Fractional Coefficients are no problem

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Objective

SWBAT solve two step equations with fractional coefficients.

Big Idea

Many students feel uneasy when they see fractions in equations. Understanding with fractional coefficients gives them confidence.

Launch

15 minutes

The entrance slip Entrance Ticket Solving with fractions contains three questions to access students prior knowledge and prepare them for solving two-step equations involving fractional coefficients. As students enter the class I hand each one of the slips.

As I walk around, I watch for common errors like cross multiplying when multiplying fractions. This students bring from working with proportions. I make sure students understand why this is done in a proportion equation and have them see the differenct between the latter and just multiplying two fractions. 

I want each student to complete the slip independently, and once everyone is done, call on students to the board. A brief discussion on any error done on the board, or on any doubt any one student has should take place before going on.

Another common mistake is thinking that the reciprocal of a negative number is a positive number, or vice versa. I tell my students that we do not take the opposite of the number when finding its reciprocal. Therefore its sign remains unchanged. Students should answer Question 2 saying that the product of a number and its reciprocal is always equal to 1. A good followup question to ask here is if there is any exception to their conclusion. Zero is the exception. 

New info

20 minutes

The goal that I have in using slides for today's New Info is to help students understand two things: 

  1. Ultimately, the goal when solving a linear equation is to make the coefficient of the variable (x) equal to 1. This does not change when we work with fractions. 
  2. The idea of "doing the same thing to both sides" does not always work and students should know when it does work, and, when it does not. 

As I show the slides I ask volunteers to read the text and to answer the questions. It is very important to discuss each slide as a whole group. When students make mistakes we will address them immediately. When possible, I will ask students to suggest alternatives when we have taken a wrong direction, rather than correcting a mistake myself. 

Application

20 minutes

To prepare for this segment of the class, I have cut out the rows of slips defined by the tables in this document:

Activity Fractional Coefficients

Each 2x2 boxed squares correspond to one pair of students. For example, if Lisa and Troy are a pair, Lisa would get the Q1-A2 slip, and Troy would receive Q2-A1 slip. Lisa solves her question Q1, but her answer is on Troy's slip, A1. Likewise, Troy answers question Q2, and his answer is on Lisa's slip, A2. There are enough slips for 18 students on the worksheet. 

I ask each student to work on their own equation. I say, "Please show all work. Please do not show the answer to your partner." Once finished, students trade slips or simply lay them across the table to assess themselves. I tell students that it is very important that they check each others work and indicate why a mistake was made, if any, and perform corrections. I emphasize the importance of partner-to-partner immediate feedback. I also emphasize the importance of showing all steps in the process. Mentally solving for x is super, I tell them, but performing the steps in the process here is as important. 

The actual assessing of each other's work in this section, closes the lesson. I walk around paying most attention to those students that had any difficulty, listening in on the team's conversation. I also take note of any common difficulties that I could address at our next class. 

 

 

Homework

Tonight's homework (fractional coefficients) is a set of practice problems based on today's work.