8th Grade Math DETAIL LESSON PLAN Lesson 8.EE.C.8 ...

Course: 8th Grade Math DETAIL LESSON PLAN Lesson 8.EE.C.8 Analyze and solve pairs of simultaneous linear equations. TSW solve real world systems of equations problems similar to what they will see in PARCC. Homework Teacher Selected Bellwork Teacher Selected Prior Knowledge

Review bellwork.

Review homework. Anticipatory Set

TODAY, will be an extra day of practice on system of equations. Teacher Input

Pass out classwork.

Have students work problems 1 – 7 independently.

Problems 8 and 9 are quite challenging. I would suggest that the teacher model how to solve problem number 8 and have the students try number 9 on their own. These two questions are similar to PARCC item number four.

Accelerated Classes may attempt problem 12 if time.

Teacher should go over the answers to the classwork to ensure understanding.

Assessment Observation and questioning.

Closure Teacher selected

8th Grade Math Name: ________________________ Classwork Assignment Date: _____________ Period: ______

Systems of Equations

Part 1

1) Two lines are graphed on the same coordinate plane. The lines only intersect at the point (5, 2). Which of these systems of linear equations could represent the two lines?

Check all that apply.

A. x = 7 – y 2x – y = 8

B. x = 2y + 11 3x + 2y = 9

C. x = 5 y = 2

D. y = 2 4x – y = 18

E. y = 3x – 8 3x – y = 12

F. y = x 3x + y = 4

2) Which point is the solution to both equations shown on the graph below?

3) Is (-1, 7) a solution for the system of linear equations below? Show your work and explain why or why not.

–

Show Work: Explain:

4) A dog sees a cat 60 feet away and starts running after it at 50 feet per second.

At the same time, the cat runs away at 30 feet per second. This situation can be represented by the following system of equations. Dog: y = 50x Cat: y = 30x + 60

a. Build a table, then graph both lines on one set of axes.

b. Write the coordinates of the point of intersection for when the dog will catch up to the cat!

5) Indicate whether each system of equations has no solution, one solution, or infinitely many solutions. ________________ ________________ ________________

________________ ________________ ________________ 6) Without graphing, determine whether each system of equations has one

solution, no solution, or infinitely many solutions. If the system has one solution, name it.

a. 2x + y = 4 b. y = x - 1 c. y = x – 2

4x + 2y = 8 x + y = 3 y = x – 5

7) Let’s practice using two different methods to solve the same problem!

Find the point of intersection to the system of equations problem below. Graphing Equal Values Method a. b.

Part 2 – Real World Problems

8) The Football Booster Club was selling car tags and bumper stickers. The table shows the number of car tags and bumper stickers in each of three recent orders. The total cost of orders A and B are given. Each car tag has the same cost, and each bumper sticker the same cost.

Order Number of Tags Number of

Bumper Stickers Total Cost of

Order (dollars)

A 4 2 18

B 1 1 8

C 2 5 ?

The system of equations shown can be used to represent this situation.

4x + 2y = 18

x + y = 8

Part A: What is the total cost of one car tag and one bumper sticker?

Part B: In the system of equations, x represents _______________________, and y represents _______________________.

Part C: If the system of equations is graphed in a coordinate plane, what are the coordinates (x, y) of the intersection of the two lines?

Part D: What is the total cost, in dollars, of order C?

9) Wal-Mart sells decks of playing cards and board games. The table below shows

the number of each item three different customers purchased. The total costs of the items are given for customer 1 and customer 2. Use the information to answer the following questions.

Customer Deck of Cards Board Games Total Cost of Order (dollars)

1 1 1 10

2 4 2 22

3 5 4 ?


y = -x + 10

4x + 2y = 22

Part A: What is the total cost of one deck of cards and board game?

Part B: In the system of equations, x represents _______________________, and y represents _______________________. Part C: If the system of equations is graphed in a coordinate plane, what are the coordinates (x, y) of the intersection of the two lines? (1,9) Part D: What is the total cost, in dollars, of customer 3’s purchases?

10) Two submarines began dives in the same vertical position and were trying to

meet at a designated point. If one submarine was on a course approximated by equation x + 4y = -14 and the other was on a course approximated by the equation x + 3y = -8, at what location would they meet? 11) During tax season Mr. Wilson wants to rent an extra copy machine for his accounting business in Southaven. Company A rents machines for $220 and charges $.02 per copy, while Company B in Horn Lake charges $150 for the machine but charges $0.03 per copy. a. Write a rule representing the cost to rent a copy machine for Company A and Company B. Rule Company A: Rule Company B: b. Set up and solve a system of equations to find the point of intersection. c. At _________ copies it will cost the same amount to rent from either

Company A or Company B.

12) The principal is taking students who had perfect attendance to the movies as a

reward. The table shows the number of teachers, the number of students, and the total cost for those who went to the movies in the 6th and 7th grades. The number of students and the total cost is given for those in the 8th grade. Each adult ticket has the same cost, and each student ticket has the same cost.


4x + 45y = 408

2x + 30y = 264

Part A: What is the cost of one student ticket? What is the cost of one adult ticket? Part B: In the system of equations, x represents _________________________, and y represents ________________________________. Part C: If the system of equations is graphed in a coordinate plane, what are the coordinates (x,y) of the intersection of the two lines? Part D: How many adult tickets were purchased for the 8th grade?

8th Grade Math Name: Answer Key

Classwork Assignment Date: _____________ Period: ______

Systems of Equations

Part 1

8.EE.8a Understand that solutions to a system of two linear equations in two variable s correspond to

points of intersection of their graphs, because points of intersection satisfy both equations

simultaneously.

8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by

graphing equations. Solve simple cases by inspection. For example 3x + 26 = 5 and 3x + 2y = 6

have no solution because 3x + 2y cannot simultaneously be 5 and 6.

1) Two lines are graphed on the same coordinate plane. The lines only intersect

at the point (5, 2). Which of these systems of linear equations could represent the two lines?

Check all that apply. Answer: A, C, D

A. x = 7 – y 2x – y = 8

B. x = 2y + 11 3x + 2y = 9

C. x = 5 y = 2

D. y = 2 4x – y = 18

E. y = 3x – 8 3x – y = 12

F. y = x 3x + y = 4

2) Which point is the solution to both equations shown on the graph below? D

3) Is (-1, 7) a solution for the system of linear equations below? Show your work and explain why or why not.

–

Show Work: Explain:

x + 2y = 13 3x – y = -11 (-1, 7) is not a solution to the system of

–1 + 2 • 7 = 13 3 • –1 – 7 = –11 equations. The coordinates must satisfy both

–1 + 14 = 13 –3 – 7 = –11 equations. However, when you plug in the

x and y (-1, 7) values into the second equation and

13 = 13 – 10 –11 solve, you find that it produces a false

result because -10 is not equal to -11.

4) A dog sees a cat 60 feet away and starts running after it at 50 feet per second.

At the same time, the cat runs away at 30 feet per second. This situation can be represented by the following system of equations. Dog: y = 50x Cat: y = 30x + 60

a. Build a table, then graph both lines on one set of axes. b. Write the coordinates of the point of intersection for when the dog will catch up

to the cat! Point of Intersection: (3,150)

5) Indicate whether each system of equations has no solution, one solution, or

infinitely many solutions. One Solution Infinitely Many No Solution

________________ ________________ ________________ Infinitely Many No Solution One Solution

________________ ________________ ________________ 6) Without graphing, determine whether each system of equations has one solution, no solution, or infinitely many solutions. If the system has one solution, name it.

a. 2x + y = 4 b. y = x - 1 c. y = x – 2

4x + 2y = 8 x + y = 3 y = x – 5

Infinitely Many (2,1) No Solution

7) Let’s practice using two different methods to solve the same problem!

Find the point of intersection to the system of equations problem below. Graphing Equal Values Method a. b. Point of Intersection (1, 3)

Part 2 – Real World Problems

8.EE.8c Solve real world and mathematical problems leading to two linear equations in two variables.

For example given coordinates of two pairs of points, determine whether the line through the first

pair of points intersects the line through the second pair.

8) The Football Booster Club was selling car tags and bumper stickers. The table shows the number of car tags and bumper stickers in each of three recent orders. The total cost of orders A and B are given. Each car tag has the same cost, and each bumper sticker the same cost.

Order Number of Tags Number of

Bumper Stickers Total Cost of

Order (dollars)

A 4 2 18

B 1 1 8

C 2 5 ?


4x + 2y = 18

x + y = 8

Part A: What is the total cost of one car tag and one bumper sticker? $8.00

Part B: In the system of equations, x represents the cost of each tag, and y represents the cost of each bumper sticker.

Part C: If the system of equations is graphed in a coordinate plane, what are the coordinates (x, y) of the intersection of the two lines? (1, 7)

Part D: What is the total cost, in dollars, of order C? $37

9) Wal-Mart sells decks of playing cards and board games. The table below shows

the number of each item three different customers purchased. The total costs of the items are given for customer 1 and customer 2. Use the information to answer the following questions.

Customer Deck of Cards Board Games Total Cost of Order (dollars)

1 1 1 10

2 4 2 22

3 5 4 ?


y = -x + 10

4x + 2y = 22

Part A: What is the total cost of one deck of cards and board game? $10

Part B: In the system of equations, x represents the cost of each deck of cards, and y represents the cost of each board game. Part C: If the system of equations is graphed in a coordinate plane, what are the coordinates (x, y) of the intersection of the two lines? (1,9) Part D: What is the total cost, in dollars, of customer 3’s purchases? $41

10) Two submarines began dives in the same vertical position and were trying to

meet at a designated point. If one submarine was on a course approximated by equation x + 4y = -14 and the other was on a course approximated by the equation x + 3y = -8, at what location would they meet? (10, -6) 11) During tax season Mr. Wilson wants to rent an extra copy machine for his accounting business in Southaven. Company A rents machines for $220 and charges $.02 per copy, while Company B in Horn Lake charges $150 for the machine but charges $0.03 per copy. a. Write a rule representing the cost to rent a copy machine for Company A and Company B. Rule Company A: y = .02x + 220 Rule Company B: y = .03x + 150 b. Set up and solve a system of equations to find the point of intersection. .02x + 220 = .03x + 150 Point of Intersection (7000, 360) c. At __7,000___ copies it will cost the same amount to rent from either

Company A or Company B.

12) The principal is taking students who had perfect attendance to the movies as a

reward. The table shows the number of teachers, the number of students, and the total cost for those who went to the movies in the 6th and 7th grades. The number of students and the total cost is given for those in the 8th grade. Each adult ticket has the same cost, and each student ticket has the same cost.


4x + 45y = 408

2x + 30y = 264

Part A: What is the cost of one student ticket? What is the cost of one adult ticket? Part B: In the system of equations, x represents _________________________, and y represents ________________________________. Part C: If the system of equations is graphed in a coordinate plane, what are the coordinates (x,y) of the intersection of the two lines? Part D: How many adult tickets were purchased for the 8th grade?

8th Grade Math DETAIL LESSON PLAN Lesson 8.EE.C.8 ...

Documents