Monday Maths: Vicki Robinson, Communications Officer

# Unusual dice in #MondayMaths

Posted: 5/12/16

Our #MondayMaths challenge might get your heads spinning this week. We’re looking at rolling two unusual dice and noting their totals.

These dice are unusual in that on one die the odd numbers are negative, and on the other die the even numbers are negative. How does this affect the distribution of possible totals?

This puzzle fits in well to this term when Year 8 students will be covering negative numbers, number facts and how to explain number problems. In the Summer term, Year 9 students will look at averages and probabilities – more knowledge that can be applied when cracking this puzzle.

Whether you’re introducing this puzzle to students this term or next, it’s a great opportunity to bring negative numbers into calculation of averages.

**Not sure where to start?**

If your students are giving this a go in your lesson, a good precursor could be to explore the distribution of totals, for pairs of normal, unbiased and six-sided dice. From here we can then compare this problem with that scenario and talk about why things are so different.

Let your students explore ways of investigating and recording these dice totals. Hopefully they will realise that creating a 6 by 6 table to record every possibility is the most efficient approach.

**Why, why, why?**

With all of the questions posed about these dice rolls, make sure your students think about why…

*Why*is this total the mode?*Why*the total of the dice cannot be more than a certain number?

Students should find that, like normal dice, the probability of scoring an odd or even total is 50%.

If we could modify a normal pair of dice, only by changing certain numbers to negatives, how could we bias the dice to increase the chance of an odd total?

And finally, can students work out the mean of all possible totals?

**The answer will be rolled out on Thursday – check our ****Twitter**** page.**