# Summer SAVY 2017, Session 6/Day 2- Secrets of the Moli Stone (Rising 2nd/3rd)

Posted by on Tuesday, July 25, 2017 in SAVY.

We started today by picking up from our first mathematical investigation from yesterday. Students searched for all the possible combinations of pennies and dimes that add to the same sum for a range of different amounts. After exhaustively searching for combinations and discussing ways to organize our data to make patterns more visible, students noticed a general pattern that as the number of dimes decreases by 1 or 10 cents, the number of pennies increases by 10 or 10 cents in every case. We used this noticing to generate a general rule that would help us determine the possible combinations of pennies and dimes for all amounts between 1 and 99 cents. Our rule was the combinations is equal to the number in the 10’s place plus 1. We then extended this new insight to understandings of place value, thinking about the affordance of using a place value system in terms of efficiency. Who wants to carry around 100 pennies when you can carry around a single dollar bill?!

We will continue diving into the properties of a place value system of the next couple of days. In a new investigation, we explored the total number of numerals needed to generate all numbers continuing onto infinite. Students used these numerals in a game played with partners to see who could make the largest two-digit number by drawing cards one at a time. Students each came up with their own strategies, and revised these strategies as they evaluated how successful their strategies were and gaining new understandings of how the placement of numerals in a place value system are important, especially the numeral, 0. We debriefed this activity by sharing our different strategies, comparing those that were most successful and ones that were not so successful.

Finally, we wrapped up the day by previewing our third mathematical investigation. We are traveling to the Land of Treble where everything comes in groups of three. Tomorrow we’ll explore what that means for how their number system works. Hmm…

-Ms. Megan