On Friday, I gave my 7th graders a quiz on two topics related to probability. In the first set of problems, I gave them a table with the unequal probabilities for some outcomes and students had to determine the probability of certain events: one which was just one of the outcomes and one which was two or more of the outcomes (requiring the students to add the probabilities). Most students got this section correct, but a few thought they were supposed to multiply the probabilities instead of add.

The place that concerned me more, however, was in the second section of the quiz. I gave a scenario that was a two-step chance experiment: drawing two marbles from a bag with replacement. In the bag, there are two, four and six of each color marble (red, yellow, and blue). Students had to draw a tree diagram and label it with the probability of each outcome, and then list the 9 possible outcomes (preferably with the 9 different probabilities, which they could find by multiplying along each branch of the tree diagram). They had to find some probabilities based on the tree diagram which required them to add some of those probabilities.

Many of the students got confused in this section and used the probability of 1/9 for each of the possible outcomes instead of the actual ones, like 1/36 or 1/12, based on the probability of the two marbles individually. A few kids tried to add the probabilities instead of multiplying.

I have to confess: it’s been years since I took a statistics and probability course, and honestly, other than a HORRIBLE one in grad school, I don’t think I took any courses past HS that included probability. I’ve been keeping up on the material by teaching myself a few days in advance, and then implementing the Engage NY lessons modified by my department head (and tweaking them for my own classes).

In the past, I might’ve interpreted the results of my exam as meaning that “I did a good job with some of my students and that some of these kids just didn’t want to study or put in the effort” – but now I recognize that the kids who did well on this probably already were familiar with this to some extent, and that many of the kids who did poorly had questions they weren’t asking in class – which concerns me. I also recognize that in retrospect, I probably should’ve given an exit ticket that I collected before giving a graded quiz.

Now I need to give back the quiz to the students and figure out a way to reteach the material to the students who didn’t get it the first time, but do an extension for the kids who did get it – OR do an activity where I have the students who got 100% help teach the kids who were struggling? I’m not sure exactly how I want to handle it. Nor do I know what a good activity would be! Guess I’ve gotta do some research for this week. Any advice?