Real Math

Alex and Simon were rather disillusioned last summer, after they had saved up their money, when they played this game at Centreville until all their money was used up, but still did not win the prize they had hoped for. They had conspired to play only against each other, effectively ensuring they would win every time.  However, they had miscalculated the number of times they would have to play in order to win the "choice" prize they wanted!

My plan is to turn this story into a math problem for my grade threes.  I believe it would be very motivating, and would provide a great opportunity for me to practise my "Bansho" for the project a colleage and I were working on.

I am thinking something like this:

Simon wants to win the "choice" prize -- a huge stuffed frog -- at a camel race game. Every time he wins a race, he gets a small toy, and he can trade smaller toys for larger ones based on the chart above. Simon has enough money to play 12 times. If he wins every game, will he be able to win the "choice" prize?

How much money will it cost Simon to win the "choice" prize?

A more complex question might be,

Alex and Simon were playing a camel race game at the fair.  They wanted to win the "choice" prize, an enormous, stuffed, purple frog toy. They decided to play against each other only, so that together, they would win every game.

Alex and Simon started saving their money so that they could play the camel race game until they won the prize they wanted. How much money would they need to save in order to win the "choice" prize?

(refer to the previous problem for the rules of the game)

I will try to do this before the end of the school year, and will report about it on my Smart Bansho blog.  Stay tuned!