# Package 3-1: Mystery spinner

Your child will make a spinner then solve a problem to strengthen their understanding of chance and probability.

Week 4 - Package 1 - Year 5 and 6 Mathematics - Mystery spinner

## Things you need

### Ideal

• pair of compasses

• card

• toothpick

• blue, yellow and red coloured pencils or textas

• pencil

• scissors

• paper

### Back up

• You can draw around the bottom of a glass twice. Once on a piece of paper and once on a piece of card. Cut out both circles. Fold the paper circle into quarters so you can find the centre of the circle. Put the paper circle exactly on top of the card one and use a sharp object such as a needle to poke through the paper circle and mark the centre of the card circle.

• Card from a cereal box or other packaging is fine.

• A matchstick or sturdy twig from the garden will do, but you will need something sharp to make a hole to put the stick through.

• Other coloured pencils - you will need three and you will need to insert the names of the new colours correctly into the problem.

## Before you start

This is a reasoning activity and is expected to take some time. Try to encourage your child to solve the problem without stepping in to help too quickly. Depending on how dextrous your child is you may need to help them create the circular spinner from the card, especially if they are using a pair of compasses. If a younger sibling is joining in the activity they will definitely need help with the compasses. See above for an alternative way of drawing a circle and finding the centre. Give your child time to practise spinning the spinner even though there are no coloured sections on it yet and check that the spinner is reasonably well balanced. It may be useful to have a chat about how sections are marked on a spinner. Below is an example. Remember it is not time to colour the spinner yet.

## What your child needs to know and do

This problem requires some understanding of chance or probability. It will give your child an opportunity to talk about fairness and about fair testing. Your child will need to understand language such as more likely, twice as likely, twice the chance, half the chance, half as likely and least likely. It is worth checking that they know this language before you start. Your child will also need to know about fractions of a whole circle.

Here is the problem they will be trying to solve:

If I spin the Mystery Spinner it is twice as likely to land on a blue section as a yellow section and half as likely to land on a yellow section as a red section.

What could the Mystery Spinner look like? Is there more than one possibility? Can you explain your answer?

## What to do next

Your child may then want to try experimenting by drawing some spinners on paper and colouring in different sections. If they really like to be neat you can find a template here but this is not really necessary.

Once your child has at least one solution to test they can colour their spinner. If they have two solutions they can flip the spinner and colour the other side too.

At this point it is important that your child has an opportunity to test their solution. They should spin their spinner 10 times to see what happens. They could record their solution in a table and count how many times the spinner landed on blue, yellow or red. If your child does not get the desired result, ask them if they think that is because their solution is incorrect or could there be other issues?

Some ideas your child could come up with are:

• The spinner is not well balanced – check.

• A round spinner is hard to read as it may land where two colours meet – find a way to have a flat edge to each section. Do the flat edges all need to be the same length? Why? How can that be done?

• 10 spins is not a large enough sample to test – keep spinning!

Talk to your child about their solutions. Were there other possibilities? What were they? Why were there more possibilities?

• What is the least number of sections in total that the spinner could have?

• What fraction of the spinner should be blue?

• What fraction should be yellow?

• What fraction should be red?

• If your spinner had ten equal sections how many tenths would be red?

• If your spinner had 20 equal sections how many twentieths would be red?

• What about the other colours?