To solve equations with variables on both sides, one can use the properties of equality and inverse operations to write a series of simpler equivalents equations.
Direct Instruction.Quickly review solving multi-step linear equations and show relationship between these and those with variables on both sides of the equation.NEW vocabulary (identity) needs to be introduced, and previously taught vocabulary for the chapter needs to be reviewed.
Guided Practice: Examine Problem 1, page 102 of the textbook.Work through this example by illustrating the solution of an equation with variables on both sides.Review the concept of bringing all variables to one side and all single, numbers to the opposite side. Also review when the change of sign when ANYTHING crosses the equal (=) sign.Teacher can use the Got It examples on page 103 as an example.Walk through Problem 2 with the students on the APPLICATION of equations with variables on both sides, then allow students time to attempt Got It, Problem 2.Continue working through examples, Problems 3 and 4.
Independent Practice: page 105, have students attempt “Lesson Check” (1-5). Examine problems #10-44 (even). Determine which 15-20 problems may be taken for a grade.
When working with literal equations, one can use the methods previously learned in this chapter to isolate any particular variable.
Direct Instruction: Explain to the students that Literal equations are any equations that involved multiple variables, and are always solved for one variable.Such an equation shows the relationship between multiple variables and allows us to rearrange these equations to solve for just one variable.
Introducing the Lesson:Give some common, useful examples of Literal Equations to the students. For example, F=ma, PV=nRT, y=mx + b.Illustrate the importance of these type equations and show how one might rearrange these to solve for the different variables.
Guided Practice:For practice, have students examine page 112 (#12-18 even)
Independent Practice:Page 112, (# 11-27)
REVIEW Literal Equations!
Page 112 (# 20-26, 28, 30, 36).
1. Independent Practice: Review concepts for literal equations. Spend time working on solving Open-Ended questions in preparation for Core Testing. Walk through rewriting verbal expressions into algebraic expressions and rearranging the questions to solve for particular variables. Page 113 #33, 35, 36, 38, 30, 45, and 47 and 48.
A ratio compares two numbers by division. The ration of two numbers a and b, where b cannot equal (undefined, no solution). One may think of a ratio as a multiplicative relationship. For example, if the ration of the number of boys to the number of girls in a class is 2:1, then the number of boys is two times the number of girls.
A ration that compares quantities measured in different units is called a rate. A rate with a denominator of 1 unite is a unit rate. One can write ratios and find unit rates to compare quantities. One may also convert units and rates to solve problems.
Guided Practice: Comparing Unit Rates (Problem 1) and Got It, page 117.Have students learn new vocabulary: ratio, rate, unit rate, conversion factor, and unit analysis.Solve problems #23 and 24 together.
Independent Practice: Page 119 (11-16), page 120, #36.
Allow students remaining 30 minutes of class to take assessment to cover sections 2.3-2.5.