# 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.

### Student Facing

• I can calculate the coordinates of a point on a line segment that partitions the segment in a given ratio.

Building On

### 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.

• point-slope form

The form of an equation for a line with slope $$m$$ through the point $$(h,k)$$. Point-slope form is usually written as $$y-k = m(x-h)$$. It can also be written as $$y = k + m(x-h)$$.

• reciprocal

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