Our Homage to Cycling Statistics!

August 17, 2014 § Leave a comment

We love statistics! Yes, we may say we hate maths, but as a nation we seem to get great pleasure from crunching those numbers and finding out what percentage of people do what, when and where.

So, as very proud sponsors of TNT BMX Club, we thought we would celebrate their first club race today with a few cycling statistics.

The Department for Transport releases walking and cycling statistics each year and this year they released the data from 2012/13:

AreaChartWell done to Cambridge and Oxford! See . . . clever people like to cycle!

AgeChartCome on girls! We need to get cycling! I know 2 people who completed the Prudential 100 last week – one was a 30-year old woman and the other was a 72-year old man, so well done to minority cyclists!

But whatever the statistics say, ENJOY YOUR CYCLING! And good luck to everyone taking part in the TNT BMX races this week!

The Murky World of BODMAS!

August 3, 2014 § Leave a comment

Recently a parent asked me about a question they had come across in one of their 11 Plus practice papers. Their child had put E as the answer and his Mum was sure this was correct, but the answer book said it should have been A.

The answer came down to BODMAS (or BIDMAS). It’s one of those awkward little things that no one ever remembers! But, it’s something that rears its head in 11 Plus, SATs and GCSE exams.
BODMAS is basically the order in which we complete a complex sum. It stands for:

Brackets
Orders (or Indices)
Division
Multiplication
Addition
Subtraction

It reminds us that when dealing with a sum, we have to do whatever is in the brackets first, then deal with any indices (e.g. square numbers or cube numbers), then we can do divisions and multiplications, then finally additions and subtractions.

We must be careful, though, because all is not as it seems when it comes to BODMAS!

Although Addition comes before Subtraction, this does not mean that all the additions have to be done before the subtractions. For instance, 6 – 3 + 1 is done from left to right, so the answer is 4. If you were to do the adding first, you would get an answer of 2, but this is not correct. So, really, BODMAS should be read as:

Brackets first
Orders or Indices next
Then any Divisions and Multiplications in order from left to right
Then any Additions and Subtractions in order from left to right

Basically, BODMAS sounds better than BOMDSA! It’s just a reminder to do your multiplications and divisions before moving on to your additions and subtractions.

So, that brings us to the question the parent raised. The question was:

Which of the following gives the same answer as 6 x 2 + 12?
A. 48 – 8 x 3     B. 3 + 11 x 2     C. 3 x 7     D. 24 ÷ 2 – 1     E. 2 + 4 x 4

Using the rules of BODMAS, 6 x 2 + 12 = 12 + 12 = 24
A. 48 – 8 x 3 = 48 – 24 = 24
B. 3 + 11 x 2 = 3 + 22 = 25
C. 3 x 7 = 21
D. 24 ÷ 2 – 1 = 12 – 1 = 11
E. 2 + 4 x 4 = 2 + 16 = 18

And that is why the answer is A, not E!

Summer Holidays and 11 Plus Revision

July 11, 2014 § Leave a comment

Your 10 year old thinks: “Yay, 6 weeks off school!”

You think: “Oh no, 6 weeks without school – what if they forget everything?!”

It’s that time of year again when parents and children are working hard towards their 11+ exams . . . and many students have to sit the exam almost immediately after a long holiday from school.

The 11 plus is, of course, a very important exam. But, we mustn’t forget that they are only 10 year olds and they have been working hard at school all year. Relaxation time is vital, otherwise they will suffer “burn out” before they get to the test. So here is a handy 11 plus revision timetable for the summer to make it an efficient and enjoyable (or as enjoyable as schoolwork can be!) experience.

11 Plus Revision Timetable

Even if you are away on holiday, take some books away with you. Your child will feel more relaxed on holiday, so may be more inclined to do some work.

The timetable is just a guideline, each child is different. 11+ revision should be varied with each child’s personality and work ethic. Try our 11+ revision worksheets to help in preparing your child. But most of all, enjoy your summer holidays!

The Wonderful World of Wimbledon

June 29, 2014 § Leave a comment

Wimbledon is in full swing: strawberries and cream and crowds of people in ponchos shivering in the rain on Henman Hill – what could be more British?!

Image

Like all sports, tennis is all based on numbers. But, unlike sports like football, there isn’t a simple one-nil scoring system; instead we have scores like thirty-love and deuce. So, where did it all come from?

There are mixed opinions out there. The most common explanation is that it comes from Medieval France, when they used a clock face to help them with scoring. They would move the hands to 15 minutes, 30 minutes, 45 minutes, then 60 when they won the game. When deuce came in, the 45 changed to 40 – they would then move the hand to 50 when there was an advantage, then 60 to win the game.

Deuce comes from the French term “à deux”, meaning “at two” (in other words, meaning they need two more points to win). And Love comes from the French term “l’oeuf” meaning “the egg” because a zero looks like an egg.

I’m afraid our British tradition looks decidedly French . . . !

But here are some other fascinating numbers from the world of Wimbledon:

  • The fastest serve recorded at Wimbledon was from Taylor Dent in 2010. It was 148mph – that’s an incredibly 66 metres per second!
  • An average of 28 000 kg of strawberries are eaten at Wimbledon during the fortnight . . . . washed down with 7 000 litres of fresh cream!
  • The longest match was played by John Isner and Nicolas Mahut in 2010. It lasted for 11 hours and 5 minutes and was played over 3 days. Their final tie-break went to 70-68. Bet they needed a foot rub after that!

Careers In Maths

June 14, 2014 § Leave a comment

So, what good is maths to you in the real world? It can sometimes seem as though maths is just one of those subjects you have to do at school, then immediately forget once all the exams are over (except for the odd bank statement you have to analyse!).

And, for those with a passion for maths, you may ask yourself what pursuing maths can actually do for you. Surely the only thing you’d end up being would be an accountant or a maths teacher. But, maths is used more than you may think in working life. Every day, we make calculations that we may not even be aware of. And some places of work involve more mathematics than others. This site has some great videos showing how some people use maths in working life: mathscareers.org

There are a whole range of sectors that like to employ graduates with mathematical skills:

Aerospace, Automotive companies, Construction, Engineering, Environmental work, Healthcare, IT, Manufacturing, Scientific Research, Telecoms, Transport, Utility companies . . . and that’s just naming a few!

There are so many apprenticeship schemes and graduate schemes out there for people who have a knack for maths. This site lists some of the options available: maths careers

So, maybe maths isn’t the dead-end option you may think it is; in fact, it opens a whole world of opportunities.

The Great Modern Abacus Debate

June 1, 2014 § Leave a comment

Recently, there has been a lot of debate over the use of calculators in the Key Stage 2 SATs exams. With the removal of the calculator paper, some are concerned that this will affect students in later stages of education.

Some may say that the calculator is a relatively recent piece of technology, but in reality we have been using tools to help us make calculations for thousands of years. The abacus is thought to have been used in Oriental lands as long ago as 3000 BC.

Since then, it has been adapted by many cultures and lands, leaving us with the abacus we recognise today. Even the Native Americans used a form of abacus called a Quipu, which was a system of knotted cords. They also used a Yupana to carry out their calculations and researchers have discovered that this was based on the Fibonacci Sequence. Image

The abacus is more than just pretty beads used to show numbers; it can be used for a number of calculations: addition, subtraction, multiplication, division and even square roots and cube roots. There are a lot of variations, but the most common abacuses that we see today consist of 2 sections of beads in rows. The two sections are 5’s and 1’s and the rows indicate place value, e.g. units, tens, hundreds. So, 623 for instance would have three “1” beads in the units row, two “1” beads in the tens row and in the hundreds row there would be one “5” bead and one “1” bead.

Image

Despite the growth in popularity of pocket calculators, abacuses are still in use in some parts of the world. Merchants and traders in certain parts of Asia and Africa still use an abacus for business. And, China and Japan still teach children in school how to use an abacus. In fact, using a Soroban (Japanese abacus), Japanese children are able to complete calculations as quickly as someone using a calculator . . . sometimes quicker!

So, whatever side of the fence we sit on when it comes to the debate on calculator papers, we can’t deny that calculation devices are a long-standing tradition in human history. And with the development of the scientific calculator, we have opened the way for students to be able to perform all sorts of mathematical functions, including trigonometry and logarithms. The important thing is that we don’t lose the ability to use our brains – there’s something to be said for mental arithmetic!

The Logic of Maths

May 26, 2014 § 1 Comment

Part of mathematical ability comes down to logic. People who are logical are able to follow mathematical processes and understand the mechanisms behind the question. This is especially helpful when it comes to solving word problems, a particular obstacle to lots of maths students.

Here’s one of the word problem questions from a GCSE Higher Maths Mock Paper:

Janice asks 100 students if they like biology or chemistry or physics best.
38 of the students are girls.
21 of these girls like biology best.
18 boys like physics best.
7 out of the 23 students who like chemistry best are girls.
Work out the number of students who like biology best.

This question can easily get you in a tangle! It needs to be tackled logically. Often, diagrams and charts are a good way to order your thought processes. For this particular question, a two-way table is helpful. We know that there are 100 students in total. 38 are girls, so 62 are boys. 21 girls like biology, 18 boys like physics, 7 girls like chemistry and 16 boys like chemistry. If we put those numbers into a table, we can then work out the rest.

So, the answer is 49.

The Great British Heatwave!

May 18, 2014 § Leave a comment

With our little mini heat wave this week, all eyes are on the weather forecast to see how long the temperature will stay at shorts-wearing level! So, where did our temperature scales come from.

We mainly use two temperature scales: Fahrenheit and Celsius.

The Fahrenheit scale was devised by a German physicist called Daniel Gabriel Fahrenheit in 1724. It has two fixed points: the freezing point of water is 32 degrees and the boiling point of water is 212 degrees. The difference between those two points is 180 degrees.

The Celsius scale, meanwhile, originates with a Swedish astronomer called Anders Celsius. The Celsius scale is preferred in modern use because it has nice round numbers! The freezing point is 0 degrees and the boiling point is 100 degrees, so the difference is 100 degrees rather than 180. This fits in better with our metric system, so is now much more widely used. The Celsius scale is also aptly called centigrade because, of course, centi means 100.

The formulas for swapping between the two are:

Fahrenheit to Celsius: (Fahrenheit – 32) x 5 / 9
Celsius to Fahrenheit: (Celsius x 9 / 5) + 32

And those will continue to be our temperature scales until the British devise a new scale that goes between the two points at which we moan about it being too hot or too cold!

And for kids who’d like to practice their thermometer skills, try taking a journey to Penguin City.

Enjoy the sunshine everyone!

Don’t Be Negative – A Common GCSE Maths Mistake!

May 11, 2014 § Leave a comment

Okay so this might be a bit of a boring blog post! But, with the GCSE exams round the corner, I thought I would highlight one of the most common mistakes seen when marking GCSE maths papers.

That problem is negative numbers. They just get students in a right old pickle! And that’s why they crop up every year in the exam papers! But they won’t be obvious . . . . they are often very sneaky and catch people off guard. For instance, you will see minus signs when expanding brackets or in substitution or indices questions.

So, here are the simple rules:

MINUS X MINUS = PLUS

MINUS X PLUS = MINUS

Take this past paper question as an example:

V = 3b + 2b2

Find the value of V when b = –4

First, substitute the number into the equation.

3b + 2b² =   3 x -4 + 2 x -4²

3 x -4 is PLUS x MINUS, so it becomes a MINUS: 3 x -4 = -12

2 x -4² is a bit more complicated because we need to do the squaring first:
-4² = -4 x -4 which is MINUS x MINUS, so it becomes a PLUS. -4 x -4 = 16

2 x 16 = 32

So, 3b + 2b² =   3 x -4 + 2 x -4² = -12 + 32 = 20

Just take it step by step and CHECK YOUR WORK! We wish everyone doing the GCSE exams all the best.

Fractions for Five Year Olds

April 27, 2014 § Leave a comment

The new National Curriculum will soon be sailing in to schools this September. It is set to make quite a difference and it’s exciting to see whether it will be a success.

One of the biggest changes is the step-up in terms of introducing topics much earlier than before. Now, your 5-year olds will be learning simple fractions, such as halves and quarters. This may sound crazy! But, don’t forget that the younger they are, the more they are able to learn and absorb.

The Department for Education has had the new curriculum published on their website for quite some time . . . . and it looks like the kids (and the poor teachers!) are going to be packing a lot in! These links show the new primary curriculum for maths and English – it shows you the topics that are going to be covered in each year group:

Primary Maths Curriculum From 2014

Primary English Curriculum From 2014

And, if you want a heads-up on simple fraction work, we’ve got it covered: How To Do Fractions

Image

Where Am I?

You are currently browsing the Uncategorized category at Maths Star.