# Solving Problems Involving Proportions

Student View (Opens in new window) # Lesson Overview

Students solve problems using equations of the form x + p = q and px = q, as well as problems involving proportions.

# Key Concepts

Students will extend what they know about writing expressions to writing equations. An equation is a statement that two expressions are equivalent. Students will write two equivalent expressions that represent the same quantity. One expression will be numerical and the other expression will contain a variable.

It is important that when students write the equation, they define the variable precisely. For example, n represents the number of minutes Aiko ran, or x represents the number of boxes on the shelf.

Students will then solve the equations and thereby solve the problems.

Students will solve proportion problems by solving equations. This makes sense because a proportion such as $\frac{x}{a}=\frac{b}{c}$ is really just an equation of the form xp = q where $p=\frac{1}{a}$ and $q=\frac{b}{c}\text{.}$

Students will also compare their algebraic solutions to an arithmetic solution for the problem. They will see, for example, that a problem that might be solved arithmetically by subtracting 5 from 78 can also be solved algebraically by solving x + 5 = 78, where 5 is subtracted from both sides—a parallel solution to subtracting 5 from 78.

# Goals and Learning Objectives

• Use equations of the form x + p = q and xp = q to solve problems.
• Solve proportion problems using equations.

ELL: ELLs may have difficulty verbalizing their reasoning, particularly because word problems are highly language dependent. Accommodate ELLs by providing extra time for them to process the information. Note that this problem is a good opportunity for ELLs to develop their literacy skills since it incorporates reading, writing, listening, and speaking skills. Encourage students to challenge each others' ideas and justify their thinking using academic and specialized mathematical language.