Lesson 2: 2-7 Literal Equations
Duration of Days: 4
Lesson Objective
Solve equations for given variables.
Use formulas to solve real-world problems.
How can you solve a literal equation or formula for a specific variable?
Why might you want to convert units?
When using dimensional analysis, which unit goes in the numerator and which unit goes in the denominator?
literal equation
dimensional analysis
N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
3A Functions
3B Functions
3C Functions
Some equations contain more than one variable. Solve these equations for one variable in terms of the other variable(s). A formula or equation with multiple variables is called a literal equation. Many formulas require using dimensional analysis.
The average weight of the chimpanzees at a zoo is 52 kilograms. If 1 gram ˜ 0.0353 ounce, use dimensional analysis to find the average weight of the chimpanzees in pounds. (Hint: 1 lb = 16 oz)
Encourage students to write units for values they are substituting into an equation. Writing the units will help them to determine the reasonableness of an answer. If the problem asks for "miles" and they have "hours," they will know something is wrong.
Error Analysis: For Exercise 37, suggest that students work backward from the equation solution. In doing so, they should discover that the only difference in the solutions is the negative sign for 5 and that Fernando overlooked it when solving for b. Tell students this is a common error they should check for when solving equations.
If students are confused by equations with more than one variable and with variables on both sides of the equation, such as Example 2,
Then have students work in pairs to analyze, discuss, and write out the steps necessary for solving the equation. They can then refer to and mark off the steps as they work through the solution.
Practice: Exercise 1 - 7
Exercises 41 - 49
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