# Probability and Tree Diagrams My fifth grade students are in the midst of a unit on probability.  This is one of my favorite units to teach for a couple different reasons.  One is that it follows a massive pre-algebra unit and it’s so different than what students have been working on for the past few months.  I feel like it’s time students see a different strand of mathematics. Another reason, is that students have to think logically about probability and it’s something that impacts their daily life.  Also, students haven’t had a lot of time to discuss probability in math class.

Near the beginning of the week students started to explore the different terms related to probability.  They completed a random selection activity the week prior and students are starting to have a better understanding of the terms.  Around mid-week students investigated tree diagrams and their usefulness in determining actual probability.  One of the highlights on Tuesday was a maze activity.  Students were given a scenario where they needed to find the probability that students would win or exit the maze without running into a dead end.  They used number cards 1-4 to accomplish this. It looked similar to the image below. Students first estimated the probability that they’d win and then created a tree diagram to find the actual results.  They tested out the game by playing six times with a partner.  The class was asked what they found and if their estimations were in the ballpark.  For the most part they weren’t, which was good news because the class used a tree diagram to find the actual probability. Students were then asked to use the maze as a fundraising activity. The next question is below.

If 100 students entered the maze, how many would end up being the winner?  Let’s say that the winner receives \$25. How much profit would be made If students were charged \$5 to enter the maze?

This was a turning point in the lesson because students started to become even more vested in what was happening.  I gave them about 3-5 minutes to work independently and then they shared their findings with their table group.  Most groups were right on target and were able to explain their math reasoning.

On Thursday, students were asked to use their probability skills with spinners and tree diagrams.  I found an amazing resources in this book that spurred me to recreate a diagram that my students could use. I gave a copy of the diagram to each student.  I placed five minutes on a timer and gave students that time to work independently to read the prompt and start to find a solution.  Students wrote on the sheet and attempted to put together a cohesive tree diagram that made sense to them.  I had a few students that thought it was impossible  After the five minutes were up, students were asked to share their strategy with partners.  The answers were interesting and all over the place.  Some students were confused with the spinners as they had to convert them to fractions.  Other students had issues with the actual directions.  I helped answer questions and students presented their ideas on the solution.  This entire activity took 30+ minutes to discuss.  Students finished up their ideas on the paper and turned it in.  I’m reviewing the results right now and can tell that I need to follow-up with the class.  The majority of students did very well, although simple mistakes seem to be evident in quite a few.  The class will be discussing this on Tuesday.