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

2. What are we going to do? CFU Students, you already know how to evaluate squared expressions. Now, we will use squared expressions solve equations with squared variables. Make Connection Evaluate the square root expressions. 1. We will solve equations with squared variables involving fractions. 2. We will estimate radicals that are not perfect squares. Learning Objective Activate Prior Knowledge Exponential Expression An exponential expression represents repeated multiplication. Bases raised to an exponent of 2 are squared. 1. 9 2 2. 10 2 9 or -910 or -10 3.4. PERFECT SQUARES 25 81 49 64 or - 5959 5 9 7878 7878 November 1, 2013

3. Square Roots Concept Development A square root is a number that is multiplied by itself to form a product. Taking the square root ( √ ) is used to isolate 1 the variable in equations with squared variables. An equation with squared variables can have two solutions, one positive and one negative. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 x 2 = 121 √x 2 =  √11 2 x =  11 x = 11 and x = -11 both make the equation true. (11) 2 = 121(-11) 2 = 121 Solutions 1 separate (synonym) Vocabulary How many solutions will each of the following equations have? How do you know? A y 2 = 36 B y 2 = 16 Explain why  7 are the solutions to the equation z 2 = 49. CFU What can you say about the product of two numbers with the same sign (example: positive x positive)? Each will have 2 solutions (+ and -)

4. 1. a 2 = 169 2. k 2 = 225 3. q 2 = 4. p 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 interpret 2 the solution(s). Solve equations with squared variables. 1 2 3 2 explain (synonym) Vocabulary How did I/you solve the equation? How did I/you check and interpret the solution(s)? CFU 2 3 Skill Development/Guided Practice 9 81 a 2 = 13 2 a =  13 a = 13 and a = -13 both make the equation true. 13 2 = 169 (-13) 2 = 169 √a 2 =  √13 2 k 2 = 15 2 k =  15 k = 15 and k = -15 both make the equation true. 15 2 = 225 (-15) 2 = 225 √k 2 =  √15 2 q 2 = ( ) 2 3939 √q 2 =  √( ) 2 3939 q =  3939 h = and h = - both make the equation true. 3939 3939 ( ) 2 = 3939 9 81 (- ) 2 = 3939 9 81 p 2 = ( ) 2 6464 √p 2 =  √( ) 2 6464 p =  6464 h = and h = - both make the equation true. 6464 6464 ( ) 2 = 6464 36 16 (- ) 2 = 6464 36 16 A square root is 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. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 and so on… 36 16 9 81 36 16

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 2 1 3 4 5 5. Jim’s family photo was placed in a frame. He knows the area of the picture frame is 196 in 2. What is the length of each side of the frame? _________________________________________________________________________________ 6. Vanessa is framed a picture from her vacation. The area of the picture frame is 144 cm 2. What is the length of each side of the frame? _________________________________________________________________________________ s 2 = 196 s 2 = 14 2 s =  14 14 2 = 196 (-14) 2 = 196 √s 2 =  √14 2 The length of each side of the tile is 14 in. (-14 in is not a solution because a length cannot be negative.) Area = 121 in 2 14 in s 2 = 144 s 2 = 12 2 s =  12 12 2 = 144 (-12) 2 = 144 √s 2 =  √12 2 The length of each side of the frame is 12 cm. (-12 cm is not a solution because a length cannot be negative.) 12 cm

6. Sometimes Square Roots are not Integers, but instead fall between integers. * 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? CFU Relevance A square root is 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. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 6262 7272 6262 7272 6 7 67 6 Why are estimates useful? Do you think an estimate can be misleading? (Pair-Share) CFU

7. What did you learn today about solving equations with squared variables? (Pair-Share) Use words from the word bank. Access Common Core Summary Closure Word Bank equation square root solution 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). Solve equations with squared variables. 1 2 3 Skill Closure 1. d 2 = 49 2. n 2 = d 2 = 7 2 d =  7 d = 7 and d = -7 both make the equation true. 7 2 = 49 (-7) 2 = 49 √d 2 =  √7 2 25 81 n 2 = ( ) 2 5959 √n 2 =  √( ) 2 5959 n =  5959 n = and n = - both make the equation true. 5959 5959 ( ) 2 = 5959 25 81 (- ) 2 = 5959 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 y 2 = 16 A square root is 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. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 25 81

8. Independent Practice 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). Solve equations with squared variables. 1 2 3 4 81 1919 g 2 = 6 2 g =  6 g = 6 and g = -6 both make the equation true. 6 2 = 36 (-6) 2 = 36 √g 2 =  √6 2 u 2 = 13 2 u =  13 u = 13 and u = -13 both make the equation true. 13 2 = 169 (-13) 2 = 169 √u 2 =  √13 2 c 2 = ( ) 2 2929 √c 2 =  √( ) 2 2929 c =  2929 c = and c = - both make the equation true. 2929 2929 ( ) 2 = 2929 4 81 (- ) 2 = 2929 4 81 v 2 = ( ) 2 1313 √v 2 =  √( ) 2 1313 v =  1313 v = and v = - both make the equation true. 1313 1313 ( ) 2 = 1313 1919 (- ) 2 = 1313 1919 A square root is 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. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 Name: ___________________ 11.1.13 4 81 1 9 1. g 2 = 36 2. u 2 = 169 3. c 2 = 4. v 2 =

9. Periodic Review 1 Access Common Core 1. p 2 = 49 2. x 2 = 225 3. b 2 = 4. y 2 = 100 25 196 p =  7 x =  15 b =  10 5 y =  6 11 1. Choose Yes or No to indicate whether each statement is true about the equation p 2 = 49. A49 is NOT a perfect square. B 49 divided by 2 = p. C p   7 DThere is more than one solution to the equation. O Yes O No 2. Choose Yes or No to indicate whether each statement is true about the equation w 2 =. A is smaller than B w  - C w   DThere are exactly two solutions to the equation. O Yes O No 8 12 8 11 64 121 Estimation Approximately where does fall on the number line to the right? 25 196 100 64 121 8 11

10. Name: __________________________ 11.1.13

11. Name: __________________________ 11.01.13