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Grade: 8th Grade

Enduring Skill 1:

Students will develop an understanding of the concept of a function and use functions to describe quantitative relationships.

Demonstrators and Related Standards:

1. Understand that a function is a rule that assigns each input one output. (8.F.1; 8.F.3)

2. Understand that function is a description of a situation where one quantity determines another. (8.F.3; 8.SP.2)

3. Translate among different representations and partial representations of functions. (8.F.2; 8.F.4; 8.SP.3; 8.EE.5)

4. Describe how the qualitative features of a function are reflected in different representations of linear and non-linear functions. (8.F.2; 8.F.3; 8.F.4; 8.F.5; 8.SP.2; 8.SP.3; 8.EE.5)

Assessment Items:

1. ES 1, Demonstrator 1, Standard (8.F.1; 8.F.3)

Each of the four items below represent a relationship between x and y. Determine which relations represent a function.

I. II. {(-2,5) (-1,0) (0,-3) (2,5)}

III. IV.

a. I. and II b. I. II. and III. c. II. and III. d. All of the above e. None of the above


Fill in the following function table based on the given rule.

Rule: 𝑦 = 6𝑥 − 3

x y

-1

2

-15

15

6

X Y -1 0

0 4

0 -6

2 7

3

4

5

6

2

4

6

8


Which set of ordered pairs represents a function?

A. (-3,2), (-1,2), (0,-1), (2,4) B. (-2,6), (-3,4), (-3,2), (-4,0) C. (11,37), (8,28), (-7,31), (8,19) D. (2,18), (-3,12), (0,9), (2,6)


The relationship between the length of the sides of a square (s) and its perimeter (P) can be modeled by the function P = 4s. Find the missing measurements in the table below. Finally, identify the dependent and independent variables.

5. ES 1, Demonstrator 2, Standard (8.F.3; 8.SP.2)

Brad is going to order new jerseys for his soccer team. The jerseys will have the team logo printed on the front. Brad receives quotes from 2 companies:

Sports Gear Prints charges $22 for each jersey and

Graphic Designs and Prints charges a one time $50 setup fee plus $16.

a. Using n for the total number of jerseys ordered and c for the total cost create an equation that Brad can use for each company.

b. Brad needs to order 25 jerseys for his team. Using your equations from part a, determine which company will be the cheapest.

Side Length (s) Perimeter (P)

1 4

2 8

6 ?

9.25 ?


What ONE thing in this function tells you it will be nonlinear.

𝑦 = 𝑥2 + 3𝑥 − 10

a. There are two terms containing x

b. The first term containing x has a power of 2

c. There is one term that is constant d. There are three terms


Which of the following equations is not a linear function?

a. y = .5x + 2

b. y = 𝑥2 c. y = 2x d. y = x - 2


Jackson, Sarah and Evan walked 20 minutes to Lake Lots of Fish to go fishing. Each caught fish at a constant rate throughout the day. The fish Jackson caught is represented by the graph shown below. The fish Sarah caught is represented by the table below. The fish Evan caught is represented by the equation below.

a. Who caught fish at the faster rate?

b. How many fish does each person have at 5 hours?

Sarah’s Fish

Hours Spent Fishing Fish Caught

0 0

1 2

2 4

3 6

Evan’s Fish

f = 3h


Which function contains all the values of x and y in the table?


Jared wants to take his MP3 player and video game player on a car trip. One hour before they leave, he realizes that he forgot to charge the batteries of each device. At that point, he plugs in both devices so they can charge for the full hour before they leave.

His video game player is new so he does not know how fast it is charging, but he recorded the battery charge for the first 30 minutes after he plugged it in.

The rate in which his MP3 player chargers and its starting charge is given in the

following equation: 𝑐 =12

15 𝑡 + 40

Which device(s) will be fully charged when they are ready to leave in one hour?

a. The MP3 player b. The video game player c. Both devices d. Neither devices

A y = - 3x + 1

B y = - 2x + 3

C y = - 3x – 2

D y = - 4x – 1


Kobe earns extra money by giving tennis lessons to elementary age students. He charges the students a one time fee of $25 and then $11 per hour. Kobe earned $74.50 last week. How many hours did he give lessons last week?


For school trips, a local water park charges a flat rate plus an additional rate for each student. The water park uses a linear function to determine the total cost in dollars (y) if x students attend the field trip. The following table shows a partial representation of this function.

Water Park Field Trip Cost

Number of Students (x) 1 2 3 4 5

Total cost in Dollars (y) 43 46 49 52 55

A. What is the rate of change represented by the table and what does it represent in the problem? Show your work and explain your answer. B. The first x-value in the table is 1. Explain why it is more appropriate for the

table to start at x = 1 instead of x = 0.


Brauck and Forrest both have a pet snake. They both believed what they feed their snake would make it grow the fastest. They begin measuring their snakes weekly to determine which diet is the best. The table below shows the growth of Brauck’s snake over several weeks.

Number of Weeks (x) 0 1 2 3 4

Length in Centimeters (y) 12.8 13.2 13.6 14.0 14.4

The equation y = 11.2 + 0.5x represents, y, the length in centimeters, of Forrest’s snake over x days. Which statement accurately compare the growth of the plants?

A. Brauck’s snake is growing at a faster rate than Forrest’s snake. B. Forrest’s snake is growing at a faster rate than Brauck’s snake. C. Both snakes are growing at the same rate. D. Forrest’s snake was growing at a faster rate than Brauck’s at first, but then Brauck’s snake began to grow at a faster rate.

14. ES 1 Demonstrator 4, Standard (8.F.3; 8.F.2)

The table below shows the relationship between the side length of a square and the area of a square.

Side Length

1 2 3 4 5

Area 1 4 9 16 25

A. Create a graph to represent the relationship between the side length of a

square and the area of the square. B. Determine if the relationship between side length and area is linear or non-linear.

C. How does the table show the relationship is linear or non-linear?

D. How does the graph show the relationship is linear or non-linear?


Ashley walks from her home to a park at a constant rate, watches a ball game and then walks home at the same constant rate.

Which graph matches the description of Ashley’s walk?

a. b.

c. d.


Determine the rate of change and initial value of the given table. x y

1 0

2 2

3 4

4 6

5 8

Rate of Change: __________________

Initial Value: ______________________


Identify each of the following functions as linear or non-linear.

A. 𝑦 = 2𝑥2 + 3𝑥 − 5 B. C.

D. E. y = 3x + 2 F.


Which of the following does NOT accurately describe the given graph?

A. The graph has two increasing intervals, one decreasing interval, and one constant interval.

B. The graph begins and ends with an interval increasing. C. The third interval of the graph is decreasing. D. Each increasing interval is followed by a constant interval.

Grade 8

Enduring Skill 2:

Students will further develop their understanding of two and three-dimensional space and figures.


1. Understand how the characteristics of a figure behave under geometric

transformations. (8.G.1a,b,c; 8.G.2; 8.G.3; 8.G.4)

2. Understand the relationship between the interior and exterior angles of a triangle and of angles formed when parallel lines are cut by a transversal. (8.G.5)

3. Understand and apply the Pythagorean Theorem and its converse to solve real world mathematical problems. (8.G.6; 8.G.7; 8.G.8, 8.EE.2)

4. Further understanding of volume to solve problems involving cones, cylinders, and spheres. (8.G.9; 8.EE.2)

Assessment Items:

1. ES 2, Demonstrator 1, Standard (8.G.1a, b, c; 8.G.2; 8.G.3; 8.G.4)

Given the graph of quadrilateral ABCD.

A. Graph A’B’C’D’ as a reflection of ABCD across the x-axis and identify the image coordinates of the reflected image.

B. Are quadrilateral ABCD and quadrilateral A’B’C’D’ similar congruent, or neither? Explain your answer.

C. Graph A”B”C”D” as a translation of ABCD 4 units left and 5 units down and identify image coordinates of the translated image.

D. Are quadrilateral ABCD and quadrilateral A”B”C”D” similar, congruent, or neither? Explain your answer.

2. ES 2, Demonstrator 1, Standard (8.G.1a,b,c; 8.G.2; 8.G.3; 8.G.4)

Given the graph of triangle ABC and its image triangle A’B’C’

A. Determine the scale factor of the given dilation. B. Are triangle ABC and triangle A’B’C’ similar, congruent, or neither? Explain your answer.

3. ES 2, Demonstrator 2, Standard (8.G.5)

In the figure below a transversal intersects two parallel lines. Find the measures of angles 1, 2, 3, and 4.


Find the measure of each numbered angle.


Market Street runs parallel with Main Street and both streets are intersected by 5th Avenue as shown below. If a car traveling northeast on Market Street turns right to go east on 5th Avenue, it turns (clockwise) through a 35 degree angle as indicated in the picture.

a. Suppose a car is traveling southwest on Market Street and turns left to go east on 5th Avenue. Draw the angle in the picture. What is the measure of this angle? Explain how you know this.

b. Suppose a car is traveling southwest on Main Street and turns right onto 5th Avenue. Draw the angle of turn in the picture. What is the measure of this angle? Explain using rigid motions. c. A car makes a 35 degree angle of turn going through the intersection of Main Street and 5th Avenue. Assuming that the car is following these two roads, what can you conclude about the car’s route through this intersection? Explain.

6. ES 2, Demonstrator 3, Standard (8.G.6; 8.G.7; 8.G.8; 8.EE.2)

Which statement best explains how to use the side measures of a triangle to show that a triangle is a right triangle?

a. Find the sum of the squares of the lengths of the legs and see if it equals the length of the hypotenuse squared.

b. Find the square root of the length of the hypotenuse and see if it equals the sum of the lengths of the legs.

c. Find the square of the length of the hypotenuse and see if it equals the sum of the lengths of the legs.

d. Find the average of the lengths of the two legs and see if it equals the length of the hypotenuse.


Keoni needs to create a right triangle. He has several squares and he know the area of each square. Which three squares will create a right triangle?


Given the diagram of a greenhouse, determine the volume of the greenhouse.


An aquarium in a doctor’s office is constructed from a cone inside of a cylinder where the fish are contained inside the cone as pictured below. The doctor wants to fill the remaining portion of the cylindrical tank with colored water. What will be the volume of the colored water?


Given the cylinder below, if you want to double the volume of the cylinder, which measurement in the cylinder will you need to double? Show your work with an example to verify your answer.

11. ES 2, Demonstrator 1, Standard (8.G.1a,b,c; 8.G.2; 8.G.3; 8.G.4)

12. ES 2, Demonstrator 1, Standard (8.G.1a,b,c; 8.G.2; 8.G.3;8.G.4)

Sarah plots the point (4,-3) on a coordinate grid. She reflects this point

over the x-axis, and then over the y-axis. What are the coordinates of

the new reflected point?

A. (-4, -3)

B. (-4, 3)

C. (4, -3)

D. (4,3)


Given the following diagram, determine the values of v, w, x, and y.


Grade 8

Enduring Skill 3:

Students will formulate and reason about expressions and equations.


1. Use linear equations and systems of linear equations to represent, analyze, and solve problems. (8.EE.7a,b,c; 8.EE.8a,b,c; 8.EE.5; 8.EE.6)

2. Understand the slope of a line as a constant rate of change or a constant of proportionality. (8.EE.5; 8.EE.6)

3. Use an efficient procedure to solve linear equations in one variable. (8.EE.5; 8.EE.6; 8.EE.7)

4. Solve and analyze systems of 2-variable equations. (8.EE.5; 8.EE.6; 8.EE.8)

Assessment Items:

1. ES 3, Demonstrator 1, Standard (8.EE.7a,b,c; 8.EE.8a,b,c; 8.EE.5; 8.EE.6)

The perimeter of an isosceles triangle is 16 inches. The length of its base is 2 times the length of its other sides. In the equations below, x represents the length of each of its equal sides, and y represents the length of its base.

2x + y = 16 y = 2x What are the side lengths of the triangle?

A. 3 inches, 3 inches, 6 inches B. 4 inches, 4 inches, 8 inches C. 4 inches, 8 inches, 8 inches D. 6 inches, 6 inches, 8 inches

2. ES 3, Demonstrator 2, Standard (8.EE.5; 8.EE.6)

The equation of a line can be represented in slope-intercept form: y = mx + b. A line contains the points listed in the table, write the equation in slope-intercept form.

X y

-4 4

-2 -2

0 -8

2 -14


A plumber charges a set fee for each house call plus an hourly rate, as shown by the graph below:

What does the slope of the graph represent?

a. the cost of materials for each plumbing job b. the total charge for any plumbing job c. the set fee for any plumbing job d. the hourly rate charged by the plumber


What is the slope of the line graphed below?

a. 100 b. 75 c. 50 d. 25

5. ES 3, Demonstrator 3, Standard (8.EE.5; 8.EE.6; 8.EE.7)

For each babysitting job, Ashley charges $2.50 for bus fare plus $8.00 per hour for each hour she works. She charged $30.50 for her last babysitting job.

a. Write a linear equation that represents the problem. Define the variable you choose.

b. Solve your equation to determine how many hours Ashley babysat during her last job. Show every step you use to solve the problem.


Sheena and Jared both graph systems of equations shown: 7x + y = 8

9x - 2y = -16

Sheena claims the lines intersect at the point (1,1). Jared claims that the lines intersect at the point (0,8). Use the equations to determine who is correct. Show your work and explain your reasoning.


Leah’s teacher tells her that the sum of two numbers is -20. Leah does not know what the two numbers are, but she has some information that can help her find out. She knows that four times the first number minus 5 times the second number is 1. She comes up with the following two equations that can be used to find the numbers:

x + y = -20

4x - 5y = 1

Using either elimination or substitution, determine the solution of this set of simultaneous equations. Show all work. What are the two numbers that Leah’s teacher is using?

8. ES3, Demonstrator 3, Standards (8.EE.7)

Given the equation 𝑡

−2 – 8 = 0, what is the first step in solving for the variable t.

A. multiplying each side by -2

B. subtracting 8 from each side

C. adding 8 to each side

D. dividing each side by -2

9. ES 3, Demonstrator 1 and 4, Standard (8.EE.8)

What is the value of y in the solution to the system of equations shown below?

3x + 7y = 15

5x + 2y = -4

A. -3 B. -4 C. 3 D. 4

10. ES 3, Demonstrator 1 and 4, Standard (8.EE.8)

The community theater is selling tickets for a fall play. On the first day of ticket sales, 9 adult

tickets and 3 student tickets were sold for a total of $75.00. On the second day of ticket sales,

the theater collected $67.00 by selling 5 adult and 8 student tickets.

a. Write an equation representing day one sales.

b. Write an equation representing day 2 sales.

c. Solve the system of equations to determine the price of each adult ticket and

each student ticket.

11. ES 3, Demonstrator 2, Standard (8.EE.6)

What is the slope of a line that passes through the points (2, -5) and (6, -2)?

A. - 4

3 B. -

3

4 C.

4

3 D.

3

4


A line has a slope of -5 and passes through the point (1, -1).

Which equation represents the equation of this line in point slope form?

A. y – 1 = -5(x + 1)

B. y – 5 = x – 1

C. y + 1 = -5(x - 1)

D. y +1 = -5(x + 1)


Compare and order the following linear functions I, II, III, and IV

from least to greatest rate of change.

I. y = 0.5x – 0.25 II. As x increases by 3 units, y increases by 2 units

III. IV.

X -2 0 2 4

Y 7 9 11 13

Grade 8

Enduring Skill 4:

Students will model and interpret bivariate data.


1. Use a linear equation to describe the association between two quantities in bivariate data. (8.SP.1; 8.SP.2)

2. Informally fit a trend line and assess its fit to the data. (8.SP.3)

3. Interpret components of a relationship (such as slope and y-intercept) in terms of the situation. (8.SP.3)

Assessment Items:

1. ES 4, Demonstrator 1, Standard (8.SP.1; 8.SP.2)

The table below shows the life expectancy according to year of birth.

A. Create a scatter plot of the data. B. Draw in the line of best fit to represent the data. C. Determine the equation of the line.

D. Use the equation to predict the life expectancy of someone born in the year 2015.

Year Born

Life Expectancy (yrs)

1900 47

1910 50

1320 54

1930 60

1940 63

1950 68

1960 70

1970 71

1980 74

1990 75

2000 77


A boy’s height was measured every year from age 2 until age 9 and is given in the table below.

A. Create a scatter plot to represent the data. B. Describe the association between the data. C. Draw a line to fit the data. D. Based on this line, how tall will the boy be when he is 13 years old?

HEIGHT (cm)

AGE (yrs)

88 2

92 3

103 4

106 5

117 6

121 7

125 8

136 9


The table below shows the amount of tips earned according to the number of hours worked.

A. Create a scatter plot to represent the data. B. What association does the data represent? C. Which of the following equations could be the equation for the line of best fit? Explain why.

A) y = 16x + 14 B) y = -16x + 14

Hours Tips (in dollars)

2 36

3 62

6 120

8 148

9 165

12 202

14 240

16 290

20 325


Determine which of the following tables of values is represented by the given

scatter plot.

A.

Avg. Temp. 82 84 86 86 87 88 89 92 94 94 96

# Visitors 80 250 350 400 125 500 550 425 450 650 600

B.

Avg. Temp. 82 84 86 86 87 88 89 92 94 94 96

# Visitors 80 225 300 360 120 450 525 450 515 600 555

C.

Avg. Temp. 82 84 86 86 87 88 89 92 94 94 96

# Visitors 80 225 400 460 220 350 425 350 415 500 455

D.

Avg. Temp. 82 84 86 86 87 88 89 92 94 94 96

# Visitors 80 200 300 400 100 400 500 400 500 600 600


Which of the following equations could be used to represent a set of data with a positive linear association?

A. y = -3x + 2 B. y = 3x +2

C. 𝑦 = −3𝑥2 + 2 D. 𝑦 = 3𝑥2 + 2


For the given scatter plot A. Identify the association shown. B. Does the data show any outliers? If so, what does this point represent?


Evaluate the function table and corresponding scatter plot shown below.

Which statement best describes the relationship between a baby’s weight and age?

A. The baby’s weight grows unevenly.

B. There is only a slight relationship between weight and age.

C. There is a strong causal relationship between weight and age.

D. There is a strong positive relationship between weight and age.



Write at least two statements that describe the association between the year and the time (in seconds) it took the men to run the 1500 m race for the gold medal.


11. ES 4, Demonstrator 2, Standard (8.SP.3)

Which of the following scatter plots shows the best fit line for the data?

A. B.

C. D.

.


For the following scatter plots, tell how the slope and y-intercept of the fitted line would need to change in order for the line to be the best fit line.


A. For each of the following scatter plots draw in the line of best fit. B. In the space provided, classify each scatter plot as having either no

relationship, a positive relationship, or a negative relationship.


15. ES 4, Demonstrator 2, Standard (8.SP.3) Determine which point is an outlier when four new points with the coordinates of (15, 16), (25, 10), (30, 32), and (45, 44) are added to the graph below.


During a particular summer, Andrew’s Car Wash recorded the number of cars washed each week. A scatter plot was created, and a line was fit to the data. The equation to model this line is y = 2.25x

A. What does the slope of this line represent? B. What does the y-intercept of this line represent?


A fitness trainer collected data comparing the resting heart rate in beats per minute and the hours of exercise for one of his clients. The data is given in the scatterplot below and is modeled by the fitted line equation y = - 4.17x + 80

A. What does the y-intercept of this line represent? B. What does the slope of this line represent?


Given the scatter plot and fitted line below, complete the following statements.

As a student’s math score ___________ his English score ___________.


The graph below show the relationship between the amount of hours worked on a subject and the grade received in that subject. This relationship is modeled by the equation y = 7.5x + 55, where x represents the hours worked, and y represents the reported grade. Refer to the graph and the equation to complete each statement.

Reported grades _________ as time worked ___________.

There is a _________ association between grades and hours worked.

The slope of the line is __________. The units of the slope are __________ per _________.

The initial value is _______. This means the reported grade was ________ when _______.



A. Two pets are adopted for every 3 TV Ads aired. B. As the number of TV Ads increases the number of adoptions increases. C. Before any ads were aired, 5 pets were adopted. D. As the number of TV Ads increases the number of adoptions decreases.