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Wenying Chen 9th Grade Educ 784.2 The outline of the presentation Lesson One • Video-Distributive Property • Form-homework Lesson Two • Podcast-giving definitions • Jing-showing the solutions • Word-the vocabulary list • Form-the assessment questions Lesson Three • Blog-the review questions (websites and video are included) Lesson One Aim: How do we simplify algebraic expressions? Do Now: Simplify each expression + 1. = 2. 5 =6 + + +4 +2 -5 3X³Y coefficient term variables Like terms are terms that contain the same variables raised to the same exponent. X and 3X 2X² and 2X 2Y² and -5Y² Are Unlike Terms r³ and t³ 3X²Y and ½X²Y 3rt³ and -0.5rt³ Are Like Terms 6 and 8 Are Like Terms Look at these 10 terms. Find all the like terms that can be combined: Construct a like term that could combine with each of these terms. 7a³b² ¾mn³ 4 Combine Like Terms Example 1 7x² - 4x² = (7-4) x² = 3x² Notice that we can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same. Practice Simplify each expression by combing like terms. A. B. C. D. 12x + 30x = 42x 6.8y² - 1y² = 5.8y² -4n + 11n² -4n and 11n² are not like terms. Do not combine them -20t – 8.5t = -28.5t Simplify the following expression by combining like terms: 6xy + 3x²y + 1xy xy + 6x²y + 10xy + + 17xy + + + 9x²y Distributive Property n n n n n n 11 11 1 1 1 1 11 1 1 3(n+2) 3n + 6 Distributive Property What is the Distributive Property? How to use the Distributive Property in simplifying algebraic expressions? Watch video Distributive Property Basics Example 2 Simplify 2(x+6) + 3x. Procedure Justification 1. 2(x+6)+3x 2. 2(x)+2(6)+3x Distributive Property 3. 2x + 12 + 3x Multiply 4. 2x + 3x + 12 Commutative Property 5. 5x + 12 Combine like terms Try this: 1) 6(x - 4) + 9 2) -12x - 5x + 3a + x Closure Answer the Aim Discuss how the Commutative, Associative, and Distributive Property to simplify expressions. Assign homework Lesson Two Aim: How do we solve equations ? What is an equation? What is a solution of an equation? How do we find the solutions of an equation? Answer An equation is like a balance scale. What are the rules for keeping an equation balanced? What ever you do to One side of the equal Sign must be done to The other side too Use opposite math to isolate the variable on one side of the equal sign Motivation How many are in one ? 2 bags + 4 blocks = 3 bags + 2 blocks - 2 bags -2 bags 4 blocks = 1 bag + 2 blocks - 2 blocks - 2 blocks 2 blocks = 1 bag Check ? = and Since and = = 8 blocks 8 blocks Example 1 Solve 3x – 8 = 7. Check your answer. +8 +8 3x = 15 3 3 x=5 Check 3x – 8 = 7 3(5) – 8 7 15 – 8 7 7 7 Example 2 Solve 4(x – 2) + 2x = 40 4x – 8 + 2x = 40 6x – 8 = 40 +8 +8 Distributive Property combine like terms add 8 on both sides of the equation 6x = 48 6 6 divide 6 on both sides of the equation x=8 Solving Algebraic Equations 1.Use the distributive property to get rid of any parenthesis 2.Combine like terms 3.Move all of the variables to one side of the equal sign (make sure it is positive!) 4.Get the variable by itself by doing opposite math to both sides of the equal sign 5.Check your answer by substituting it into the original equation Practice 1. 2. 3. -4 + 7x = 3 2a + 3 – 8a = 8 9 = 6 – (x + 2) Click here, if you need help. Closure Go over the Vocabulary List Finish the Assessment Questions Sheet Homework: finish Equations WebQuest Lesson Three Aim: How do we solve systems of linear equation in two variables by elimination? Do Now: A farmer has ducks and cows. There are 8 heads and 22 feet. How many ducks and cows does he have? Guess and Check has __ has __ 2 feet ; a 4 feet a The # of Ducks 1 The # of Cows 1 Total # of Heads 2 Total # of Feet 6=1*2+2*2 2 2 4 12 3 3 6 18 4 4 8 24 4 3 7 20 5 3 8 22 Method one: Use one variable to set up an equation. Let x = the amount of ducks, then 8-x = the amount of cows the # of ducks’ feet * the # of ducks + the # of cows’ feet * the # of cows =total # of feet 2 * x + 4 * (8–x) 2x + 32 – 4x = 22 -2x + 32 = 22 -2x = -10 x=5 the amount of cows = 8 – x = 8 – 5 = 3 So, there are 5 ducks and 3 cows. = 22 The Idea of Elimination + 1. 2. +5 6 +4 + +2 - -5 Development Example 1 elimination using addition x – 2y = -19 (1) by elimination 5x + 2y = 1 (2) Step 1 Add (1) and (2) to eliminate the y-terms. 6x = -18 Step 2 Simplify and solve for x. x = -3 Step 3 Write one of the original equations. x – 2y = -19 Step 4 Substitute -3 for x. -3 – 2y = -19 Step 5 Simplify and solve for y -2y = -16 y=8 Solve Development Example 2 elimination using subtraction Solve 3x + 4y = 18 (1) by elimination -2x + 4y = 8 (2) Step 1 Subtract (1) and (2) to eliminate the y-terms. 5x = 10 Step 2 Simplify and solve for x. x=2 Step 3 Write one of the original equations. 3x + 4y = 18 Step 4 Substitute 2 for x. 3(2) + 4y = 18 Step 5 Simplify and solve for y 6 + 4y = 18 4y = 12 y=3 Go Back to the Do Now Let d = the # of ducks and c = the # of cows d + c = 8 (1) 2d + 4c = 22 (2) In some case, we will first need to multiply one or both of the equations by a number so that one variable has opposite coefficients. This will be the new step 1. (1) * 2 2(d+c) = 8*2 2d + 2c = 16 (3) (2) – (3) 2c = 6 c = 3 cows Substitute c=3 into (1) or (2), but (1) would be easier d + c = 8 d + 3 = 8 d = 5 ducks Therefore, the farmer has 3 cows and 5 ducks. Closure Answer the Aim Summarize the elimination method in solving systems of linear equations in two variables. Homework: finish the review sheet