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6th Grade Math - Rates - Lipman School

Clip 8/11: Post Lesson - Part 1


Lesson study teams reflect on student learning, and Condon shares lesson observations. "I am struck by the level of participation and confidence of students. This is a heterogeneous group. Our school doesn't track." Teachers and coaches discuss several specific observations of students from their notes. They are probing student language and understanding around use of labels. Linda Fisher observes that some students only paid attention to one measure, number of seconds. They weren't paying attention to the relationship seconds to beans. Colleague Becca Sherman observes that sometimes students used 1 bean per period of time, but most used beans per second. She refers back to POM posters, where one group uses seconds per bean, another group uses beans per second, and a third group uses both units. All groups were able to make the correct conclusion.

They then discuss how students are comfortable with mental math and how working with that process throughout the year has contributed to the flexible thinking of students. Condon describes how for each number talk, 5 or 6 methods are shown on the board. Then students copy down a strategy they didn't use in their math journals.

Teacher Commentary

COACH LINDA FISHER: I am thinking about what it means to be fluent in the language of rate and use language to describe a relationship: “the ratio of wings to beaks in the bird house was 2:1, because for every 2 wings there was 1 beak.”(from CCSSM) As I have watched the unit unfold from the Rate Palooza, where students couldn’t even think of any common rates, to now, I see how highly complex this idea is. Students need multiple experiences with rates and opportunities to use mathematical language to describe their ideas or thinking, to help them communicate their ideas to others. In many cases students talked about “something” in an amount of time, sometimes a rate is “the number of something” to “the number of something else,” or often the term used is a measure per some other measure. So the language varies with the situation. How do students connect these to the same mathematical ideas?

Our original goal was to get students to understand that if the numerators were the same, we could compare the denominators or if the denominators were the same, then we could compare the numerators. But Becca observed that different groups chose different measures for the numerator. I was surprised that maybe if the complex unit was really understood then students could compare if one term was beans per second and the other was second per some amount of beans.

I enjoyed getting a glimpse of how the classroom culture developed over time, to have students who were so confident and able to discuss their ideas and be comfortable with a variety of strategies.