Eighth Grade Math Domain: Functions Cluster: Define, evaluate, and compare functions.

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Eighth Grade Math

Domain: Functions Cluster: Define, evaluate, and compare functions.

Common Core Standard: 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.

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

Functions y-value x-value

vertical line test input

output rate of change linear function non-linear function

Understand that functions describe relationships where one variable determines a unique value of the other.

Recognize a graph of a function as the set of ordered pairs consisting of an input and corresponding output.

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.

1.) Worksheet to be used as extra practice.

2.) Determining if a relation is a function video to be used within instruction.

3.) Lesson plans with activities and guiding questions on input and output.

1.) https://ccgps.org/8.F.html

http://www.gradeamathhelp.com/supp ort-files/determining-functions-a.pdf

2.)

http://www.youtube.com/watch?fe ature=player_detailpage&v=QvFgtQ _c1WQ

http://www.youtube.com/watch?featur e=player_embedded&v=vO5qqfsWz hc

3.)

http://www.shodor.org/interactivat e/lessons/GraphsAndFunctions/

http://www.shodor.org/interactivate/le ssons/IntroLinearFunction/

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4.)

http://www.mathsisfun.com/sets/f unction.html

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Eighth Grade Math

Common Core Standard: 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.

output rate of change linear function nonlinear function

7.RP.2 Recognize and represent proportional relationships between quantities.

Compare two linear functions each represented a different way and describe similarities and differences in slopes, y-intercepts, and values.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

1.) Within groups students can analyze various forms of a function.

2.) Utilize activities 2 and 3 of this resource on graphing functions and interpreting slope and y-intercept.

3.) Unit that students will be able to recognize, explain, and translate functions numerically, graphically, verbally, and algebraically.

4.) Different representations of functions activity worksheet.

1.)

https://wikis.uit.tufts.edu/confluenc e/pages/viewpage.action?pageId=33 416542

2.)

http://marshallteachers.sandi.net/te acher_sites/honda/peerfolder/FAFol der/The%20Pattern%20and%20Func tion%20Connection.pdf

3.)

https://www.georgiastandards.org/

Common-Core/Common%20Core%20Framew orks/CCGPS_Math_8_8thGrade_Uni t4SE.pdf

4.)

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Common Core Standard: 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 = s

2

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.

output rate of change linear function nonlinear function

Distinguish between linear and non-linear

functions given their algebraic expression, a table, or a graph.

Recognize functions written in the form

y = mx + b are linear and that every linear function can be written in the form

y = mx + b.

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.

1.) Video to use within instruction to interpret functions in slope-intercept form.

2.) Utilize activities 6 and 10 of this resource pertaining to linear and nonlinear functions.

3.) Interactive graphing in slope-intercept form.

1.)

http://www.youtube.com/watch?fe ature=player_embedded&v=NZibBP bk9gQ

http://www.youtube.com/watch?featur e=player_embedded&v=uk7gS3cZVp 4

2.)

http://marshallteachers.sandi.net/te acher_sites/honda/peerfolder/FAFol der/The%20Pattern%20and%20Func tion%20Connection.pdf

3.)

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Eighth Grade Math

Domain: Functions Cluster: Use functions to model relationships between quantities.

Common Core Standard: 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.

linear relationship rate of change slope

initial value y-intercept

Determine and interpret the initial value and rate of change given two points, a graph, a table of values, a geometric representation, or a story problem (verbal description)

of a linear relationship.

Write the equation of a line given two points, a graph, a table of values, a geometric

representation, or a story problem (verbal description) of a linear relationship.

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 table.

1.) Real-world situations to motivate the study of linear functions, their parameters, and behaviors.

2.) Lesson plans to simulate how rate of change and initial values vary.

3.) Utilize activities 7, 8, and 9 of this resource to determine slope and intercept using tables and graphs.

4.) Worksheet to create equations in slope-intercept form.

5.) Matching game for slope and y-intercept.

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http://middlemathccss.files.wor dpress.com/2012/09/8th-

grade-domain-3-writingequationsforlines.pdf

5.)

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Eighth Grade Math

Domain: Functions Cluster: Use functions to model relationships between quantities.

Common Core Standard: 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.

linear relationship rate of change slope

initial value y-intercept

“Tell a story” of the functional relationship represent by a graph such as the one shown here.

Draw the graph of a functional relationship that is described in a “story.”

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional

relationships represented in different ways.

1.) Activities that provide qualitative graph examples and exercises.

2.) Assessment project on qualitative graph lesson.

3.) Students will create stories to go along with qualitative graphs.

1.)

http://www.glencoe.com/sites/ north_carolina/support_studen t/additional_lessons/Course_1/ Qualitative_Graphs_NC_Course _1_SE.pdf

http://www.learner.org/courses/lea rningmath/algebra/session1/pa rt_c/graphs.html

http://opi.mt.gov/pdf/CCSSO/Interp TimeDistance.pdf

http://www.opusmath.com/commo

n-core-standards/8.f.5- describe-qualitatively-the- functional-relationship-between-two-quantities

2.)

http://opi.mt.gov/pdf/CCSSO/In terpTimeDistance.pdf

3.)

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5.) Power point presentation with interactive problems that can be used as a lesson.

http://www.math.wisc.edu/~qdeng/ teaching/math132sum10/hw6.p df

4.)

http://www.youtube.com/watc h?v=Il8hN81Nm-I

5.)

https://www.google.com/url?sa =t&rct=j&q=&esrc=s&source=w eb&cd=7&cad=rja&ved=0CFQQ FjAG&url=http%3A%2F%2Fclass rooms.tacoma.k12.wa.us%2Fsot a%2Ftwaits%2Fdocuments%2Fd ownload%2Falg_1_interpreting _qualitative_graphs_day1_and_ 2.pptx%3Fid%3D86935&ei=8LTJ UfJOktL0BK_SgaAO&usg=AFQjC NF7tCGGyWY9NCkBadSIcWkyd bZwsA