Common Core Learning Standards - Mr. small's eighth grade ...



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. | |Identify a function as a set of ordered pairs on a graph. | |

|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 relation as a function from a graph, equation, or set of | |

| | |ordered pairs. | |

|Scaffolded Sample Tasks |

|I. The table below shows a relation. |

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|x |

|-5 |

|-3 |

|-1 |

|0 |

|1 |

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|Y |

|-3 |

|-6 |

|0 |

|-3 |

|3 |

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|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. |

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|Domain Range |

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

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

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|[pic] |

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|III. State whether each relation is a function. If it is not a function explain your reasoning. |

|{(5,0), (4,0), (-1,-4), (-8,9)} |

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|_________________________________________________________________________ |

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|x = 1 |

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|Input |

|0 |

|2 |

|4 |

|6 |

|8 |

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|Output |

|4 |

|1 |

|0 |

|1 |

|4 |

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|d.) |

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|e.) |

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|IV. Complete the table of values below using the function [pic]. |

|Graph the function on the coordinate plane. |

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|x |

|y |

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|-1 |

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|0 |

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|2 |

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|-5 |

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|5 |

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|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. |

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|(5, 12) (7, 17) (9, 20) (x, y) |

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|___________________________________________________________________________ |

|___________________________________________________________________________ |

|___________________________________________________________________________ |

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|2) The ordered pairs (x, y) in this table of values do not form a function. |

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|Input |

|Output |

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|-9 |

|15 |

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|3 |

|12 |

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|a |

|-7 |

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|0 |

|b |

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|What could be possible values of a and b? Explain why the values you chose do not form a function. |

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|___________________________________________________________________________ |

|___________________________________________________________________________ |

|___________________________________________________________________________ |

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|3) The following shows an input output table. |

|Input |

|Output |

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|-4 |

|15 |

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|2 |

|12 |

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|3 |

|-7 |

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|11 |

|10 |

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|2 |

|0 |

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|5 |

|15 |

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|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? |

|________________________________________________________________________________________________________ |

|________________________________________________________________________________________________________ |

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|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. | |Write the linear function from a verbal description. | |

|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. | | | |

| | |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 |

|A linear function is graphed below. |

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|[pic] |

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|Complete the table of values for this function. |

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|x |

|y |

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|-6 |

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|-2 |

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|1 |

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|2 |

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|3 |

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|Write the linear equation for this function. y = _____________________________ |

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|What is the slope of this linear function? _________________________________ |

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|What is the y-intercept of this linear function? _____________________________ |

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|What is the x-intercept of this linear function? _____________________________ |

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|II. |

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|x |

|y |

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|-9 |

|-10 |

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|-6 |

|-6 |

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|-3 |

|-2 |

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|3 |

|6 |

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|6 |

|10 |

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|Function A is represented by the following table. |

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|Function B is represented by the following statement. |

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|The value of y is equal to three-fourths of x increased by 2. |

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|When making a comparison between function A and Function B, which of the following choices below is true? |

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|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. |

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|III. Function A is represented by the table below. Function B is represented by the graph below. |

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|x |

|y |

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|-2 |

|-7 |

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|-1 |

|-4 |

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|0 |

|-1 |

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|1 |

|2 |

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|2 |

|5 |

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|Describe a similarity between these two functions. Explain your reasoning. |

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

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|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 = [pic]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. |

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|Who swims faster? _________________ |

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|What evidence do you have to prove your answer? |

|______________________________________________________________________________________________________________________________________________________________________________ |

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|Using the equation y = [pic]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 |

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|Which company works faster and by how many seconds? |

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|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? |

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|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 |

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|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). |

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|Macintosh __________ Cortland __________ Gala __________ |

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|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. | |Identify linear functions as having graphs that are straight | |

|Interpret the equation y = mx + b as defining a linear | |lines. | |

|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 in tables. | |

| | |Compare/contrast linear vs. non-linear functions represented as | |

| | |equations, tables, and graphs. | |

|Scaffolded Sample Tasks |

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|Part A Circle the linear function below. |

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|A B C [pic] D [pic] |

|[pic] |

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|Part B Explain your reasoning on the lines below. |

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|Compare and contrast the graphs below. |

|[pic] [pic] |

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|Label each function as linear or non-linear. |

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|Input |

|1 |

|2 |

|3 |

|4 |

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|Output |

|1 |

|4 |

|9 |

|16 |

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|[pic] |

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|c.) y = x2 + 2 |

|IV. Circle the function below that best represents [pic]? |

|[pic] [pic] [pic] [pic] |

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|Explain your reasoning. |

|_________________________________________________________________________________________________ |

|_________________________________________________________________________________________________ |

|_________________________________________________________________________________________________ |

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|V. |

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|A. |

|B. |

|C. |

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|[pic][pic][pic] |

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

|______________________________________________________________________________________________________________________ |

|______________________________________________________________________________________________________________________ |

|_____________________________________________________________________________________________________________________ |

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|Rigorous Sample Tasks |

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|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. | |Calculate the initial value/y-intercept from a table, graph, equation, | |

|Construct a function to model a linear relationship between two | |or two points. | |

|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. | | | |

| | |Describe the slope and y-intercept from a graph or table in terms of the| |

| | |situation. | |

|Rigorous Sample Tasks |Scaffolded Sample Tasks |

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|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. | |Sketch a graph that has been described verbally. | |

|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. | | | |

| | |Describe the features of a graph (increasing/decreasing, | |

| | |linear/nonlinear, or constant). | |

|Rigorous Sample Tasks |Scaffolded Sample Tasks |

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y

x

[pic]

[pic]

9

8

7

6

5

4

3

2

1

Mary’s Speed

1 2 3 4 5 6 7 8 9

Time (minutes)

Laps Swam

Find the rate of change (slope) for each:

Mary __________ Clark ____________

Cortland

|Months |0 |1 |2 |3 |

|Height (in) |3 |7.5 |12 |16.5 |

Macintosh

y = 5 + 4x

(y is the total height in inches and x is the number of months since planted)

|X |Y |

|1 |1 |

|2 |8 |

|3 |27 |

|4 |64 |

|5 |125 |

Figure B

Figure A

Dist

105

215

330

450

7

13

Minutes

5

10

15

20

Dist

105

210

315

420

7

13

Minutes

5

10

15

20

Dist

100

200

300

400

7

13

Minutes

5

10

15

20

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