Week 12Prime Time Y8

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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.
  • Finish by midnight on Sunday if your whole class is doing parallelograms.
  • Your score & answer sheet will appear immediately after you hit SUBMIT.
  • Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.

1. Primes against the clock

Below is a simple website that tests how well you know your prime numbers and how quickly you can apply some prime tests. It will show you a series of numbers and you have to decide whether or not they are prime. If you do not know straight away, then there are some easy checks that you can apply to filter out the non-primes:

  • If it is even, then it is divisible by 2.
  • If the digits add to 3, 6, or 9, then it is divisible by 3.
  • If it ends with a 0 or 5, then it is divisible by 5.
  • Remember, 1 is NOT a prime.

Just visit the Is this a prime? website and see how many numbers you can identify as primes or non-primes.

There will be a prize for the top Y8 student, and 100 bonus badge points for everyone in the top 5. If you score more than 10, then email us at prizes@parallel.org.uk – just send us a screengrab showing your score by midnight on December 11th, and in the subject line write Y8 and the number of numbers identified. For example, if you scored 13, then your subject line should read “Y8 13”.

2. Don’t celebrate too early

Watch and learn a lesson from this video.

Don’t celebrate too early. Check your work. Don’t leave a job half done.

3. Junior Maths Challenge Problem

2 marks

3.1 The diagram shows a square divided into strips of equal width.

Three strips are black and two are grey.

What fraction of the perimeter of the square is grey?

  • 15
  • 14
  • 425
  • 13
  • 25

Two sides of the square are wholly black, and 25 of two sides are grey.

So the length of the perimeter that is grey is equal to 2 × 25 = 45 of the length of one side.

The length of the perimeter is 4 times the length of one side.

So the fraction of the perimeter that is grey is 454=15

3 marks

3.2 A square is divided into seven strips of equal width. Four of the strips are black and three are grey.

What fraction of the perimeter of the square is grey?

  • 128
  • 314
  • 17
  • 37
  • 1114

Two sides of the square are wholly black, and 37 of two sides are grey.

So the length of the perimeter that is grey is equal to 2×37=67 of the length of one side.

The length of the perimeter is 4 times the length of one side.

So the fraction of the perimeter that is grey is 67÷4=628=314.

3 marks

3.3 A square is divided into an odd number of strips of equal width.

The strips are alternately black and grey, with one more black strip than grey strips. The fraction of the perimeter that is grey is 625.

How many strips are there?

Correct Solution: 25

We know that 2 lengths have no grey, because there is no grey strip that touches any corner or which stretches along any side. We don’t know the number of strips, but we could call it NS, and we know that the number of grey strips is ½NS1. So, the fraction of grey is:

[ ½(NS – 1) + ½(NS – 1) ] ÷ 4 = 6/25

If you rearrange and simplify this equation, then NS = 25.

5 marks

3.4 Imagine that the square has trillion-and-one black strips and a trillion grey strips What fraction (give or take a bit) of the perimeter of the square is grey?

  • 0
  • 116
  • 15
  • 14
  • 12
Show Hint (–2 mark)
–2 mark

Two sides of the square will be black, as previously. The other two sides will effectively be half black and half grey, because the difference between a trillion and a trillion-and-one is insignificant.

Two sides of the square will be black, as previously. The other two sides will effectively be half black and half grey, because the difference between a trillion and a trillion-and-one is insignificant. So, the fraction of the perimeter that is grey is ( ¼ + ¼ ) ÷ 4 = ¼.

4. Another Junior Maths Challenge Problem

3 marks

4.1 What is 2014 − 4102?

  • -2012
  • -2088
  • -2092
  • -2098
  • -2112

It is easier to subtract the smaller number, 2014, from the larger number, 4102. Now

4102 − 2014 = 2088

and so

2014 − 4102 = −2088.

Before you hit the SUBMIT button, here are some quick reminders:

  • You will receive your score immediately, and collect your reward points.
  • You might earn a new badge... if not, then maybe next week.
  • Make sure you go through the solution sheet – it is massively important.
  • A score of less than 50% is ok – it means you can learn lots from your mistakes.
  • The next Parallelogram is next week, at 3pm on Thursday.
  • Finally, if you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelogams.

Cheerio, Simon.