DO NOW Friday, November 1, 2013

Please have Planners open with Homework and Signed Progress

Report on your desk.

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

62

base

exponent

Exponential ExpressionAn exponential expression represents repeated multiplication.• Bases raised to an exponent of 2 are squared.

1. 92 2. 102

9 or -9 10 or -10

3. 4. PERFECT SQUARES25

814964

or - 59

59 or - 7

878

November 1, 2013

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 isolate1 the variable in equations

with squared variables.• An equation with squared variables can have two solutions, one

positive and one negative.Perfect Squares

12 = 122 = 432 = 9

42 = 1652 = 2562 = 3672 = 4982 = 6492 = 81102 = 100

x2 = 121√x2 = √112

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 y2 = 36

B y2 = 16

Explain why 7 are the solutions to the equation z2 = 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 -)

1. a2 = 169 2. k2 = 225

3. q2 = 4. p2 =

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).

Solve equations with squared variables.1

23

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

981

a2 = 132

a = 13a = 13 and a = -13 both make the equation true.

132 = 169(-13)2 = 169

√a2 = √132

k2 = 152

k = 15k = 15 and k = -15 both make the equation true.

152 = 225(-15)2 = 225

√k2 = √152

q2 = ( )239

√q2 = √( )239

q = 39h = and h = - both make the equation true.

39

39

( )2 = 39

981

(- )2 = 39

981

p2 = ( )264

√p2 = √( )264

p = 64

h = and h = - both make the equation true.

64

64

( )2 = 64

3616

(- )2 = 64

3616

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

12 = 122 = 432 = 9

42 = 1652 = 2562 = 3672 = 4982 = 6492 = 81102 = 100

and so on…

3616

9

81

36

16

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 in2. 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 cm2. What is the length of each side of the frame?

_________________________________________________________________________________

s2 = 196s2 = 142

s = 14

142 = 196(-14)2 = 196

√s2 = √142

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 in214 in

14 in

s2 = 144s2 = 122

s = 12

122 = 144(-12)2 = 144

√s2 = √122

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

12 cm

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

12 = 122 = 432 = 9

42 = 1652 = 2562 = 3672 = 4982 = 6492 = 81102 = 100

62 72 62 72

6 7

6 7

6 Why are estimates useful?

Do you think an estimate can be misleading? (Pair-Share)

CFU

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

equationsquare 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

23

Skill Closure

1. d2 = 49 2. n2 =

d2 = 72

d = 7d = 7 and d = -7 both

make the equation true.

72 = 49

(-7)2 = 49

√d2 = √72

2581

n2 = ( )259

√n2 = √( )259

n = 59

n = and n = - both make the equation true.

59

59

( )2 = 59

2581

(- )2 = 59

2581

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

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

12 = 122 = 432 = 9

42 = 1652 = 2562 = 3672 = 4982 = 6492 = 81102 = 100

25

81

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

23

481

19

g2 = 62

g = 6 g = 6 and g = -6 both make the equation true.

62 = 36

(-6)2 = 36

√g2 = √62

u2 = 132

u = 13 u = 13 and u = -13 both make the equation true.

132 = 169

(-13)2 = 169

√u2 = √132

c2 = ( )229

√c2 = √( )229

c = 29

c = and c = - both make the equation true.

29

29

( )2 = 29

481

(- )2 = 29

481

v2 = ( )213

√v2 = √( )213

v = 13

v = and v = - both make the equation true.

13

13

( )2 = 13

19

(- )2 = 13

19

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

12 = 122 = 432 = 9

42 = 1652 = 2562 = 3672 = 4982 = 6492 = 81102 = 100

Name: ___________________11.1.13

481

19

1. g2 = 36 2. u2 = 169

3. c2 = 4. v2 =

Periodic Review 1

Access Common Core

1. p2 = 49 2. x2 = 225

3. b2 = 4. y2 =10025

25196

p = 7 x = 15

b = 105

y = 611

1. Choose Yes or No to indicate whether each statement is true about the equation p2 = 49.

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.

O Yes O NoO Yes O NoO Yes O NoO Yes O No

2. Choose Yes or No to indicate whether each statement is true about the equation w2 = .

A is smaller than B w = - C w = D There are exactly two solutions to the equation.

O Yes O NoO Yes O NoO Yes O NoO Yes O No

812

811

64121

Estimation

Approximately where does fall on the number line to the right?

75

25

25

196

100

64121

811

Name: __________________________11.1.13

Nam

e: _

____

____

____

____

____

____

_ 1

1.01

.13