Category Archives: Statistics

Scatter Plots

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I was really excited to teach my Algebra Honors students about scatter plots and lines of best fit today.  I have been looking forward to this lesson because it allows me to teach statistics, which I love, to my students but also because we were going to use for the first time the HP Prime graphing calculator app on their iPads.  I knew I wanted to make this lesson interactive working with data they collected that would be interesting to them.  I found a PowerPoint that had 20 pictures of celebrities and students were supposed to guess their ages.  The students loved seeing pictures of Justin Bieber, Kim Kardashian, Nick Jonas, etc. and guessing their ages.  It definitely grabbed their interest!  I was feeling really confident about this lesson.  I then gave students the actual ages of the celebrities.  Students now had two rows of data and it was time to have some fun with the HP Prime.

Mistake #1:  I had thought that the HP Prime app was automatically downloaded on all freshmen iPads but I never checked with the students prior to class if this actually was the case.  Some students had it but many did not.  I thought this was easily fixed, the app was free, the students could just download it.  For the majority of students this worked but there were 3 students that were unable to download any apps. They unfortunately had to just watch on with a partner.

Mistake #2:  The HP Prime calculator is very different from the TI-84 calculator and there is a learning curve.  I had budgeted some time to play around with the basic functions of the calculator before we started the activity.  I was thinking of the first time I used the HP Prime at a conference last summer and how I was intimidated to push buttons randomly so I waited for the instructor to walk me through step by step initially.  What I didn’t anticipate was students feeling much more comfortable with new technology and have them start pushing all the buttons and not paying much attention to my tutorial.  This resulted in many students asking me how to do the same things over and over.

Mistake #3:  Once I got everyone back on track and stressed the importance of staying with me while we entered data we started creating our scatter plot.  Students did great entering their two columns of data but as soon as I showed them how to graph the points they immediately got excited about the touch screen of the graph and started going off in a bunch of different directions.  This resulted in a similar replay of mistake #2.  It was fine at first that they were playing around with zooming in on their window but when it became time to sketch a graph with their finger many instinctively hit OK which then saved their line – even if it was a line they didn’t feel represented their data well.  Rather than ask for help they continued to draw multiple lines which I had to walk around and delete.

While we did finish the lesson and I think I demonstrated to my students that the HP Prime calculator is superior to the TI-84, the lesson did not go at all how I envisioned or wanted.  In hindsight I think it might have worked out better if I gave students written step-by-step instructions for how to enter the data and do the functions working in their groups.  I then could have circulated around the room to see how things were going and troubleshoot if needed.  The girls are way more comfortable with technology than I gave them credit for and I think they could have figured out what I wanted them to do working together.  We then could have had a class discussion on the different lines of fit each student created and discussed the similarities of them.  Overall I would do things differently but I am glad that we approached scatter plots this way rather than just completing problems in the textbook in a more traditional sense.

Designing a Probability Game

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My Probability & Statistics students have been studying probability.  I wanted to plan a lesson that would help them review what we’ve learned this chapter but that would also let them be creative.  I asked them to work in groups of 3 to design a probability game of their choice.  The only parameters I gave them was that it must include at least 3 probability events (for example you couldn’t just roll a die once and have the game be over) and they need to have clearly written instructions for how to play the game.  I provided students with dice, spinners, or pawns if they wanted to use them in their games.

At first many students were frustrated to have such open ended instructions.  When students asked for help I would ask them some questions about games they enjoy playing to get them thinking about different possibilities.  Students had two class periods to create their game.  On the third day they set up their game and instructions and students walked around playing all of the games.


I was amazed at what my students came up with for this lesson!  Some students reimagined classic board games while others created their own game all on their own.  Mathland was similar to Candyland. 

We had a game modeled after Guess Who? but the pictures were all students in our class.

As students were playing the games they were commenting on how some games were very complex while others were much simpler but still a lot of fun to play.

 
Groups were required to turn in a write up of their game which included instructions for how to play the game as well as calculating the probability for winning the game.  Students were also required to write an individual reflection on this project.  Here are some of their comments:


“Projects that require creativity and give me the freedom to create something of my choice are very interesting for me. This project allowed me to see probability in the real world while also allowing me to be creative and have fun.”  

“I have not done a group project in math before and I enjoyed this project because it allowed me the opportunity to listen to other people’s opinions and take into consideration different ways of assembling things.  This was a fun hands on approach to practicing probability.”


“After completing this project, I am able to understand the concept or probability more clearly with the different methods of determining it.”


“This project provided a great opportunity for us to apply the information we learned about probability towards building a game.  I really enjoyed all aspects of this project.  I never really thought we would have the opportunity to be this creative in math class.  It was fun to create a probability based game, and it was very interesting to be tasked with finding the details of the math behind winning the game.”  


We had a few minutes after students played the games to discuss their take aways from this assignment.  Many students said they enjoyed seeing how math can be creative (one of my goals of this project!) and liked thinking about probability in a different way.  The class made the connection between what we are learning in an abstract way and how probability is applied in many situations.  They also said they never realized how probability is used in designing games.  Some students also said that after playing a game once and not doing well, they began to think about the probability behind each move and played it again taking this into consideration and did much better.  I loved that!  I hope through this project my students will see the connection of math, and more specifically probability, in their every day lives and that they continue to see that math is open ended and creative.