Lesson 10Different Options for Solving One Equation
Learning Goal
Let’s think about which way is easier when we solve equations with parentheses.
Learning Targets
For an equation like
, I can solve it in two different ways: by first dividing each side by 3, or by first rewriting using the distributive property. For equations with more than one way to solve, I can choose the easier way depending on the numbers in the equation.
Warm Up: Algebra Talk: Solve Each Equation
Problem 1
Activity 1: Analyzing Solution Methods
Problem 1
Three students each attempted to solve the equation
Noah’s method:
Elena’s method:
Andre’s method:
Activity 2: Solution Pathways
Problem 1
For each equation, try to solve the equation using each method (dividing each side first, or applying the distributive property first). Some equations are easier to solve by one method than the other. When that is the case, stop doing the harder method and write down the reason you stopped.
Lesson Summary
Equations can be solved in many ways. In this lesson, we focused on equations with a specific structure, and two specific ways to solve them.
Suppose we are trying to solve the equation
divide each side by
apply the distributive property
In order to decide which approach is better, we can look at the numbers and think about which would be easier to compute. We notice that
Sometimes the calculations are simpler if we first use the distributive property. Let’s look at the equation