Summer SAVY 2016 (Session 5, Day 2) – Secrets of the Moli Stone
We started to day by reviewing our activity from yesterday—figuring out how many combinations of pennies and dimes make 47 cents and proving that we really had found all the combinations. Students found that when we organize our data this often helps patterns become more visible. In this case, most students decided that organizing their combinations by increasing number of dimes highlighted that the number of pennies also decreased by a consistent amount. As we explored these patterns, students noted that because dimes always count as 10, there will always be a minimum of 7 pennies and at most there can only be 4 dimes. Thus, we decided that because we exhausted all the combinations of dimes and pennies between these two values, we had indeed found all possible combinations. A question that we still need to explore—is there a rule that lets us know the possible dime and penny combinations for all amounts of money 99 cents and below?
Our exploration of dimes and pennies led us to making a connection to base 10 blocks that students routinely encounter in school. We decided that pennies are equivalent to the 1’s blocks and the dimes are equivalent to the 10’s blocks. As we discussed more about place value and the role that the number 10 play’s as the base in our number system, students were presented with their first number system to decode. We visited an imaginary land called the Land of Treble where rather than liking groups of 10, the people like groups of 3. Students worked together to figure out why in the land of treble what we would call 17 blocks, they would represent as 122 blocks (1 group of 9, 2 groups of 3, and 2 ones). Students used our number system to help lead their investigations, noting that in order to go from one’s to ten’s we have to have 10 one’s, so in the Land of Treble maybe you would only need 3 one’s. After we discovered how a base 3 number system works in the Land of Treble, we then explored a base 4 number system. Students quickly caught on to how a base dictates each place value within a system. Current questions that are still lingering: how many number systems are there? How many numbers are even in a number system? What is the base of the number system used on the Moli Stone?