Catalog of Lessons by Subject > Math > Collaboration

Catalog of Lessons by Subject > Math > Collaboration 2017-10-06T01:32:49+00:00
View Lessons by Subject > Math > Collaboration
(Algebra 2): My most effective lesson was one in which my students applied their knowledge of matrices and used it for a scavenger hunt. This hunt was graded and they worked in teams. It took them around the school, where they used matrix multiplication, solving systems of equations, and cryptology, to get from one clue to the next. I enlisted the help of several adults in the community, who relayed to me how engaged each member of the group was. The class consisted of sophomores in Algebra 2. The scavenger hunt was in place of a written assessment, however, the groups needed to present the work that they performed for each clue so it was in fact clear that they used their knowledge of matrices to get from one adult to the next. The girls loved working in teams and loved the competitive nature of the hunt (while there was no prize for the group that finished first, they all attempted to finish first). This activity required knowledge of the content, collaborative group work, and a positive outlook to complete this alternative assessment.
In 5th grade, I had an experience in Math class that made me motivated to work extremely hard. We had started a project where we could choose any partner or work alone, and could study anything related to math. My partner and I worked on a project related to skiing, an activity we both enjoy. We are best friends, so we worked well together and could easily tell each other if we didn't like something having to do with the project. First, we estimated how long it would take to go straight down a blue-rated slope. Afterwards, we figured out how much time it would take with turns. Next, we decided to see how long it would take with moguls, which are bumps that you have to avoid. Once all of the math was done, we put each of the steps onto a chart displaying our math. The last step was to put everything into a presentation and present it to the class! During the process, I was interested and excited to find out more every math class.
I had difficulty motivating and engaging my class recently as we studied a method of integration that is called substitution of variables. I began the lecture in my typically rigorous, analytical manner and the students were clearly not with me. They took notes, and appeared to be attentive, but when I asked them if they understood the new technique, there was a resounding "no." So, I placed them in pairs at the board. I suggested that the student on the left of each pair be the first scribe and record what the other student proposed in solving their problem. First, I asked them to summarize what they had learned during my brief, theoretical lecture. Then I posted on the projector various problems to be solved. I moved around the room continually and was able to clearly see their work as they attempted to solve each problem. After the entire class of paired students had completed each problem successfully, then and only then did the girls move as a group to the next problem. The girls switched being the scribe for each new problem. If one pair finished first, and another pair was really struggling, I suggested that that pair assist the pair that could not solve the problem…The time flew by and all of the girls expressed how much fun they were having and how much they had accomplished during that brief 25 minutes at the board. The class was definitely a success and the girls clearly mastered the material.
We have been doing a lot of problem solving in Grade 7 to get them used to problem solving in middle and high school mathematics. Students generally believe that a problem, especially a math problem, has a unique and precise answer, which is often true - but not always. We used Fermi problems not only to review and deepen the concepts of approximation, estimation, order of magnitude, as well as understanding and discussing assumptions, causes of errors and so on, but also to allow the students to develop creative ways of facing an open-ended problem and to realize how much they can do with the knowledge they have or they can easily find. So we started by solving examples of Fermi problems as a group, with the teacher as a leader. Then we solved simple or even very simple Fermi problems as homework, individually. As a second step I organized the girls in groups of four and they worked together to solve some Fermi problems together, discussing assumptions and their final solution, and comparing and discussing their answer with that of other groups. Finally, I created a Fermi problem - which we called "The Million Dollar Give-Away" that had to be solved in three stages. In the first stage, each girl, working with a partner, had to find out how many one-dollar bill would fit in a large suitcase I brought in for the occasion. Each pair therefore had to measure the suitcase, and the one-dollar bill; they also had to find a way to measure the height and the weight of a (or in-fact a stack of 20) one-dollar bill. Each pair had to work through a worksheet together, explaining their assumptions, why these assumptions were reasonable, what was the procedure they were using to solve the problem etc. The second and third stage was to be done at home by each student, and required them to think about what was the source of their major error(s) and to continue answering other questions related to same problem (such as what was the smallest denomination that they would be able to use to bring home $1,000,000 with the given suitcase, how much the full suitcase would weight etc.) The girls enjoyed this project because they thought it was very challenging: for example one remarked that when she asked her dad for help (the to-go-to-person in her family for math), he walked away because he didn't know what to do. They also liked that they had to think of the various possibilities, and that the answers could be right - even if they were different - as long as they themselves had a clear idea of their own assumptions. The girls also liked that they could do different things - get up and measure the suitcase, figure out how to use a scale (and what to use, grams or pounds). They liked the freedom and creativity that the problem allowed them. They also enjoyed that the project involved working with a partner and also working alone. They kept coming to my room with questions, talking about the problem with each other, discussing and comparing with each other outside of class. I think they really liked how different this sort of problems was compared to those they were used to.