## Sample Size and Reliability

Monday was my school’s first day back from break. The students had two weeks off and many students and teachers are still getting back into school mode.  The teacher coffee machine was is still working overtime.  The first day tends to ease students back into the concepts taught back in mid-December. One of the better ways to transition is to debrief with the students about their break. This is also an opportunity for students to make connections and reconnect with their peers.

After debriefing with the students about their break one of my classes delved a bit deeper into a data analysis unit. This class studied different types of graphs back in December. We explored stem-and-leaf plots, bar graphs, pie graphs and even took a look at box plots. One of the objectives of the lesson on Monday was to explore the relationship between sample size and the reliability of the results.

This lesson was actually adapted from a fifth grade Everyday Math lesson. Before class I decided to use different colored unifix cubs to represent candy colors. I’d prefer to use regular candy but we have so many allergies and a wellness policy that nixes the use of candy in the classroom. Anyway, I took 100 unifix cubes and split them up into 50 being chocolate, 30 cherry, 10 lime and 10 orange. I didn’t tell the students how many cubes there were or the color allocation.

Before digging into the manipulatives the class discussed why using sampling was important. Students discovered how sampling is much less time-consuming compared to surveying all people/objects. We then discussed how much of a sample is appropriate. Students were all over the place with their estimates. Throughout the conversation I was attempting to sett the stage for students to make some connections and find clarity on the concept through this activity.

Students were placed in groups of two for this activity. Each partner randomly chose five unifix cubes.

The groups then combined their cubes and documented their total. About 80/100 cubes were taken after all the students documented their total. Each group reported out their findings. Some groups had almost all chocolate while other groups had zero orange or lime. It was interesting to see how the students reacted as other groups reported out their results. It seemed like they wanted to question their own results.  Students were then asked to make a prediction of the actual results based on the sampling.  The class then combined the results of the groups and shared the results.

I brought the students to the back table in the classroom and dumped the cube container. We counted each color to see how accurate our class sample was to the actual result. Students then compared their group results to the class and then to the actual results.

I then gave the students an opportunity to reflect on the comparison as a class. Some groups were very close to the actual percentage while others were way off.  I explained that this is part of the sampling process.   Students were then asked to journal about their experience and the class will explore this topic in more detail later in the week.