This video series looks at how to use students' natural thinking about rates and how these ideas are developed, expanded, and formalized over a period of time by using the Problem of the Month "First Rate." At Joe Condon's middle school, the Problem of the Month is introduced by having students do a series of activities: Rate Palooza, going from room to room to try different experiments with rate. Each math teacher has a set of 1 to 3 experiments. The first video series, at Ida Price Middle School, shows a public lesson, developed by a lesson study team, of how to introduce the idea of rate prior to starting the Problem of the Month. The second video series, at Lipman Middle School, shows a lesson near the end of the work on the Problem of the Month, where students are using the knowledge developed over time and formalizing ways to represent rates.

At Lipman Middle School, Condon asks a series of questions about rate, referring back to one of the experiments in the Rate Palooza. He asks questions to get students to explore ways of writing rates and then develop arguments for comparing and making conclusions about rates. This lesson really highlights the growth in student thinking over time resulting from the use of the Problem of the Month. The series of questions helps show how students write ratios and helps them formalize their ideas by making justifications. During the lesson students also grapple with multiple representations for the same rate.

At Ida Price Middle School, Condon teaches a public lesson from a lesson study on introducing rates. He is using students from another school to show a lesson developed over time with the lesson study group. Several teachers from other middle schools come to observe and take notes on the lesson. This lesson represents the beginning activity before students start working on the Problem of the Month: First Rate. This lesson is developed with the idea of giving students some common experiences with rate and to help them think about the importance of units in describing a rate. Teachers wanted to see what students' natural understanding of rates were before the unit to help them think about the learning needed during the course of the work on rates and what questions would help bring out important ideas that needed to be explored or clarified.

The lesson study group was working on the idea that an instructional unit should have an experiential activity to start a concept. Then students could hook their ideas on the activity as the unit progressed. They wanted students to have a reference: this is like when we did "_____." The lesson study group made some important changes to the original lesson. One significant change was having students record their data in a complete sentence, hoping this would focus students on the importance of units. Students were then asked to record data as a rate. The hope was that writing a sentence would focus them on the words used with the numbers making it easier to then write the compound rate unit. Because of the school schedule for the public lesson, the lesson was shorter than time planned by the lesson study team.

Taught by: Joe Condon, Lipman Middle School, Brisbane School District, Brisbane, California

Mathematical Strand:

- Ratios & Proportional Relationships