Respond completely in your Answer Document. (2 points) Name________________________ Extended...

Respond completely in your Answer Document. (2 points)

Name________________________Extended Response Practice #4

/4 points

Jen is paddling a canoe from one side of alake to the other. She is paddling at a rate of35 yards per minute.

In your Answer Document, write an equationto find y, the number of yards she paddles inx minutes.

Use your equation to determine how long itwill take her to paddle the 840 yards fromone side of the lake to the other.

Learning Target:I can…Visually represent and solve

equations

To Draw an Equation

1.Identify what will represent a

_____________________ and what will

represent ______________________

2.Make sure each side of your equation

is a side of your _____________________

Solving Equations Symbolically

Both sides of an equation are the same2c + 5 = 9

One way we can show this is by using a scale

x represents variables and o represent numbers

2) If X’s represent variables and O’s represent the known amounts, draw a

model of the equation 10 = 4a + 2

Variables: ________

Numbers: ________

3) Draw a representation of the equation 3a – 7 = 8

Variables: ________

Numbers: ________

Which picture represents 3x + 3 = 2

4) If X’s represent variables and O’s represent the known amounts, which of the following pictures represents 3x + 2 = 2x

+ 3?

Other ways to represent equations

*assume the unit tiles are numbers2x + 1 = 7

What equation does this model represent?

What equation does this model represent?

OAA PRACTICE

What is the value of ?

To Solve Equations Visually:

1.Anything that appears on both

side of the scale _________________

2.Isolate the

____________________________

Solving Equations Visually

What is the value of ?

What is the value of ?

What is the value of ?

Write the equation that this model represents.

What is the value of ?

EXIT

Visual Representation Activity

Word ProblemsJustin bought 2 apples and 1 pear

for $4.00. The pear was $1.78. Write an equation and solve to find the cost of the apples.

Word ProblemsMark bought 4 pens and 1 notebook

for $3.25. The notebook was $2.25. Write an equation and solve to find the cost of the apples.

ExampleSara bought 2 bags of chips and a

coke for $7.50. The coke was $1.50. How much were the chips?

Equation _______________

Answer ________________

The fair costs $3 to get in and $2 for every ride. If John spent $21, how many rides did he go on?

Equation _________________

Answer ______________

Logo Shirts, Inc. is going to charge General Sherman $6 for each t-shirt they make for the school. The company will also charge the school a flat fee of $35 to set up the design. The school spent $575 all together. Which equation represents this situation?

A.35x + 575 = 6B.6x + 575 = 35C.-6x + 35 = 575D.6x + 35 = 575

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?

a.6x + 7 = 331b.7x + 6 = 331c.331x + 6 = 7d.7 + 331x = 6

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?

A.5x + 25 = 20B.5x + 4 = 25C.4x + 5 = 25D.-4x + 5 = 25

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?

Equation: ___________________

Answer:_________________

=

+

-

+

-

Representing Equations2x – 6 = 4

=

+

-

+

-

You try3x + 1 = 7

=

+

-

+

-

You try4x – 2 = -6

4. -3x + 8 = -1

5. 2x – 3 = -7

6. Challenge*2(x + 4) = 2

Solving Equations - Example

15

16

Solving Equations – Example 2

Uses of a variablesA variable can be used for :

1. An unknown that can change.

2. A generalization of a patternExample: Find the nth term with the rule 2n + 1

3. A formulaThe formula to change from

Celcius to Fahrenheit isC = 5/9(F – 32)

Simplifying ExpressionsCOMBINE LIKE TERMSExample: 2a + 6b – 5 + 4a – 2b + 11. Circle one term (and each sign

before the term!)2. Square the next term (and signs!)3. Underline the last term4. COMBINE!

18p + 13p + pSimplify the expression

18p + 13p + p =

a. 22pb. 32pc. 31pd. 32p²

CANNOT COMBINEDifferent powers (x + x²)Different letters (2a + 3b)Plain numbers with variables (2a +

5)

8f + 2t + 3f + t11f + 3t

3x + 2y – 6x + 7y

-3x + 9y

You try!

a. 13x + 9b. 2xc. 5x – 3d. 5x + 3

Simplify 2x + 4y + 2 – x + 9y + 6x - 5

a. 9x + 13y - 3b.21xy – 3 c. 7x + 13yd.8xy - 11

a. 6x² - 2xb. 6x² - 2c. -2x² - 2xd. -4x²

Simplify and solve for x3x – x + 4x = 54

Simplify6x = 54Solvex = 9

What is the simplified equation? What is x?

4x – 10x + x = 45

a. -6x = 45; x = -7.5b. -5x = 45; x = -9c. -7x = 45; x = -6.42d. -5x = 45; x = 9

2x – 4 + 4x + 2 – x = -17

a. 5x – 4; -2.6b.6x + 6; -3c. 5x – 2; 3d.5x – 2; -3

What is the simplified equation? What is x?

Problem of the Day (Tuesday)

Calculate your class average for the problem of the day. Round to the nearest tenth and answer numerically.

Review

Simplify the expression.a. 7x² -3x -1 b. 8x² -4xc. 8x² - 3xd. 7x² - 4

Distributive Property

Multiply the outside number by everything in the parenthesis4(a + 5) =

4a + 20-3(b + 6) =

-3b – 182(3c + 12 + a) =

Simplify and solve3(x + 10) = 90

2(b – 12) = 8

Problem of the Day (Wednesday)

Simplify the expression 4(k + 7) + 2k

a. 4k + 9b. 6k + 28c. 6k + 7d. 4k + 28

Review – Simplifying Expressions

1. Always do the Distributive Property first!Multiply the outside number by everything in the parenthesis

2. Simplify the rest of the expression by combining like terms

3a + 5(a – 6) 7 + 5(a – 6)3a + 5a – 30 7 + 5a – 308a – 30 -23 + 5a

Simplify 28k + 36(7 + k)

a. 64k + 252b. 29k + 252c. 29k + 36d. 28k + 252

Signs!

Simplify –(x + 10)a. -x + 10b. -x – 10c. x – 10d. -x – 1

Simplifying Expressions

Multiplying variables m ∙ m = m² 3m² ∙ 2m³ = 6m⁵ 2a ∙ b² ∙ 4a ∙ b⁵

Example:2c ∙ 3c = 864

Simplify2x² ∙ x ∙ -4x³

3(a + 7 – b)

c(4 + c – d)

9x² ∙ 9x

Solve with variables on both sides

2x + 10 = -4x – 21. Get the variable on one side

2x + 10 = -4x – 2 + 4x +4x

6x + 10 = -2

2. Solve the two step equation6x + 10 = -2 -10 -106x = -12x = -2

8x + 9 = 3x + 49 1. Get the variable on one side

8x + 9 = 3x + 49 -3x -3x

5x + 9 = 49

2. Solve the two step equation5x + 9 = 49 - 9 - 95x = 40x = 8

Problem of the Day (Thursday)

CPS Learning Series Question

Problem of the Day (Monday)

Writing Algebraic Expressions

1. Identify the variableRemember the variable is the

unknown or element that changes in the problem.

Example:Justin is x years old. Jackie is two

years younger than twice Justin’s age. How old is Jackie?

2. Identify what’s WITH the variable

Justin is x years old. Jackie is two years younger than twice Justin’s age. How old is Jackie?

3. Write the expression

Jackie’s age = 2x – 2

You try!

Jeremy did 2 fewer than 3 times the hours of work that Haley did.

A.2x – 3B.2 – 3xC.3x – 2D.3 – 2x

1. Identify the variableh = number of hours

2. Write the expression

Total Cost = 12 + 2h

Using your expression 12 + 2h, how much would it cost to rent the bicycle for 4 hours?

$20

If Katie spend $26, how many hours did she rent the bicycle for?

12 + 2h = 26

h = 7

You try!

First half + Second half = Total8 + 3x = 23

1. Identify the variablex = how much they need to save per month

2. Write the equationAlready saved + Need to Save = Total

80 + 6x = 200

3. Solve for xThey need to save $20 a month

1. Identify the variablex = number of paperbacks

2. Write the equationAdmission + paperbacks bought = Total spent 2.50 + .25x = 4.503. Solve for x

You bought 8 paperbacks

Problem of the Day (Friday)

Relating a Table to an Equation

Problem of the Day (Tuesday)

Equations to BootExample:Sam’s boots are 3 sizes less than

twice the size of Toni’s.(s = Sam’s boot size, t = Toni’s size)

s = 2t – 3

Example 2Sam‘s socks have one more than

twice the number of holes as Zoey’s.

A.s = 2(z + 1)B.2z + 1 = sC.z = s + 1 x 2

Example 3Matt’s right sock has 2 less than 6

times the holes as his left sock.A.6L – 2 = RB.2(L + 6) = RC.R = (6 x 2)

1. Basha’s boots cost $80 more than Chad’s.A. b + 80 > cB. c = b + 80C. c + 80 = b

2. Yolanda’s boots cost $5 less than twice the cost of Sam’s.A. 2s – 5 = yB. y + 5 = 2sC. 5 + s = y

3. Zoey’s new boots cost $8 more than Toni’s and Chad’s combined.

A. z = t + c + 8B. 2(t + c) = z – 8C. z + 8 = c + t

4. Toni dried out her boots 4 hours more on Friday than on Thursday.

A. f + t = 4B. 4f = tC. t + 4 = f

5. On Monday, Mike’s boots traveled 3 times longer than on Tuesday.

A. mt = 3B. t = 3mC. m = 3t

6. On Sunday, Chad’s boots traveled 6 miles less than on Wednesday.

A. w + 6 = sB. s + w = 6C. w – 6 = s

7. Yolanda’s boot size is one less than ½ the size of Chad’sA. c = y – 1½B. y + ½ + 1 = cC. y = ½c - 1

8. Sam has 8 more than 4 times as many blisters on his left foot as on his right.

A. L = 8R + 4B. 4R + 8 = LC. L + R = 4 x 8

Writing Expressions Stations

6

Justin went to the store to buy snacks for his class at school. He bought soda for $2.00. He bought cookies for $0.45 a piece. If he spent $11.00, how many cookies did he get?

1. On my last birthday I weighed 125 pounds. One year later I have put on x pounds. Which expression gives my weight one year later?

A. 125 + xB. 125xC. 125 – xD. 125/x

2. Jane and her three college friends are going to be sharing the cost of a 3 bedroom apartment. The cost of rent is n dollars. What expression can you write that will tell you what Jane's share is?

A. n/3B. n/4C. 4nD. 3n