Monday, March 21, 2011

Problem Solving: Organized Counting

Stoplights challenges students to figure out how many different stoplights they can create with 3 different color linking cubes if each stoplight must have one cube of each color. Use linking cubes so that students can assemble all possible stoplights. 

NOTE:  You may choose to have students use any three different colors so that each student pair has enough linking cubes to assemble all possible combinations using one of each color to create the stoplight. 

Discussion:  In these types of problems, it is important that students know when they have found all of the possible combinations.  Be sure to ask students to explain how they know they have all of the combinations.  How did they know when they could stop looking?
Try to let students work on the problem without organizing their thinking.  Let pairs of students work together.  Ask students to explain their method and their thinking.  Peer explanations are so powerful in problem solving.  

You may be surprised at how students organize the challenge.  I remember a first grader telling me that he knew when he had them all because each color got to be on top twice.  He simply switched the bottom two cubes, then let another color be on top, etc.  To him, it was like being in the front of the line.  It was such a succinct explanation from a young learner.  Amazing!

Download Stoplights which includes the student handout and a brief explanation.  Be sure to make extra copies available to students,  so they aren't led into believing they must find 6, which is the correct answer. 

Suggestion:  To keep this task truly open-ended, hand out blank paper and have students draw their answers.  This method does not prompt students and also mimics state testing.


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