My 7th grade class is always somewhat of a challenge to me because I never know exactly what will motivate them and more importantly, keep their attention. So far throughout this year I have stumbled upon lots of random activities that they like for no apparent reason. There have also been times when I plan and plan and plan for an activity I think they will like and it is a total flop. Needless to say, they are about as unpredictable as any other 7th grader I know.
This week, with the semester wrapping up and Christmas break so close at hand, I decided to slowly introduce concepts we will learn next chapter by doing a hands-on activity with estimation and ratios. I found this activity in one of my NCTM math books (Navigating through Mathematical Connections in Grades 6-8) and I really like the idea of this one. Basically you get a large bag or bowl of some small, countable object; I found some small beans at the grocery store to use. Then you use a method called "capture-recapture" to estimate the number of beans in the bowl.
You first take out a small handful and make a mark on each bean and count them. You put the colored beans back and proceed to take another handful and count both the total number of beans you grabbed and the number of those that have your mark on them. You repeat this seven or eight times and average your results at the end. Finally, you can figure out how many beans are in the bag by using the ratio of total beans you pulled out each time compared to the number of those that were marked which should be a similar ratio to the total number of beans in the bag compared to the total number you marked in the beginning. Environmental scientists use this method often to guess how many fish are in a pond for example.
What I liked about this idea in theory was that the 7th graders would be working with their hands and working in small groups- both things that I thought the boys would excel at. For these very reasons, I split my class up into two groups, four girls in one group and the four boys in the other. Never again will I make this mistake. The differences between boys and girls in the 7th grade is so astronomical and I keep forgetting this; my girls had finished with the entire activity by the end of the hour while the boys hadn't even finished with their first handful after marking their first batch of beans. Needless to say, I also learned a lot during this activity...I learned that girls are better bean counters :)
Overall, I liked the activity, but I think I would structure it a little differently next time and perhaps even try it with older grades.
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