Week 3The Big Bang

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. a portmanteaux word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.
  • Tackle each Parallelogram in one go. Don’t get distracted.
  • When you finish, remember to hit the SUBMIT button.
  • Finish by midnight on Sunday if your whole class is doing parallelograms.

IMPORTANT – it does not really matter what score you get, because the main thing is that you think hard about the problems... and then look at the solution sheet to see where you went wrong, and then next time you’ll know what to do.

1. Is zero odd or even?

This video is from the terrific Numberphile channel, and it features Dr James Grime and Professor Roger Bowley (University of Nothingham) talking about zero and asking if it is odd or even. Watch and answer the questions below.

1 mark

1.1. Is zero odd or even?

  • Odd
  • Even
2 marks

1.2. Is zero positive or negative?

  • Positive
  • Negative
  • Neither
  • Both
2 marks

1.3. According to James Grime, which of these is the most even number?

  • 0
  • 1
  • 2
  • 3
  • 4
  • 5

If being even means being divisible by 2, then a number is very even if it can be divided by 2 several times. By this definition, 4 is more even than 2, because 4 can be divided by 2 to get an answer of 2, which can be divided by 2 again to get an answer of 1, but that is the end of the road, because 1 is not divisible by 2. Therefore, 0 is the most even number, because it can be divided by 2 an infinite number of times.

2 marks

1.4. According to James Grime, which is the most even number among the list below?

  • 2
  • 4
  • 6
  • 8
  • 10
  • 12
  • 82 = 4
  • 42 = 2
  • 21 = 1

So, 8 can be divided by 2 three times, which makes it the most even of the five numbers. By comparison, 4 and 12 can be divided by 2 twice. Also, 6 and 10 can be divided by 2 only once.

2. The Big Bang

Last week’s Parallelogram included a silly (but brilliant) mathematics song by the band Barenaked Ladies. Here is the band’s song about the big bang theory, which is the theme tune to the comedy show, The Big Bang Theory. Incidentally, I am very proud that the band’s lead singer Ed Robertson wrote the song because he had just read my book BIG BANG.

1 mark

2.1 The song mentions that mathematics was created by the Big Bang, and it then mentions two other subjects. What are the two other subjects?

  • Science and Physics
  • Chemistry and Physics
  • Chemistry and Biology
  • Geography and Biology
  • Science and History
1 mark

2.2 According to the song (and scientific observations) when did the Big Bang occur?

  • Fourteen thousand years ago
  • Fourteen million years ago
  • Fourteen billion years ago
  • Fourteen trillion years ago

3. Junior Maths Challenge Problem

If you are a Year 7 student, then it is likely that you will be taking part in the United Kingdom Maths Trust (UKMT) competition known as the Junior Maths Challenge (JMC). If you do particularly well, you might earn yourself a gold, silver or bronze certificate, but you will have to work hard as you will be competing against Year 7 and Year 8 (!) students from across the country.

Your teachers will help you prepare for this national maths competition, but in each week's Parallelogram we will always include one UKMT Junior Maths Challenge question.

3 marks

3.1 When painting the lounge, I used half of a 3 litre can to complete the first coat of paint. I then used two thirds of what was left to complete the second coat.

How much paint was left after both coats were complete?

  • 150 ml
  • 200 ml
  • 250 ml
  • 500 ml
  • 600 ml

The first coat uses half the paint, so half remains. Two thirds of this is then used so one third of one half, that is one sixth remains.

So the volume remaining is 16×3 litres. So there remains 0.5 litres, that is, 500 ml of paint.

If you missed the first two Parallelograms, then try to go back and complete them. After all, you can earn reward points and badges by completing each Parallelogram. Find out more by visiting the Rewards Page after you hit the SUBMIT button.

There will be another Parallelogram next week, and the week after, and the week after that. So check your email or return to the website on Thursday at 3pm.

In the meantime, you can find out your score, the answers and go through the answer sheet as soon as you hit the SUBMIT button below.

It is really important that you go through the solution sheet. Seriously important. What you got right is much less important than what you got wrong, because where you went wrong provides you with an opportunity to learn something new.

Cheerio, Simon.