One of the very first problems my students encounter is
Soccer Game:
At the conclusion of a soccer game whose two teams each included 11 players, each player on the winning team "gave five" to (slapped hands with) each player on the losing team. Each player on the winning team also gave five to each other player on the winning team. How many fives were given?
Soccer Game:
At the conclusion of a soccer game whose two teams each included 11 players, each player on the winning team "gave five" to (slapped hands with) each player on the losing team. Each player on the winning team also gave five to each other player on the winning team. How many fives were given?
My students are generally assigned one to two problems of the day (PODs) each evening. After orally presenting their solutions on the board on the second day of class, these two sections of students were not satisfied with the multiple solutions arrived at on that day, those where 231 high fives and 352 high fives. In each section, I had one student suggest that they "act out" the problem. The first section of the day actually moved outside to the hallway and grabbed students that were passing by to actually have 11 students on each team! The second section had enough students in the class to act it out, they stayed inside of the classroom. After acting out the scenario they discovered that both solutions are actually correct, depending upon how the problem was interpreted.
This problem usually sets the stage for what is to come the rest of the semester, the students realize that depending upon interpretation a word problem may have more than one correct solution. This is a difficult concept for some of them to grasp because typically in mathematics you are either right or wrong. The students also realize they will be depending upon each other to solve the variety of problems they will encounter throughout the semester and that they each will have a different approach to solving the problems at hand. They also realize early on, that they will have fun!
This problem usually sets the stage for what is to come the rest of the semester, the students realize that depending upon interpretation a word problem may have more than one correct solution. This is a difficult concept for some of them to grasp because typically in mathematics you are either right or wrong. The students also realize they will be depending upon each other to solve the variety of problems they will encounter throughout the semester and that they each will have a different approach to solving the problems at hand. They also realize early on, that they will have fun!
At the end of every semester, I read this children's book about important things to my students. It serves as a way to end the semester on a positive note and it also begins to get them thinking about the final reflection they will be writing as part of their final portfolios.
After reading several pages, they are required to do a "quick write" on: "The important thing about Problem Solving is...." Each semester I have a couple of students whose quick writes jump out at me, this past semester those were:
After reading several pages, they are required to do a "quick write" on: "The important thing about Problem Solving is...." Each semester I have a couple of students whose quick writes jump out at me, this past semester those were: