Recall the vase problem from the second lesson. The vase in the classroom is 6 inches wide and 3 ft tall. It is going to be used in a classroom as a reward system. Each time the class does something positive, the teacher will deposit a marble into the vase. When the vase is full, the class will earn a free day and a party! The teacher wants to know how many marbles the class will need to earn in order to completely fill the vase to the top. Each marble has a diameter of one inch.

Provide an estimate for the number of marbles. How did you determine your answer? What, if any, further information would you need in order to solve this problem?

If the teacher only wants to give out 10 marbles maximum per day, how many days would it take for the class to earn enough marbles to fill the vase? Is it possible for them to accomplish this in one school year (180) days? How many marbles would the teacher need to give out each day if this is to be accomplished in 180 days?