Experimath - Experiment 29

Syllabus links

Key Stage 2 (age 7 to 11)

How can understanding fractions help you to eat more sweets?

This experiment gives children an opportunity to practise using fractions, percentages and decimals.

The child will learn about simple probabilities.

a packet of sweets

a bowl

some paper

a pencil

Gather the equipment you will need. Don't forget a packet of multi-coloured sweets!
Count the total number of sweets and make a note of this.
Write a list of the different colours on the left of your paper.
Next to each colour, write the number of sweets of that colour.
Convert each number to a fraction in its simplest terms and write this next to the number.

For example, if there are 6 red sweets out of 36 total then the fraction is 6/36.

This can be simplified to 1/6, so you would write 1/6 in the red row.

for each colour, write the fraction as a percentage to two decimal places.
Put all the sweets in a bowl.
Show your workings to friends and family and ask them to join in a guessing game.
Everyone including you takes turns to play.
Pick one sweet at random from the bowl without looking at it. Ask the current player to guess what colour it is. If they are right, they can eat it, otherwise it goes back in the bowl.
Keep going until all the sweets have been eaten.

Discuss with other players how they used the initial data in choosing a color.
Did players change their tactics as the game went along?
When a players eats one colour, does it affect the chance of that colour of being picked again?

It makes sense to pick the colour that is the biggest fraction. This has the highest probability of being chosen.
Players with good memories have an advantage. For example, if you know that all the sweets of a certain colour have already been eaten then there is no point in guessing that colour any more.
Yes. The fractions that were worked out at the start will be constantly changing throughout the game as different coloured sweets are eaten.

The only exception is when there is only one colour of sweets left. For example, suppose the only sweets left were three green ones. 100% of the remaining sweets are green. If someone guesses "green" and eats a sweet, 100% of the remaining sweets are still green.

Open another packet of sweets. Does it have the same total number of sweets? Does it have the same number of each colour?
What is your favourite colour of sweet? If you bought a 1 kg jar of sweets, how many would you expect to get of that colour.

Each packet proabably has about the same number of sweets, since they are sold by weight. However, the distribution of colours may vary.
You can make an estimate based on the weight of the packet. For example, if red sweets are the favourite and a 25g packet contained 6 red sweets then we can estimate that 1kg (1000g) contains (1000 ÷ 25) × 6 = 240 red sweets.

Experiment 29 v2