Students will be able to relate the concepts of center of mass and balance.

Students balance masses in 1 and 2 dimensions to see how the center of mass changes.

During the previous lesson students solved problems that required them to apply the concept of center of mass, so our goal today is to expand that knowledge in a lab activity (SP3, SP4, SP5, & SP8). Specifically, students determine the center of mass for a 1-dimensional and 2-dimensional system (HS-PS2-1). I start the class with a 1-minute essay introduction, then we move into the lab activity, before doing a hand signal closure.

This lab uses the following materials: binder clips, various masses, meter sticks, string, ring stands, and cardboard trays. Prior to students arriving, I have a complete set of these materials at each lab station around the room.

5 minutes

To start class today, students come into the room and take out a blank sheet of notebook paper. On the board I've written "**How is calculating the center of mass for a 1-d system different than calculating it for a 2-d system?**"

This is a one minute essay strategy, where students get only 1 minute to answer the question and must work individually. The goal is to get students thinking about what they already know before they even start the center of mass lab. I do actually use a stopwatch, but because some of my students need a little time to process, I usually give them about 90 seconds.

After their time is complete, I ask for volunteers to share an essay. I try to only be a facilitator during this process and let students consider the responses of their peers. For example, if a student makes an assumption that is not valid, I let another student speak up and question the invalid statement. I also encourage students to write down any valid ideas that they had forgotten to include.

The goal of this strategy was to remind students that center of mass is not only useful in 1-dimensional situations, but can be applied to 2-dimensional systems as well. Once these concepts are shared in an essay, I emphasize their importance and move into the lab time. Students are able to keep their mini-essays as a reference throughout the lab time.

40 minutes

Students get to choose their partners for this lab since it may need to be completed outside of class time and I want to make sure they are comfortable contacting the people in their group. I suggest that students work in groups of 3, although I allow students to work in pairs or groups of 4 if they are more comfortable. One person from each group should come forward to get the materials and a copy of the lab. The lab sheet is broken up into 2 sections so that students can identify the differences in calculating the center of mass for 1-dimensional and 2-dimensional situations.

In the first part of the lab, students hang 4 different masses from different locations along their meter sticks in an attempt to balance the meter stick. By using the center of mass equation, the students should be able to determine where the center of mass exists with the 4 masses. Then, students compare this prediction with the actual location of the masses and calculate the percent error. The second part of the lab repeats this process, but students use a cardboard tray at one end of the meter stick. This cardboard tray transforms the system into a 2-dimensional situation and forces students to calculate the center of mass for both x and y coordinates.

Even though the procedure of the lab is straight-forward, I make sure to circulate throughout the room and check-in with each of the groups. I'm offering feedback on their calculations, reminding them to be careful when using the heavier masses, and answering any questions. When there is approximately 10 minutes prior to the end of class (5 minutes left of the time I've allowed for this lab), I ask students to put everything back the way they found it and return to their seats. I also tell them at this point that the lab will be due at the start of the next class period.

This lab sample is a wonderful example of what I hope students are able to accomplish. They have well organized data, neat and thorough calculations, and their percent errors are low. After looking at their lab, I feel confident that they have a clear understanding of center of mass in both 1 and 2 dimensions.

5 minutes

To assess how my students are feeling about applying center of mass in the lab, I ask students to show me hand signals. Before I share the prompt, I show students their 3 options: a thumbs-up for agreement, a thumbs-down for disagreement, and a flat hand for uncertainty.

Once the students are ready, I say "I can apply and explain the concept of center of mass in both a 1-dimensional and 2-dimensional system." I then pause and repeat the prompt before asking students to share their hand signals, so that they have a moment to fully embrace and think about how they are feeling. The atmosphere is mostly quiet during this closure so that students are individually assessing their own level of understanding.

As students show their hand signals, I make a mental note of how many students are showing a flat hand or thumbs-down. Luckily, there was only 1 student who felt this way after the lab, so I went over and spoke with him privately. Because he had been absent recently and was still not feeling well, he was confused and behind on the material covered. We found a time where he could come in for extra help and he was eventually able to apply the center of mass equation to a variety of situations.