Parallelogram 35 • Level 1 • 2 May 2024A piece of pizza

Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

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. Slice it right

One of the best uses of maths is to ensure you (and your friends) each get your fair share of whatever tasty treat you’re about to eat.

Here, ‘fair’ simply means that you all get the same amount.

It’s easy enough to do with circular cakes, pies, and pizzas, but how can you make sure everyone gets the same when your cuisine is oval-shaped?

Luckily Dr Katie Steckles is here to save the day by cutting her oval pizza in a mathematical way.

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

1 mark

1.1 In the first method for cutting circular pizzas, the slices are created with equal angles at the centre.

What would the central angle be for a pizza with five slices?

1 mark

1.2 The size of a pizza can be described by its diameter.

Using the formula:

Circumference = 3.14 × diameter

Find the circumference of a 12 inch pizza.

1 mark

1.3 Describe the method used for oval-shaped pizza sharing:

Find the centre and cut slices with equal angles
Divide the perimeter equally and slice towards the centre
Imagine it's a round pizza, slice equally, then stretch those slices onto the oval pizza
Fold the pizza in half and slice in equal sized strips
(Not answered)

3 marks

1.4 Some friends share a 32cm circular pizza.

They each have a slice with a crust length of 12.56cm.

How many friends were in the group? (use the approximation pi = 3.14)

Show Hint (–1 mark)

–1 mark

First, find the full circumference (total crust length) of the pizza.

We can use the formula Circumference = 3.14 × diameter.

Then find how many slices of 12.56cm can be made from this length.

Thank you Stecks for that excellent oval pizza method.

Next on the list: how would you slice this pizza pi?!

2 marks

2.1 This shape, called a sphinx, is made of identical equilateral triangles.

How many of these identical triangles are needed to make this sphinx?

Show Hint (–1 mark)

–1 mark

Draw lines inside the shape to form equal sized equilateral triangles.

Once split into 6 triangles it looks like this:

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.