Lesson 15
Weighted Averages
Lesson Narrative
In this lesson, students partition segments in given ratios. They begin by calculating midpoints, then attempt more difficult ratios in the subsequent activities. They’re introduced to a weighted average and asked to connect weighted averages to segment partitioning. Finally, they link segment partitioning to concepts of similarity transformations from earlier units. In each case, students are presented with a problem with little direction and expected to make sense of the problem and find a strategy on their own (MP1).
Learning Goals
Teacher Facing
 Calculate the coordinates of a point on a line segment that partitions the segment in a given ratio.
Student Facing
 Let’s split segments using averages and ratios.
Learning Targets
Student Facing
 I can calculate the coordinates of a point on a line segment that partitions the segment in a given ratio.
CCSS Standards
Glossary Entries

opposite
Two numbers are opposites of each other if they are the same distance from 0 on the number line, but on opposite sides.
The opposite of 3 is 3 and the opposite of 5 is 5.

pointslope form
The form of an equation for a line with slope \(m\) through the point \((h,k)\). Pointslope form is usually written as \(yk = m(xh)\). It can also be written as \(y = k + m(xh)\).

reciprocal
If \(p\) is a rational number that is not zero, then the reciprocal of \(p\) is the number \(\frac{1}{p}\).