Monday Maths: Vicki Robinson, Communications Officer

# A mysteriously mean #MondayMaths

Posted: 21/11/16

Although this week’s #MondayMaths might seem like some kind of magic trick (we’re looking at six mystery numbered balls in a bag), we’re getting *mean* and mathematical.

When a seventh ball with a value of *a* is added to the mix it decreases the mean of the numbers by two.

Using this information, how can you and your class prove that the total of the original six numbers can be expressed as 6*a* + 84?

**Joining up the dots**

At first puzzle-solvers may find this difficult to digest as there is no obvious link from the scenario to the question being asked. Nonetheless, students should be encouraged to write down what they know as well as any relevant expressions they can derive from that information.

As part of our mastery curriculum this term, Year 7 students are starting to look at the mean, while Year 9 students are delving deeper into the topic by rearranging equations. Having an understanding of both areas will be needed to tackle this problem.

Here are a few quick questions you can ask your students to get them started:

- Find an expression for the mean of the first 6 balls
- Find an expression for the mean once the 7
^{th}ball is added - What do you know about the comparative value of these expressions?
- Can you write an equation to compare these two means?

Your students should have the number and algebra skills to solve this puzzle, but the main challenge lies in forming a strategy to apply those skills into an effective method.

**A head start**

One way of easing them into this problem could be to play with simpler ‘means of hidden number’ problems. For example…

*‘If I had three numbers whose mean is 5 and I added a fourth ball that increased the mean by one, what is the value of the 4 ^{th} number?’*

You get the idea.

**Check out the answer on ****Twitter****, this Thursday. We hope your class enjoy it and let us know how you get on!**