Did Buffon’s Needle with my classes today with 200 pencils. Students thought it was really fun and we got pretty good results! Fun day.
Since it’s Pi day on Friday, I had students measure the diameters and circumferences of several circular objects in our classroom to see exactly what pi is and where it comes from. It’s amazing to see 7th graders, who have used pi for several years to make calculations, know that its decimal approximation is 3.14 but have no idea where that number comes from. The sounds of “ooooh,” after seeing that it’s the ratio of the circumference to diameter of a circle was great. Taking the mystery out of math, one concept at a time.
Inspired a while back by Chris Lusto’s “What’s in a Circle?” blog post, I’ve been saving this question for this week specifically, since it’s Pi day this Friday. So I asked students, “What is a circle?” I had them write a definition on their own, then share with their groups, then pick the “best” definition to share with the class. Finally, I had each group write a set of instructions for drawing a circle, for someone with no idea of what a circle is or the concept of what “round” means. It was great. Tons of struggle and debate over the best way to do this. Then I had groups rotate through the room and follow other groups’ instructions, which produced plenty of odd shaped figures, none of which were circles. It’s always great to see students struggling with ideas that seem very straightforward on the surface, but have much more to offer when you dig in. Great lesson.
We had an extra 15 minutes at the end of my 7th grade classes today, and since they enjoyed this so much last time, I decided to give my students another Canstruction problem from Yummymath. Once again, every student went right to work trying to estimate how many cans were used in the figure. What was REALLY awesome is that one group in each of my two classes that worked on this problem actually got the EXACT number of cans listed on the Yummymath solutions page! They, and the entire class, got so excited and were cheering for them! It was really cool!
LOVED this tweet from Dan Meyer yesterday, so I gave my classes the Day 46 calculator problem from Math Arguments 180 today. It was awesome! Immediate confusion, questioning, and arguing. Some students changed their minds half a dozen times while listening to the reasoning of others, and some even wanted to argue that both calculators were correct. Great discussion! My only regret is that I didn’t “drop the mic, and walk away,” like Dan suggested. Maybe next time.
If you would have been observing me today you wouldn’t have noticed anything unusual, but one of my 8th grade boys, you know, one of my “rambunctious” ones, was totally engaged during our class today and was focused and participating the whole time. He even tried to start working ahead. It’s always great when students display the potential we see in them.
For our number talk today I gave my 8th graders the question from Day 37 of Math Arguments 180, involving 0.9999… being equal to 1. It was great. They had a great argument back and forth and when I told them it was equal to 1 some were up in arms. They refused to accept it (even after I proved it to them) and wanted to find a mathematician and tell him that he was wrong. Some of them got really worked up about it. It was awesome!
We started our Barbie proportions/scale project today. I bought all of the Barbies from a local thrift store and most of them didn’t have any clothes. So, you can imagine the reaction from the middle school boys in my classes. It was pretty entertaining. All of the students were also engaged in the task and working hard. They’re excited to see how it turns out!
We’re starting our geometry unit with the 7th graders with scale. I never mentioned the word “scale” today, but instead gave students a very open ended task: draw an accurate diagram of the classroom. One of my classes spent some time at their desks, looking around and noting things to include in their diagrams. But in another class, every group immediately jumped up, grabbed yard sticks, and started measuring the walls, doors, everything. It was great to see that with no prompting they’re already starting to move toward the idea of scaling down the measurements of the room!
So I felt like the students (and me) just needed a day of some good critical thinking and problem solving. Enter Yummy Math’s “Have a Heart” problem. Such an accessible problem for every student, yet it led to fantastic discussions between students as they attempted to estimate how many cans made up the structure. It ended up being everything I hoped it would be. Really great stuff!!!