Name Extended Response Practice 4 4 points Respond

Name____________ Extended Response Practice #4 /4 points Respond completely in your Answer Document. (2 points)

Jen is paddling a canoe from one side of a lake to the other. She is paddling at a rate of 35 yards per minute. In your Answer Document, write an equation to find y, the number of yards she paddles in x minutes. Use your equation to determine how long it will take her to paddle the 840 yards from one 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 same 2 c + 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 = 4 a + 2 Variables: ____ Numbers: ____

3) Draw a representation of the equation 3 a – 7 = 8 Variables: ____ Numbers: ____

Which picture represents 3 x + 3 = 2

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

Other ways to represent equations *assume the unit tiles are numbers 2 x + 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 ?

EXIT Write the equation that this model represents. What is the value of ?

Visual Representation Activity

Word Problems Justin 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 Problems Mark 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.

Example Sara 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. 35 x + 575 = 6 B. 6 x + 575 = 35 C. -6 x + 35 = 575 D. 6 x + 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. 6 x + 7 = 331 b. 7 x + 6 = 331 c. 331 x + 6 = 7 d. 7 + 331 x = 6

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost? A. 5 x + 25 = 20 B. 5 x + 4 = 25 C. 4 x + 5 = 25 D. -4 x + 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 Equations 2 x – 6 = 4 + + = - -

You try 3 x + 1 = 7 + + = - -

4. -3 x + 8 = -1 5. 2 x – 3 = -7 6. Challenge* 2(x + 4) = 2

Solving Equations - Example 15 16

Solving Equations – Example 2

Uses of a variables A variable can be used for : 1. An unknown that can change. 2. A generalization of a pattern Example: Find the nth term with the rule 2 n + 1 3. A formula The formula to change from Celcius to Fahrenheit is C = 5/9(F – 32)

Simplifying Expressions COMBINE LIKE TERMS Example: 2 a + 6 b – 5 + 4 a – 2 b + 1 1. Circle one term (and each sign before the term!) 2. Square the next term (and signs!) 3. Underline the last term 4. COMBINE!

18 p + 13 p + p Simplify the expression 18 p + 13 p + p = a. b. c. d. 22 p 31 p 32 p²

CANNOT COMBINE Different powers (x + x²) Different letters (2 a + 3 b) Plain numbers with variables (2 a + 5)

3 x + 2 y – 6 x + 7 y 8 f + 2 t + 3 f + t 11 f + 3 t -3 x + 9 y

You try!

a. b. c. d. 13 x + 9 2 x 5 x – 3 5 x + 3

Simplify 2 x + 4 y + 2 – x + 9 y + 6 x 5 a. 9 x + 13 y - 3 b. 21 xy – 3 c. 7 x + 13 y d. 8 xy - 11

a. b. c. d. 6 x² - 2 x 6 x² - 2 -2 x² - 2 x -4 x²

Simplify and solve for x 3 x – x + 4 x = 54 Simplify 6 x = 54 Solve x=9

What is the simplified equation? What is x? 4 x – 10 x + x = 45 a. b. c. d. -6 x = 45; x = -7. 5 -5 x = 45; x = -9 -7 x = 45; x = -6. 42 -5 x = 45; x = 9

What is the simplified equation? What is x? 2 x – 4 + 4 x + 2 – x = -17 a. 5 x – 4; -2. 6 b. 6 x + 6; -3 c. 5 x – 2; 3 d. 5 x – 2; -3

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. 7 x² -3 x -1 b. 8 x² -4 x c. 8 x² - 3 x d. 7 x² - 4

Distributive Property Multiply the outside number by everything in the parenthesis 4(a + 5) = 4 a + 20 -3(b + 6) = -3 b – 18 2(3 c + 12 + a) =

Simplify and solve 3(x + 10) = 90 2(b – 12) = 8

Problem of the Day (Wednesday) Simplify the expression 4(k + 7) + 2 k a. b. c. d. 4 k + 9 6 k + 28 6 k + 7 4 k + 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 3 a + 5(a – 6) 3 a + 5 a – 30 7 + 5(a – 6) 7 + 5 a – 30

Simplify 28 k + 36(7 + k) a. b. c. d. 64 k + 252 29 k + 36 28 k + 252

Signs!

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

Simplifying Expressions Multiplying variables Ø m ∙ m = m² Ø 3 m² ∙ 2 m³ = 6 m⁵ Ø 2 a ∙ b² ∙ 4 a ∙ b⁵ Example: 2 c ∙ 3 c = 864

Simplify 2 x² ∙ x ∙ -4 x³ 3(a + 7 – b) c(4 + c – d) 9 x² ∙ 9 x

Solve with variables on both sides 2 x + 10 = -4 x – 2 1. Get the variable on one side 2 x + 10 = -4 x – 2 + 4 x +4 x 6 x + 10 = -2 2. Solve the two step equation 6 x + 10 = -2 -10 6 x = -12 x = -2

8 x + 9 = 3 x + 49 1. Get the variable on one side 8 x + 9 = 3 x + 49 -3 x 5 x + 9 = 49 2. Solve the two step equation 5 x + 9 = 49 -9 -9 5 x = 40 x=8

Problem of the Day (Thursday) CPS Learning Series Question

Problem of the Day (Monday)

Writing Algebraic Expressions 1. Identify the variable Remember 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 = 2 x – 2

You try!

Jeremy did 2 fewer than 3 times the hours of work that Haley did. A. 2 x – 3 B. 2 – 3 x C. 3 x – 2 D. 3 – 2 x

1. Identify the variable h = number of hours 2. Write the expression Total Cost = 12 + 2 h

Using your expression 12 + 2 h, 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 + 2 h = 26 h=7

You try!

First half + Second half 8 + 3 x = = Total 23

1. Identify the variable x = how much they need to save per month 2. Write the equation Already saved + Need to Save = Total 80 + 6 x = 200 3. Solve for x They need to save $20 a month

1. Identify the variable x = number of paperbacks 2. Write the equation Admission + paperbacks bought = Total spent 2. 50 +. 25 x = 4. 50 3. 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 Boot Example: Sam’s boots are 3 sizes less than twice the size of Toni’s. (s = Sam’s boot size, t = Toni’s size) s = 2 t – 3

Example 2 Sam‘s socks have one more than twice the number of holes as Zoey’s. A. s = 2(z + 1) B. 2 z + 1 = s C. z = s + 1 x 2

Example 3 Matt’s right sock has 2 less than 6 times the holes as his left sock. A. 6 L – 2 = R B. 2(L + 6) = R C. R = (6 x 2)

1. Basha’s boots cost $80 more than Chad’s. A. b + 80 > c B. c = b + 80 C. c + 80 = b 2. Yolanda’s boots cost $5 less than twice the cost of Sam’s. A. 2 s – 5 = y B. y + 5 = 2 s C. 5 + s = y 3. Zoey’s new boots cost $8 more than Toni’s and Chad’s combined. A. z = t + c + 8 B. 2(t + c) = z – 8 C. z + 8 = c + t 4. Toni dried out her boots 4 hours more on Friday than on Thursday. A. f + t = 4 B. 4 f = t C. t + 4 = f

5. On Monday, Mike’s boots traveled 3 times longer than on Tuesday. A. mt = 3 B. t = 3 m C. m = 3 t 6. On Sunday, Chad’s boots traveled 6 miles less than on Wednesday. A. w + 6 = s B. s + w = 6 C. w – 6 = s 7. Yolanda’s boot size is one less than ½ the size of Chad’s A. c = y – 1½ B. y + ½ + 1 = c C. y = ½c - 1 8. Sam has 8 more than 4 times as many blisters on his left foot as on his right. A. L = 8 R + 4 B. 4 R + 8 = L C. 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 + x B. 125 x C. 125 – x D. 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/3 B. n/4 C. 4 n D. 3 n