a narrative phrase to describe the character's reaction or movements and so identify the speaker without using a tag.

This also allows you to place the dialogue in a world which has a physical dimension that the reader can perceive, thus making your writing more vivid. Otherwise, the conversation appears to be taking place in thin air, and this is much less interesting.

(Re-read the dialogue at the beginning of this article in order to see how the author has used narrative in both of these ways.)

12. However, do be careful. Just as you shouldn’t stifle a good free-flowing conversation by over-tagging it, neither should you kill it by putting too much narrative in between each spoken response!

LINKS:

1.  Scheme of Work

2.  Animation - 'Thunder'

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. 

Applying maths to the real world

The activities this month are aimed at helping children see the application of mathematics in the real world, while at the same time discovering things about some different parts of the world.

Key Stage 1

A Rangoli is an Indian design often used to decorate floors near the entrance to homes to welcome guests. They are traditionally drawn using rice grains, flour, sand or chalk. Here are some:

• What patterns do you notice?
• Is there anything symmetrical about these patterns? What makes them symmetrical?
• Design your own Rangoli similar to those above.
• Try designing a Rangoli that uses colour. Can you make your design symmetrical?

Lower Key Stage 2

Fairtrade Fortnight runs from Monday 25th February, 2013 to Sunday 10th March, 2013. Fairtrade aims to help farmers and workers in developing countries achieve better prices, decent working conditions, local sustainability, and fair terms of trade. Sixty percent of the Fairtrade market involves food products such as coffee, tea, chocolate, sugar, honey, and bananas. Non-food commodities include crafts, textiles and flowers.

Fairtrade products can often be identified by this symbol: 

• Visit your local superstore and investigate differences in the Fairtrade and non-Fairtrade prices of each of these products: coffee, tea, chocolate, sugar, honey and bananas.
• Over 3,000 products are Fairtrade certified. What other Fairtrade products can you find in your local superstore? How do these prices compare with non- Fairtrade prices?
• Which countries do Fairtrade products tend to come from?

For further information and activities about Fairtrade Fortnight go to www.fairtrade.org.uk.


Upper Key Stage 2

On January 26, India celebrated Republic Day, which honours the date the constitution of India came into force in 1950.  Also on January 26, Australia celebrated Australia Day, which commemorates the arrival of the first fleet at Sydney Cove in New South Wales in 1788.

The chart below shows the price of different food products in India (Hyderabad) and Australia (Sydney) in February, 2013.

• To compare the price of these products we need to convert the cost of each product to the same currency.
  What is the exchange rate of the India rupee (INR – ₹ or Rs.) to the British pound (GBP – £)?
  What is the exchange rate of the Australian dollar (AUD – $) to the British pound (GBP – £)?
  What is the cost in GBPs (£) of each of the food products purchased in India?
  What is the cost in GBPs (£) of each of the food products purchased in Australia? 
• Investigate what each of the food products costs in the UK.
  How does the cost of the food products purchased in India and Australia compare with their cost in the UK?
• What conclusions can you make about the cost of these food products in India, Australia and the UK?

Peter Clarke

Series editor, Collins New Primary Maths

Why not also try Belair's Crafty Rangoli Pattern Ideas