Parallelogram 32 Year 7 18 Jun 2020Number Sense

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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. Finding something odd

The 1st odd number is 1.

1 mark

1.1 What is the 9th odd number?

Correct Solution: 17

2 marks

1.2 What is the 99th odd number?

Correct Solution: 197

1st odd number is 1,
2nd odd number is 3,
3rd odd number is 5,
...so the rule is “double the position of the number and subtract 1 to find the appropriate odd number.”

Therefore the 99th odd number is (2 × 99) – 1 = 197.

2. Junior Maths Challenge Problem (UKMT)

3 marks

2.1 The perimeter of the regular decagon P is 8 times the perimeter of the regular octagon Q.

Each edge of the regular octagon Q is 10 cm long.

How long is each edge of the regular decagon P?

  • 8 cm
  • 10 cm
  • 40 cm
  • 60 cm
  • 64 cm

An octagon has eight edges. Therefore the perimeter of the regular octagon Q is 8×10cm=80 cm.

The perimeter of the regular decagon P is eight times that of the regular octagon Q and is therefore 8×80 cm, that is, 640 cm.

A decagon has 10 edges. Therefore the length of each edge of Q is given by

640÷10cm=64 cm.

3. Number Sense

This is another interesting video by Jo Boaler. Like last week’s video from Jo, I think it illustrates how we might all see a problem differently and how there are many ways to solve a problem, but they all lead to the same answer.

4. Junior Maths Challenge Problem (UKMT)

3 marks

4.1 How many digits are there in the correct answer to the calculation 123,123,123,123 ÷ 123?

  • 4
  • 6
  • 8
  • 10
  • 12
Show Hint (–1 mark)
–1 mark

The answer isn't 4!

From the long division sum shown below, we see that

123 123 123 123 ÷ 123 = 1 001 001 001.

We see that there are 10 digits in this answer.

5. Simple Code

2 marks

5.1 There is a rule that transforms 4-digit numbers into a new number. Try to work out the rule and find out what the number 1,000 would be transformed into

  • 8809 = 6
  • 7111 = 0
  • 2172 = 0
  • 6666 = 4
  • 1111 = 0
  • 3213 = 0
  • 1000 = ?

Correct Solution: 3

Show Hint (–1 mark)
–1 mark

Look at the number of circles or loops in each digit.

The rule involves counting the number of circles or loops in each digit (e.g., 1, 2 & 3 have no loops, but 6, 9 & 0 have one loop each, and 8 has two loops). This means 1,000 has 3 loops and the answer is, therefore, 3.

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.