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DO NOW Friday, November 1, 2013

DO NOW Friday, November 1, 2013 Please have Planners open with Homework and Signed Progress Report on your desk. Learning Objective. November 1, 2013. 1. We will solve equations with squared variables involving fractions. 2. We will estimate radicals that are not perfect squares.

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DO NOW Friday, November 1, 2013

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  1. DO NOW Friday, November 1, 2013 Please have Planners open with Homework and Signed Progress Report on your desk.

  2. Learning Objective November 1, 2013 1. We will solve equations with squared variables involving fractions. 2. We will estimate radicals that are not perfect squares. What are we going to do? CFU Activate Prior Knowledge • An exponential expression represents repeated multiplication. • Bases raised to an exponent of 2 are squared. Evaluate the square root expressions. 1. 92 2. 102 Exponential Expression 9 or -9 10 or -10 Students, you already know how to evaluate squared expressions. Now, we will use squared expressions solve equations with squared variables. Make Connection PERFECT SQUARES 3. 4. 25 81 49 64 5 9 7 8 or - or - 5 9 7 8

  3. Concept Development • A square rootis a number that is multiplied by itself to form a product. • Taking the square root(√ )is used to isolate1 the variable in equations with squared variables. • An equation with squared variables can have two solutions, one positive and one negative. CFU How many solutions will each of the following equations have? How do you know? A y2= 36 B y2 = 16 Explain why 7 arethe solutions to the equation z2 = 49. Square Roots x2 = 121 √x2 = √112 x = 11 Solutions Each will have 2 solutions (+ and -) (11)2= 121 (-11)2= 121 1 separate (synonym) Vocabulary x = 11 andx = -11 both make the equation true. What can you say about the product of two numbers with the same sign (example: positive x positive)?

  4. Skill Development/Guided Practice • A square rootis a number that is multiplied by itself to form a product. • Taking the square root(√ )is used to isolate the variable in equations with squared variables. • An equation with squared variables can have two solutions, one positive and one negative. How did I/you solve the equation? How did I/you check and interpret the solution(s)? CFU Solve equations with squared variables. 2 Rewrite the numerical term as a squared expression. Solve the equation by taking the square root of both sides of the equation. Check and interpret2 the solution(s). 1 3 2 3 √a2 = √132 √k2 = √152 152= 225 132= 169 k2 = 152 (-15)2= 225 a2 = 132 (-13)2= 169 k = 15 and k = -15 both make the equation true. a = 13 and a = -13 both make the equation true. k = 15 a = 13 3 9 6 4 9 36 9 81 ( )2 = ( )2 = 36 16 9 81 36 16 6 4 3 9 6 4 3 9 p =  √q2 = √( )2 p2 = ( )2 √p2 = √( )2 q =  q2 = ( )2 3 9 6 4 6 4 3 9 9 81 36 16 (- )2 = (- )2 = 81 16 3 9 6 4 6 4 3 9 h = and h = - both make the equation true. h = and h = - both make the equation true. 2 explain (synonym) Vocabulary

  5. Skill Development/Guided Practice (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 4 14 in √s2 = √122 √s2 = √142 5 s2 = 196 142= 196 Area = 121 in2 s2 = 142 (-14)2= 196 14 in s = 14 The length of each side of the tile is 14 in. (-14 in is not a solution because a length cannot be negative.) 12 cm s2 = 144 122= 144 s2 = 122 (-12)2= 144 12 cm s = 12 The length of each side of the frame is 12 cm. (-12 cm is not a solution because a length cannot be negative.)

  6. Relevance • A square rootis a number that is multiplied by itself to form a product. • Taking the square root(√ )is used to isolate the variable in equations with squared variables. • An equation with squared variables can have two solutions, one positive and one negative. Sometimes Square Roots are not Integers, but instead fall between integers. * 62 72 62 72 How can you estimate a square root of a number that is not a perfect square ? (Pair-Share) Square roots can have how many solutions? Why are estimates useful? Do you think an estimate can be misleading? (Pair-Share) CFU CFU 6 7 6 7 6

  7. A square rootis a number that is multiplied by itself to form a product. • Taking the square root(√ )is used to isolate the variable in equations with squared variables. • An equation with squared variables can have two solutions, one positive and one negative. Skill Closure Solve equations with squared variables. Rewrite the numerical term as a squared expression. Solve the equation by taking the square root of both sides of the equation. Check and interpret the solution(s). 1 2 3 25 81 25 Word Bank √d2 = √72 Word Bank equation square root solution 72 = 49 81 d2 = 72 (-7)2 = 49 d = 7 and d = -7 both make the equation true. d = 7 Access Common Core 5 9 ( )2 = 25 81 Which equation below can be solved by taking a square root? Explain your answer. Explain why the other equations cannot be solved by taking a square root. A x = 49 B y2 = 16 5 9 5 9 √n2 = √( )2 n2 = ( )2 n =  5 9 5 9 25 81 (- )2 = 5 9 5 9 n = and n = - both make the equation true. Summary Closure What did you learn today about solving equations with squared variables? (Pair-Share) Use words from the word bank.

  8. Independent Practice Name: ___________________ • A square rootis a number that is multiplied by itself to form a product. • Taking the square root(√ )is used to isolate the variable in equations with squared variables. • An equation with squared variables can have two solutions, one positive and one negative. 11.1.13 Solve equations with squared variables. Rewrite the numerical term as a squared expression. Solve the equation by taking the square root of both sides of the equation. Check and interpret the solution(s). 1 2 3 62 = 36 132 = 169 √u2 = √132 √g2 = √62 g2 = 62 (-6)2 = 36 u2 = 132 (-13)2 = 169 g = 6 u = 13 g = 6 and g = -6 both make the equation true. u = 13 and u = -13 both make the equation true. 4 81 1 9 4 1 1 3 2 9 ( )2 = ( )2 = 4 81 1 9 2 9 1 3 2 9 1 3 v =  √v2 = √( )2 c =  v2 = ( )2 √c2 = √( )2 c2 = ( )2 1 3 2 9 2 9 1 3 4 81 1 9 (- )2 = (- )2 = 81 9 1 3 2 9 1 3 2 9 v = and v = - both make the equation true. c = and c = - both make the equation true.

  9. Periodic Review 1 x = 15 p = 7 100 25 25 196 100 25 1. Choose Yes or No to indicate whether each statement is true about the equation p2 = 49. 2. Choose Yes or No to indicate whether each statement is true about the equation w2 = . 25 196 A is smaller than B w= - C w= D There are exactly two solutions to the equation. O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No A 49 is NOT a perfect square. B 49 divided by 2 = p. C p=7 D There is more than one solution to the equation. Estimation Approximately where does fall on the number line to the right? Access Common Core 10 5 6 11 y =  b =  64 121 8 12 64 121 8 11 8 11

  10. Name: __________________________ 11.1.13

  11. Name: __________________________ 11.01.13

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