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7th & 8th Grade Math - Comparing Linear Functions

Clip 13/14: Faculty Debrief - Part A Comparing Linear Functions


Sally Keyes (math coach), Kamaljit Sangha (7/8 math teacher/department leader), Deb Negrete (principal), and Cecilio Dimas (7/8 math teacher) have a conversation following the lesson to share observations and discuss next steps.

The team made some modifications to the lesson based on the continuous reflection that took place before and after this lesson, such as reiterating the purpose of the tables and connecting them to the prompt, the role of zero, and having students reflect on how they started organizing their own table(s) as a way to activate prior knowledge for this particular lesson.

Based on this lesson, the team found that Student J would provide an opportunity for students to show their thinking and understanding of using tables to depict the three different DVD rental plans and whether the three plans would ever cost the same amount of money on their own. The lesson study team assigned this as homework and processed it in a class discussion.

Teacher Commentary

CECILIO DIMAS, TEACHER: During the lesson Charles articulated his interpretation of the three different plans and the mathematical reasoning of the student work that was presented. It wasn’t until the student interview that I realized that he wasn’t quite sure about one of the student errors, which was contrary to what he had written down. Melanie and Daniel did not speak much on film. However, Melanie did share with the class her understanding of the mathematical sense found in the error made on Online Flix. I was happy to hear the conversation that occurred between Tracy and Tricia. Their voices aren’t often heard. Jocelyn and Charles was an interesting partner pair. She was persistent in clarifying her questions and gaining full understanding, even when Charles was quick to reply. The benefits of participating in a lesson study centered on addressing student misconceptions through the creation of re-engagement lessons have enhanced my lessons and teaching. The level of excitement and interest during our meetings has been energizing. Bringing this enthusiasm into the classroom and continuously sharing it with my students is another one of my goals as a middle school math teacher actively participating in lesson study. SALLY KEYES, MATH COACH: As the math coach, it has been a truly remarkable experience working in a lesson study situation. Determining the mathematical purpose and goal of the re-engagement lesson, selecting student work to specifically address and highlight the mathematical purpose and goal, determining the prompts and questions to ask of students to flesh out and make transparent to all students this mathematical purpose and goal, teaching the lesson, reflecting upon the lesson, and using the observation notes to make changes to improve the lesson with these two teachers who are intently focused upon improving instruction for all students by using data to inform all aspects of instruction has been remarkable. The merits and demerits of each question and sequence has been thoughtfully and thoroughly discussed among the three of us always keeping in mind the purpose and goal of maximizing the mathematical understanding of the lesson for the students. After our math team taught these lessons to all eleven 7th grade math classes (accelerated and regular) we began drafting the next phase of this lesson that was based on the MARS/MAC task Gym. Our lesson study team increased in number by adding the other grades 7 and 8 math teachers in the department to the team. We created a new scenario, going to the Fair/Carnival and compared the cost of regularly priced tickets, a one time cost of a bracelet regardless of the number of tickets used, and a discounted ticket price. In the DVD Plans, our focus had been on verbal and tabular representations. However, the focus of Carnival Ticket Plans began with the verbal and tabular representations leading to graphing the three plans. Analysis of the graphs was the focal point of Carnival Ticket Plans. As a math coach, it was a thrill having the remainder of the upper grade math department join the lesson study team for the next lessons. They have added to our deep discussions, reflections, and focus as well as providing another opportunity to solidify the professional learning community fostered, encouraged, supported and expected by our site principal.

Materials & Artifacts