As evidence of their practice, teachers submit a written commentary, videotape, and optional instructional artifacts that demonstrate how they are able to engage students in mathematical discourse as the whole class investigates, explores, or discovers important mathematical concepts, procedures, or reasoning processes. The teachers will also demonstrate how they create a stimulating and inclusive environment that promotes student development of mathematical power. Students shared, tested and revised their conjectures on the second day, and then extended their thinking to determine how to find the vertex based on the equation. Students know that the roots of the quadratic equation are the x-intercepts of the quadratic function. Students understand the relationship among the coefficients, factors, roots, intercepts, the vertex of a quadratic function, and the direction its graph opens.
Students apply the concept of symmetry when graphing quadratic functions.
This lesson comes near the end of the quadratics unit. Earlier in the unit, students had modeled contextual problems using quadratic tables, graphs and equations. They had then practiced techniques to expand and factor quadratic expressions. At this point in the unit I decided to adapt a lesson from a Connected Math unit called Frogs, Fleas and Painted Cubes in order to allow my students to see how all of their earlier work in this unit connected together. This lesson attempts to link together the four learning goals listed on page two in order to engage students in the process of making connections between graphs, equations and factoring.