The document provides examples of working with literal equations, which are formulas written as equations. It shows how to transform a formula by solving it for a different variable. For example, rewriting the volume formula V=lwh to solve for width by isolating w on one side. Students are assigned a project to research two formulas, write them, describe the variables, show a real-life application by substituting values, and present their findings.

1. Do Now October 26 Simplify 16 + 3x - 9x - (x + 8) 16 + 3x - 9x - x - 8 16 -7x - 8 8 - 7x Solve the equation 2/3 x + 7 = 1/6 x - 7 6(2/3 x + 7) = 6(1/6 x - 7) 4x + 42 = x - 42 -x -x 3x + 42 = -42 -42 -42 3x = -84 x = -28 2/3(-28) + 7 = 1/6(-28) - 7 -18 2/3 + 7 = -4 2/3 - 7 -11 2/3 = -11 2/3

2. Literal Equations Sometimes formulas and equations can be transformed to be more user friendly. Example: the formula for Volume of a rectangular prism is V = lwh; V = volume, l = length, w = width and h = height Let's say the volume = 308 cm 3 , length = 4 and width =11 I could solve the equation for the width by substituting the values into our formula.

3. Let's say the volume = 308 cm 3 , the length = 4 and the height =11 I could solve the equation for the width V = lwh 308 = 4*w*11 308 = 44w 7 = w An alternate way is to transform the formula first so that the unknown variable is alone. V = lwh (treat the w and h like coefficients) V = w (divide both sides by l * w) lh lh V = w lh No w I use the transformed equation. V = w lh 308 = w 4*11 308 = w 44 7 = w The width is 7 cm.

5. These are also called literal equations. We transform an equation with all variables, solving for one of the variables using the rules for equation solving. Example: Solve rd - s = x for d rd - s + s = x + s (add s to both sides) rd = x + s (simplify) rd = x + s (divide both sides by r ) r r d = x + s (simplify) r

6. 7 th Grade Algebra1 Mini-Project - Collecting Formulas Due Date: ________________: A formula is a literal equation that states a relationship between two or more quantities. For this project, find two interesting formulas. Do the following for each formula. c Write the formula as it is generally found. IF possible, write it a second time, solving for a different variable. c Describe what the symbols represent and their units of measure c Describe what the formula is used for (see examples below, you may not use these formulas in your project). You may not know exactly how to manipulate the numbers or symbols, but you should be aware of the formula’s applications. c Show the real life problem that this formula would solve and demonstrate by substituting values and finding the solution (use correct units of measurement and a correct solution). c Final Project Options: (All options should show all the information described above, as well as an illustration of your formula’s application.) o Display the formulas on a small (11 x 17) poster. o Create a powerpoint. o Create a website (wordpress.com) o Other ideas - check with me first

7. Examples: From Baseball: To determine a Pitcher’s Earned Run Average (ERA), the formula is ERA = ER*9 IP Where ER represents the number of earned runs that the pitcher allows during a given time, and IP represents the number of innings pitched in that time. Curt Schilling pitched 226.2 innings and allowed 82 earned runs. Curt’s 2004 ERA is calculated as follows: ERA = 82*9 226.2 = 3.26 ERA

8. F rom Aviation: To determine the ability of a hang glider to glide and soar, you need to find its aspect ratio (R), the formula is: R = s 2 A Where A = area of the wing, and s is the length of the wingspan. If a hang glider has a wing area of 36 square feet, and a wingspan of 10 feet, find it’s aspect ratio. R = 10 2 = 2.78 aspect ratio 36

9. Grading Rubric Totals 25 points maximum 5-4-3-2-1 over all Neatness & effort 1 per formula Relevant Illustration 3 per formula Real life applicationSubstitute realistic values & solve correctly 3 per formula Purpose of formula, What is it used for? 2 per formula Description of symbols and units of measure 1 per formula Correctly written formula Formula 2 Formula 1 Max Points Requirement

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