PROBLEM OF THE WEEK How many rectangles are in this checkerboard? The rectangles can be a variety of sizes as long as they follow the requirements of a rectangle.

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Algebra 1

The ProblemHow many rectangles of any size are there in an 8-by-8checkerboard?

Strategies and Hints1. Have you tried simplifying the problem? Start with a grid

that is smaller than 8-by-8.2. Consider the squares separately from the other rectangles.3. Record your data in a table or an organized listing.4. Do you see any patterns in the numbers that can help you

determine the answer without counting all possibilities?

Problem-of-the-WeekRectangle Rampage

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Algebra 1

The ProblemHow many rectangles of any size are there in an 8-by-8checkerboard?

Strategies and Hints1. Have you tried simplifying the problem? Start with a grid

that is smaller than 8-by-8.2. Consider the squares separately from the other rectangles.3. Record your data in a table or an organized listing.4. Do you see any patterns in the numbers that can help you

determine the answer without counting all possibilities?

RAISING THE BAR ***Guess the problem of the week ACCURATELY by Monday, December 6th (due to Testing) and your name will be included in the weekly raffle for a candy bar. Each Scholar only gets ONE submission.****

GOOD LUCK! Shhhh… itʼs a secret. The answer to this problem can be found somewhere in your Algebra class! Pay attention

Warm-Up (Monday) Name: Objective: Solving for y Date: Solve the following equations for x: 1. 3x – 2y = 15 2. 5y – x = 7 3.

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12x + 2y = −8 4. –3x – 4y = 10

Example #1) y= 4x 3x+y=-21 Steps: 1. Solve for one variable in one equation. 2. Substitute for that variable in the other equation. 3. Solve. 4. Replace to find the other variable. 5. Check your solution. In Class EXAMPLES: 1. x + y = 10 2. y = 2x - 2 3. 2a – 3b = 7 5x – y = 2 2x + 3y = 10 2a – b = 5 You try the following systems: USE SUBSTITUTION. 4. x = y - 6 5. t = 2s - 3 6. 2x + y = 10 2x + 3y = 33 s + t = 9 x – 3y = -2

Linear Equations Self-Test Name SOL’S covered: A.6, A.7, A.8

1. Find the slope given the following points.a) (8, 3), (2, 5) b) (-2, 5), (2, 9) c) (-3, 6), (-3, 4)

2. Write an equation in slope-intercept form given the following information.a) m = -2, b = -3 b) (4, -6), m = 3 c) (0, 5), (-2, 0)

3. Graph using the table below.a) y = x + 4 b) 2x + 2y = 8

x y x y0 01 12 2

4. Graph using x- and y-intercepts.a) 4x + y = 8 b) -2x + 6y = -6

x-int: x-int:

y-int: y-int:

5. Graph using slope and y-intercept.a) y = 3x – 2 b) y = -1/2x + 1

slope: slope:

y-int.: y-int.:

6. Answer the following questions for the word problem.We currently have $50 and spend $5 a day.

a) Write an equation for the amount of money you have.

b) Define the variables.X = Y =

c) Slope =

d) Y-intercept =

e) Graph using SLOPE-INTERCEPT FORM.Show the points you used on the graph!!

f) Explain why the equation increases/decreases.

g) How much money did we have 5 days ago?

h) What is our financial situation in 15 days?

7. Answer the following questions for the word problem.You have $20 and spend $2.50 a day for lunch

a) Write an equation for the amount of money you have.

b) Define the variables.X = Y =

c) x-intercept =

y-intercept =

d) Complete the table and draw the graph.x y

e) Slope of the line =

f) Does the graph increase or decrease?

Warm-up for Tuesday Name: Date: Warm-up Pd: Add or subtract the following polynomials. 1. 3x + 2y = 10 2. 5y – x = 7 + 4x – 3y = 1 + 9y + 4x = -1 3. 6x + 2y = -8 4. 3x – 4y = 10 - (6x – 10y = 20) - (2x – 9y = 18)

© Glencoe/McGraw-Hill 60 Algebra 1

NAME DATE

Study Guide Student EditionPages 482–486

8-5

Graphing Systems of InequalitiesThe solution of a system of inequalities is theset of all ordered pairs that satisfy bothinequalities. To find the solution of the system

y � x � 2y � �2x � 1,

graph each inequality. The graph of eachinequality is called a half-plane. Theintersection of the half-planes represents the solution of the system. The graphs of y � x � 2 and y � �2x � 1 are the boundaries of the region.

An inequality containing an absolute valueexpression can be graphed by graphing anequivalent system of two inequalities.

Solve each system of inequalities by graphing.

1. y � 2x 2. 5x � 2y � 6y � �1 y � �x � 1

3. |y| � x 4. �x � y � 6x � y � 2

5. Write a system of inequalities for thegraph at the right.x � y ! 2x > 1

O

y

x

2

2–2

O

y

x

2

4

–4

–2

2 4–4 –2O

y

x

2

4

–4

–2

2 4–4 –2

O

y

x

2

4

–4

–2

2 4–4 –2O

y

x

2

4

–4

–2

2 4–4 –2

O

y

x

2

4

6

–6

–4

–2

2 4 6–6 –4 –2

y � x � 2

y � �2x �1

Chapter 3.4 Name: ______________________ Graphing Systems of Inequalities Date: _______________________ Classwork

Graph the system of inequalities.

1. 3 1 2y xy x

2. 2 4 xx y

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

3. 4 2yx

4. 2 3 12 3 4

x yx y

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

Chapter 3.4 Name: ______________________ Graphing Systems of Inequalities Date: _______________________ Classwork

5. 3 6 3 4x yx y

6. 4 5 3 3 2 1

y xx y

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y 7. 3 1

3 2

4

xy

y x

8. 3 3 4 2 3 18

x yx yx y

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

Independent Practice Equations and InequalitiesA.9

Read and solve.

1. What is the solution of the following system of equation? 2x – 6 = 2y

3 – 2x = y

A. x = -2, y = -3

B. x = 0, y = -3

C. x =1, y = -2

D. x = 2, y = -1

2. The length of a rectangle is 2 centimeters longer than its width. The perimeter is 16

centimeters. What are the length and width of the rectangle?

A. 7 cm, 5 cm

B. 6 cm, 4 cm

C. 5 cm, 3 cm

D. 4 cm, 2 cm

3. Which is the solution of the following system of equations: 2x + y = 4

3x – y = -14

A. (-2, 8)

B. (-2, 0)

C. (2, 0)

D. (0, -2)

4. One competitor in a 100-mile bicycle race took a total of 5 hours to complete the

course. His average speed in the morning was 23 miles per hour. His average speed in

the afternoon was 13 miles per hour. How many hours did he ride in the morning, and

how many hours did he ride in the afternoon?

A. Morning: 2.5 hours, Afternoon: 2.5 hours

B. Morning: 3 hours, Afternoon: 2 hours

C. Morning: 3.5 hours, Afternoon: 1.5 hours

D. Morning: 4 hours, Afternoon: 1 hour

5. Which is the solution of the following system of equations: y = -x

2x – y = 6A. (6, -6)

B. (2, -2)

C. (0, 0)

D. (-2, 2)

6. Which is the solution of the following system of equations: -3x + 7y = 3

y = 6A. (3, 6)

B. (13, 6)

C. (-6, 6)

D. (-15, 6)

Independent Practice—continued

7. The sum of two numbers is 25. One number is twice the second plus seven. What arethe two number?

A. 2, 23B. 5, 7C. 6, 19D. 12, 13

8. Which is the solution of the following system of equations: 2x + y = 5 3x – 2y = 4

A. (-1, 2)B. (0, 9)C. (1, 2)D. (2, 1)

9. The concession stand sells pizza and drinks during football games. Jack bought 4drinks and 6 slices of pizza and paid $6.70. Amy bought 4 slices of pizza and 3 drinksand paid $4.65. What price is each drink and each slice of pizza?

A. drinks: $1.00 each, pizza: $1.50 eachB. drinks: $0.75 each, pizza: $1.00 eachC. drinks: $0.55 each, pizza: $0.70 eachD. drinks: $0.55 each, pizza: $0.75 each

10. Which is the solution of the following system of equations: x = 4 y = 6x – 3

A. (7/6, 4)B. (4, 7)C. (4, 21)D. (7, 4)

EXTRA CREDIT OPPORTUNITY!!!! Complete the following puzzle with the correct answer and receive 15 pts on the next quiz. You must show all of your work on the sheet (front and back!) Good Luck!

QUOTABLE PUZZLES Equations and Inequalities A.9

Directions: Solve the following problems. Match that answer to the correct letter ofthe alphabet. Enter that letter of the alphabet on the blank corresponding to theproblem number.

___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 2 10 7 9 5 3 9 4 8 7 1 4 11

___ ___ ___ ___ ___ ___ ___ 2 4 10 6 4 9 5

A B C D E F G H I J K L M 5 7 1 10 2 6 -3 8 4 -6 3 0 -2

N O P Q R S T U V W X Y Z-8 -1 -4 1.5 -5 -7 9 -9 3.4 -12 -2 11 14

Find the x-coordinate for the solution toeach system of equations.

7. 2x + 3y = 13 x – 3y = 2

1. y = 3x – 8 y = 4 – x

8. 13x + 5y = -11 13x + 11y = 7

2. x + y = 0 3x + y = -8

Find the y-coordinate for the solution toeach system of equations.

3. 4x + 5y = 11 y = 3x – 13

9. 2x + y = 5 3x – 2y = 4

4. x – 5y = 2 2x + y = 4

10. 7x + 3y = -1 4x + y = 3

5. x + 3y = 12 x – y = 8

11. 8x – 3y = -11 2x – 5y = 27

6. x + y = 8 x – y = 4