Unit 6, Lesson 10
Different Options for Solving One Equation
Grade 7
10.1
Warm-up
Solve each equation mentally.
10.2
Activity
Three students each attempted to solve the equation , but they got different solutions. Here is their work. Do you agree with any of their methods? Explain or show your reasoning.
Noah’s method:
Elena’s method:
Andre’s method:
10.3
Activity
- Solve each of these equations twice, one time using each method.
-
applying the distributive property first:
dividing each side first:
-
applying the distributive property first:
dividing each side first:
-
-
Solve each of these equations once. Choose whichever method you think will be easier for that equation.
-
Student 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 . Two useful approaches are:
- 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 will be hard, because 27 isn't divisible by 5. So, distributing the is not the best method. But gives us , and 16 is divisible by 4. So, dividing each side by is a good choice.
Sometimes the calculations are simpler if we first use the distributive property. Let's look at the equation . If we first divide each side by 100, we get or 0.21 on the right side of the equation. But if we use the distributive property first, we get an equation that only contains whole numbers.
None