A Combining Problem: Correct Postage

Yesterday I did problem solving with a number of classes at Charlie Lake School. Since it is early in the year and students have not yet had a chance to develop a range of strategies for problem solving, I used a problem that I could specifically base around manipulatives. The problem, originally created by someone at the University of Wisconson (and I apologize that I cannot locate a specific name, group, or link), was this: Jeff is sending a small package to Kelsi, who lives in another city. Jeff has to put 18 cents worth of stamps on the package. Jeff has 10-cent stamps, 4-cent stamps, and 2-cent stamps that he can use. Show different ways that Jeff could make 18 cents using his stamps. I used 18 cents as a total for the grade 2’s, but gave the grade 3’s the same question with a total of 24 cents (thus allowing for more possible combinations). Each student had 18(or 24) counters which could be moved into groups of 10, 4 or 2 to represent the value of each stamp. Because it was a hands-on approach, every student was able to be successful. We shared our solutions and I recorded them on chart paper.  Some of the students realized that the repeated addition of similar stamps could be combined using “groups of” the value, so these ideas were recorded also. The students all worked hard and had a great time — many of them saying so when going out the door! Isn’t that what you want to hear?! Mathematically yours, Carollee