This lesson is about extending the concept of solving equations in one variable to solving a formula for any one particular variable. My experience is that many students have problems solving formulas despite being able to solve equations. Some of the techniques students use to solve equations cannot be used to rewrite formulas. Tables, for example, don't help in finding solutions, and graphs aren't always possible. Therefore, I make sure I expose my students to many different types of formulas. We also review the properties of equality, to help students make the necessary associations.
To launch this lesson, I project the Launch Questions for Solving Formulas. I give students a couple of minutes for each question. I have chosen the questions based on the experiences I've had with student errors in prior years of teaching students to work with formulas:
Question 1: Many times students, especially ELL students, confuse what it means when an equation or formula is solved for a specific variable. As we discuss this question I make sure that students are aware that the isolated variable can be on either side of the equation.
Questions 2-5: A quick review of the equality properties is a very good way to begin the lesson. Students should observe that the multiplication property of equality was used incorrectly. Also, there is an incorrect use of the addition property of equality: "3" had to be subtracted from both sides first.
Analysis of common errors helps students to avoid making them when solving formulas. To end the Launch section, I ask students to answer each question and write the correct process on the board.
The New Info section today is conducted as guided practice using the Application Solving Formulas.doc worksheet. I use the classic Fahrenheit/Celsius conversion in the first guided example to motivate the idea of equivalent formulas. What I want students to understand is that when we have equivalent formulas, the pairs of numbers (input-output) that work for one formula must also work for the other.
I inform students that some people call the Celsius scale Centrigrade, because of its 100 degree interval. I like to tell students that very few countries in the world use the Fahrenheit scale. I remind students that the freezing and boiling points of water are 0 and 100 Celsius, and 32 and 212 Fahrenheit respectively.
Formulas used in the Practice Problems
When my students get to Question 5, they often make a mistake that they don't make with Question 1. The mistake is when solving for p in B = h/p, the student may multiply both sides of the equation by h instead of by p. If this happens, the student has obviously memorized a pattern without comprehension. I "go back to the drawing board" with these students, giving them fractions to multiply by whole numbers and help them see when and why denominators cancel.
To close today's lesson I re-organize the class choosing different pairs of students to work together. I ask each student to take out a blank sheet of paper and write an equation containing at least two variables and identify the variable for which they should solve. On the back of the paper, I ask students to solve their equations for that variable.
After they solve it, I ask that they exchange papers with their partners and solve their partner's equation. (I walk around and make sure that the students are following directions) When everyone is done, students should then turn their papers over and compare their work to their partner's work. Their solutions should match and if they don't, they should discuss why not and find a solution that both agree with.