Parallelogram 31 Level 1 4 Apr 2024A quick trick

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. a portmanteau 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. Speedy sums

How quickly can you add up ten numbers?

Watch this video where James Grime shows us a quick number trick that will have you adding at the speed of light and putting calculators to shame.

(If you have problems watching the video, right click to open it in a new window)

1 mark

1.1 After your volunteer has generated their ten numbers, how do you find the sum?

  • Add the numbers column by column
  • Add the two biggest numbers
  • Multiply the 4th from last number by 11
  • Multiply the 4th number by 10
  • (Not answered)
1 mark

1.2 The maths behind this trick is based on a famous sequence where you add the previous two terms to get the next term.

What was the name of the sequence?

  • The golden ratio
  • Fibonacci sequence
  • The Mersenne primes
  • Triangular numbers
  • (Not answered)
3 marks

1.3 James described a lightning speed method for multiplying by 11.

Use that method to calculate 251 × 11.

Correct Solution: 2761

To quickly multiply a 3 digit number by 11 we know the first and last digits will stay the same:

To find the second digit, we add the first two digits together, in this case 2 + 5:

To find the third digit, we add the last two digits together, 5 + 1:

2 marks

1.4 There is a quick way to check if numbers are divisible by 11:

  • Alternate between subtracting and adding the digits
  • If the result is in the 11 times table then the number is divisible by 11.

Which of the following is NOT divisible by 11?

  • 2,442
  • 21,648
  • 123,321
  • 11,111
  • (Not answered)

2. Some tricky puzzles

2 marks

2.1 The sum of the first 5 odd positive numbers is 25.

What is the sum of the first 5 even positive numbers?

  • 30
  • 35
  • 40
  • 45
  • 50
  • (Not answered)

You could work this out by simple addition, but there is a quicker way:

As each even number is 1 more than the previous odd number, if the sum of the first five odd numbers is 25, the sum of the first five even numbers must be 25 + 5 = 30.

2 marks

2.2 Mr Fussy wants to buy a new house, but he does not want a house with the digit 4 in the door number!

The new houses are numbered 1 to 100.

How many houses can Mr Fussy choose from?

  • 19
  • 20
  • 80
  • 81
  • 90
  • (Not answered)

There are 10 numbers starting with 4.

There are 9 more numbes containing a 4 (i.e., 4, 14, 24, 34, 54, 64, 74, 84, 94).

For a total of 19.

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 Parallelograms.

Cheerio, Simon and Ayliean.