Common Core Learning Standards s3

Common Core Learning Standards

GRADE 8 Mathematics

FUNCTIONS

Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Define, evaluate, and compare functions. / Functions / Identify a function as a one-to-one correspondence. / § Function
§ Function rule
§ Input
§ Output
§ Ordered pair(x,y)
§ Coordinate(x,y)
§ Relation
§ One-to-one correspondence
§ Domain
§ range
§ Vertical line test
Find the input/output of function given a value from the domain or a value from the range.
Plot an ordered pair on a coordinate axis.
Define the x-coordinate as the input(domain) and the y-coordinate as the output(range).
8.F.1.
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. / Identify a function as a set of ordered pairs on a graph.
Identify a relation as a function from a graph, equation, or set of ordered pairs.
Scaffolded Sample Tasks
I. The table below shows a relation.
x / -5 / -3 / -1 / 0 / 1
Y / -3 / -6 / 0 / -3 / 3
Part A Identify the domain and range for the relation above. Then list the domain and range in the boxes below and create a mapping diagram for this relation.
Domain Range

Part B Is this relation also a function? Explain your reasoning.

II. This coordinate plane does not represent a function. Name an ordered pair you could remove to make this relation a function. ______

III. State whether each relation is a function. If it is not a function explain your reasoning.
a.) {(5,0), (4,0), (-1,-4), (-8,9)}
b.) ______
c.) x = 1
Input / 0 / 2 / 4 / 6 / 8
Output / 4 / 1 / 0 / 1 / 4
d.)

e.)

IV. Complete the table of values below using the function .
Graph the function on the coordinate plane.
x / y
-1
0
2
-5
5
Rigorous Sample Tasks
1) A relation between two variables consists of the following four ordered pairs. Choose values
for x and y that make the relation a function. Explain why the values you chose form a function.
(5, 12) (7, 17) (9, 20) (x, y)
______
______
______
2) The ordered pairs (x, y) in this table of values do not form a function.
Input / Output
-9 / 15
3 / 12
a / -7
0 / b
What could be possible values of a and b? Explain why the values you chose do not form a function.
______
______
______
3) The following shows an input output table.
Input / Output
-4 / 15
2 / 12
3 / -7
11 / 10
2 / 0
5 / 15
Choose a value from the above table to turn this non-function into a function.
Which value in the above chart can you change to make the relationship a function? ______
What value could you change it to and why will that value make the relationship a function? ______
______
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Define, evaluate, and compare functions. / Properties of functions / Write the linear function from a table of values. / § Slope(m)/rate of change
§ Linear function
§ Table of values
§ Verbal description
§ Point of intersection
§ Parallel
§ Overlapping
§ y/x-intercept
Write the linear function from a graph.
8.F.2.
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. / Write the linear function from a verbal description.
Identify the different properties of a function (slope/rate of change, y-intercept, x-intercept, point of intersection, parallel, overlapping).
Compare the properties of two functions represented in different ways (algebraically vs. table vs. equation vs. verbal description).
Scaffolded Sample Tasks
I. A linear function is graphed below.

a.) Complete the table of values for this function.
x / y
-6
-2
1
2
3
b.) Write the linear equation for this function. y = ______
c.) What is the slope of this linear function? ______
d.) What is the y-intercept of this linear function? ______
e.) What is the x-intercept of this linear function? ______
II.
x / y
-9 / -10
-6 / -6
-3 / -2
3 / 6
6 / 10
Function A is represented by the following table.
Function B is represented by the following statement.
The value of y is equal to three-fourths of x increased by 2.
When making a comparison between function A and Function B, which of the following choices below is true?
A Function A has a greater rate of change.
B Function B has a greater rate of change.
C The y–intercepts are not the same.
D The graphs of the linear functions are parallel.
III. Function A is represented by the table below. Function B is represented by the graph below.

x / y
-2 / -7
-1 / -4
0 / -1
1 / 2
2 / 5
Describe a similarity between these two functions. Explain your reasoning.

Describe a difference between these two functions. Explain your reasoning.

IV. Mary and Clark are always in a competition to see who swims faster. They have been training together since they were in middle school. The equation y = x represents how fast Clark can swim, where y is the total number of laps he swam and x is the number of minutes spent swimming. The graph below shows how fast Mary can swim.

Who swims faster? ______
What evidence do you have to prove your answer?
______
Using the equation y = x determine how long would it take Clark to swim 15 laps?
V. Nascar drivers not only have the tough job of driving in the races they also have to help hire pit crew. Sal is the manager of Grease Lightening pit crew and on average their drivers take 8 pit stops for a total pit time of 360 seconds all together. Cole is the manager of Fender pit crew and the equation below represents the total amount of time in seconds his drivers spend in a pit stop (y) based on how many stop they make (x).
y = 51x
Which company works faster and by how many seconds?
If each of their drivers needed to make 12 pit stops in a race, how much time would the drive spend at the pit stops?
Grease Lightening ______Fender ______
Rigorous Sample Tasks
Mr. Jenkins recently planted a crop of trees in his orchard. He planted three different types of apple trees, Macintosh, Gala, and Cortland. Below is the information on how the trees are doing since he planted them

Which tree was the tallest when the trees were planted?
Which of the trees is growing the fastest? How do you know?
How tall will each tree be at the end of 6 months? (Show your work).
Macintosh ______Cortland ______Gala ______
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Define, evaluate, and compare functions. / Defining linear functions / Identify a linear function as y=mx + b. / § linear function
§ non-linear function
§ ordered pairs(x,y)
Identify functions that are not linear from equations tables, and graphs.
8.F.3.
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. / Identify linear functions as having graphs that are straight lines.
Identify linear functions in tables.
Compare/contrast linear vs. non-linear functions represented as equations, tables, and graphs.
Scaffolded Sample Tasks

I. Part A Circle the linear function below.
A B C D

Part B Explain your reasoning on the lines below.

II. Compare and contrast the graphs below.

III. Label each function as linear or non-linear.
a.)
Input / 1 / 2 / 3 / 4
Output / 1 / 4 / 9 / 16
b.)
c.) y = x2 + 2
IV. Circle the function below that best represents ?

Explain your reasoning.
______
______
______
V.
A. / B. / C.

Which one of the coordinate planes above shows the function y=4x-3 correctly graphed? On the lines below, explain your reasoning.
______
______
______
Rigorous Sample Tasks

Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Use functions to model relationships between quantities. / Linear function models / Write a linear function rule for a given relationship. / § Function
§ Function rule
§ Linear
§ Y-intercept
§ Initial value
§ Slope(m)
§ Rate of change
§ Ordered pair(x,y)
§ Input
§ Output
Calculate the slope/rate of change from a table, graph, equation, or two points.
8.F.4.
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. / Calculate the initial value/y-intercept from a table, graph, equation, or two points.
Describe the slope and y-intercept from a graph or table in terms of the situation.
Rigorous Sample Tasks / Scaffolded Sample Tasks
Common Core Learning Standards / Concepts / Embedded Skills / Vocabulary
Use functions to model relationships between quantities. / Interpreting graphs / Identify the type of function given a graph. / § Function
§ Linear
§ Non-linear
§ Slope (m)
§ Qualitative
§ Increase/decrease
§ Independent
§ Dependent
§ Constant
§ Y-intercept
Describe the qualitative functional relationship given a graph.
8.F.5.
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. / Sketch a graph that has been described verbally.
Describe the features of a graph (increasing/decreasing, linear/nonlinear, or constant).
Rigorous Sample Tasks / Scaffolded Sample Tasks