Week 12Prime Time Y7

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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 Y7 student, and 100 bonus badge points for everyone in the top 10. If you can 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 Y7 and the number of numbers identified. For example, if you scored 13, then your subject line should read “Y7 13”.

2. Area questions

1 mark

2.1. Square A has sides 24 cm in length, but Square B has a perimeter of 1 m. Which has a larger area?

  • Square A has the larger area
  • Square B has the larger area

If square B has a perimeter of 1 m, then it has sides of length 25 cm, so it will have a larger area.

3 marks

2.2. Which triangle has the larger area? Triangle A has sides 5, 5, 6, but Triangle B has sides 5, 5, 8.

Show Hint (–1 mark)
–1 mark

Split both triangles into two right-angle triangles and use Pythagoras’ Theorem to work out the height of each right-angle triangle.

  • Triangle A has the larger area
  • Triangle B has the larger area
  • Both triangles have the same area

You would need to draw the triangles and see that they can be split into two right-angle triangles. Then use the Pythagorean theorem to work out the height of each right-angle triangle. Then you will see both of the big original triangles is built from two 3-4-5 triangles, but they are arrange differently. So they have the same area.

2 marks

2.3. What is the area of a triangle with sides 23 cm, 13 cm and 10cm?

Correct Solution: 0 cm2

The quick way to do this is to notice that 23 = 13 + 10, so the two short sides add up to the length of the long side... so we have a flat triangle with no area.

3. Sculpture mystery

2 marks

3.1 This sculpture of a train coming out of a tunnel is by the artist Cindy Chinn. How long is the steam engine, roughly?

  • 1 cm
  • 10 cm
  • 1 m
  • 10 m
  • 100 m
Show Hint (–1 mark)
–1 mark

What is the sculpture made from? Why are the tracks and the train black? Why is everything else made of wood?

It’s carved from a pencil, so the steam engine is about 1 cm long.

4. Junior Maths Challenge Problem

2 marks

4.1 What is the difference between the smallest 4-digit number and the largest 3-digit number?

  • 1
  • 10
  • 100
  • 1,000
  • 9899

The smallest 4-digit number is 1000. The largest 3-digit number is 999. So their difference is equal to 1000 − 999 = 1.

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.