In this lesson, students partition segments in given ratios. They begin by connecting prior work with midpoints to partitioning in a ratio and are introduced to a new notation for finding an average between two endpoints. Next, students are introduced to a weighted average and partition segments into other ratios. As students attempt to partition segments using multiple methods, they are making sense of problems involving weighted averages in the coordinate plane (MP1). Finally, students link segment partitioning and weighted averages to concepts of similarity transformations from earlier units.
Learning Goals
Calculate the coordinates of a point on a line segment that partitions the segment in a given ratio.
Student-Facing Goal
Let’s split segments using averages and ratios.
Student-Facing Targets
I can calculate the coordinates of a point on a line segment that partitions the segment in a given ratio.
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).