Parallelogram 25 Level 1 22 Feb 2024Speedy squaring

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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. Calc-you-later!

How long would it take you to square 98? Would you need a piece of paper?

Well get ready to perform that calculation in the blink of an eye with this lightning quick trick from Howie Hua!

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

1 mark

1.1 When is this trick best applied?

  • squaring any number
  • squaring numbers which start with 9
  • squaring numbers a little below 100
  • squaring numbers a little above 100
  • (Not answered)
1 mark

1.2 Calculate 992 using this method.

  • 9,901
  • 9,910
  • 9,801
  • 9,810
  • (Not answered)

The difference between 99 and 100 is 1.

Step 1: 99 - 1 = 98, these are the hundreds and thousands column of our answer.

Step 2: 12 = 1, this is the units column of our answer.

So this gives 9,801.

2 marks

1.3 Calculate 942 using this method.

Correct Solution: 8836

2 marks

1.4 Always be on the lookout for ways to build up your repertoire of mental math tricks.

Have a look at what happens when you multiply by 11:

  • 45 × 11 = 495
  • 25 × 11 = 275
  • 63 × 11 = 693
  • 18 × 11 = 198

Can you notice a rule which will let you do this quickly?

  • There is no pattern.
  • Add the digits together and pop the answer in the middle.
  • Square both digits and concatenate.
  • (Not answered)

A quick way to multiply by 11 is to add the digits together and pop the result in the middle!

But what happens when the sum is more than 10, like in 58, I hear you cry!

Not to worry, this trick still works but you have to carry over into the hundreds column.

  • 5 + 8 = 13
  • The 3 goes between the 5 and the 8, so 538
  • And the one carries over, so 638

2. Puzzle time

Have a go at this puzzle, without using a calculator and flex your mental maths skills!

2 marks

2.1 Betty Bott's beans each weigh 2.5 grams.

How many beans will Betty have in half a kilogram?

  • 25
  • 40
  • 50
  • 100
  • 200
  • (Not answered)

Half a kilo is 500g.

Grouping the beans in pairs will give 5g per pair.

100 pairs are needed for 100g, which gives 200 beans overall.

Work smarter, not harder!

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.