Dice Challenge

Looking for a new game for your middle kids?  Make a dice tower.  They are allowed to walk around it but not to touch it.  The goal: Find the sum of all the faces that cannot be seen.

This begins as a logic puzzle.  If we can see these numbers, what numbers are missing?  The resulting long addition problem is a useful opportunity to increase speed by using the Commutative and Associative Properties.  Group numbers so that they are easy to add mentally (e.g. into groups that form 10).

Challenge older kids to determine the pattern so that they can find the sum without walking around the tower.  Once they have the pattern, write it down.  Discuss the order of operations while solving.  This problem involves multiplication, subtraction, addition, and grouping symbols.

You can incorporate sets as well.  Find all the possible sums for a stack of six dice, for example.  Probability follows close behind.  If a stack is made of seven dice, what is the probability that the sum of the hidden faces will be 52?  How about greater than 50 but less than 55?

This whole project also works backwards.  Make a tower of dice such that the sum of the hidden faces is 82.  Find three sums that it is impossible to make.  PROVE that it is impossible!

If your big kids are big enough for Algebra, have them derive a formula that will yield the sum of the hidden faces when you have variables for the number of dice stacked and the value of the face on the very top of the tower.

Then let the baby knock it down.  See?  Fun for all ages!

Hopefully that just bought you enough time to drink a hot cup of coffee.

Can you and your kiddos come up with any other activities to do with a simple tower of dice?