# Solving Equations with Fractions

## Objective

SWBAT solve two step equations with fraction constants and fraction solutions.

#### Big Idea

Students create a foldable study aid and solve equations that contain fractions as constants and/or coefficients.

## Do Now

15 minutes

(5 mins) Students enter silently according to the Daily Entrance Routine. There are Do Now assignments at their desks. This worksheet includes addition and subtraction problems with rational numbers. Students will use the problems in the Do Now for a foldable study aid at the end of this section of class.

(6 – 7 mins) We review the correct answers for each problem as I justify the process for calculating the answers. For example, for problem #1 I may explain that I am “combining two negative rational numbers. This means my answer will be negative and I must add the absolute values of the numbers”. This is the type of language and vocabulary I expect students to use when justifying the process for calculating these answers. Each problem is used as an example for the rules of adding and subtracting rational numbers. These examples will be written under the appropriate section of the foldable.

## Create Study Tool

10 minutes

(10 – 12 mins) Once we have reviewed the answers I give students the template for the foldable study aid. I explain to students that this tool will remind them about the rules when adding and subtracting rational numbers. They are to use this tool during the task today. Students must take each of the problems in the do now and write them into the appropriate section for the rule followed when solving for the answer. There are two examples per rule. Students must fold the paper in half, lengthwise, and cut along the solid line in the center to create two different sections (one for addition and one for subtraction). If students finish these basic steps with time left, they may decorate the outside of their foldable.

## Class Notes

10 minutes

Students are asked to copy the aim which is written on the white board at the front of the class (KWBAT solve two step equations with fraction coefficients, constants and/or fraction solutions. ), as well as the definition of equation written on the black board. It’s important for students to understand that an equation is made up of two expressions separated by an equal sign. Many students are struggling to understand this concept which affects their ability to correctly isolate the variable terms as well as their ability to correctly complete check steps.

For example, in an equation such as 3x + 3/2 = 9 students often divide the variable term by 3 to isolate the variable and divide the constant on the right side of the equation by three. If the student does not also divide the improper fraction 3/2 by 3, they are making a mathematical error in solving the equation. Understanding that both sides of the equation are equivalent quantities allows me to explain these types of errors to students. I have attached a sample of the work used to illustrate this error.

I use the class notes’ examples to show students how to use their study aid to solve the equations. For example, 5/6 – m = –11/12, I ask student to identify the variable terms. This is the term we want to isolate first. Since a positive 5/6 makes up the expression, we must first cancel out +5/6 with –5/6 on both sides. This results in the expression

–11/12 – 5/6

on the opposite side. We will follow the rule “when subtracting from a negative, the answer will remain negative and you must add the absolute values”. In order to add 11/12 and 5/6 we must write an equivalent fraction for 5/6 with a common denominator of 12:

– m = –11/12 – 5/6

– m  = –11/12 – 10/12

– m  = – [ 11/12 + 10/12 ]

– m  = – [ 21/12 ]

– m  = – 1 9/12 = – 1 ¾

The last step is to isolate the variable:

– m  = – 1 ¾

(divide by –1 on both sides)

m  = 1 ¾