Chap 2, Sec 5, Part C

Solving Literal Equations and Formulas GOAL: I can solve for variables that have exponents (squared variables). Text reference: Chapter 2, section 5, pages: 109 ─ 114  Illinois learning standard: 8.C.3  NCTM standard: XX─XX Lesson Vocabulary    Literal Equation  A literal equation is an equation that has two or more variables in it.  Some examples include: y² = 9x + 4 4x² ─ 25y = 100 2x² = 98x² ─ 16  Formula  Formulas are special types of literal equations.  A formula is an equation that gives the relationship between the variables.  Some examples include: P = 2•L + 2•W A = L • W C = 2 π r Strategies and Content Practice  Notes  Begin (prepare)  Exponents Exponent variables present their own set of challenges when solving algebra problems.  In this section the focus is on solving for variables that are raised to the second power (squared variables).  The concepts taught in this lesson for squared variables apply to higher power exponents like third power variables (cubed variables), forth power variables, etc.  The following are some examples of exponent variable problems: In the first example, the X is all alone by itself on the left side of the equal sign, so all that needs to be done to solve for X is to "unsquare", that is, to take the square root of both sides of the equation. In the second example, Y has a coefficient in front of it.  Before the square root can be taken of both sides of the equation, the coefficient need to be removed. In the third example, Z is being divided by a coefficient.  Before the square root can be taken of both sides of the equation, the coefficient need to be removed. Yet again, a Super-Hero algebra tools are used to get the variables X, Y, and Z all alone on one side of the equal sign.   Engage The Super-Hero tool needed to solve for variables with exponents is the square root. The example problems above can be solved by first getting the target variable all alone on one side of the equation.  The next step is to then take the square root of both sides of the equation to get the target variable in its lowest term.  For example, here is how the first problem is solved: The following is how we would solve the last example problem.   Assess (formative)   Give students selected problems from the practice worksheets below. Circulate to check for understanding. Select students to work their problems at the board and have them explain their answers.   Apply  Practice Assignments. Worksheet 2-5, Version E. Worksheet 2-5, Version F. Assess (formative)  Answers to the Practice Assignments. Answers to Worksheet 2-5, Version E. Answers to Worksheet 2-5, Version F.