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Common Core Math

High School Functions Teaching and Learning Resources

Domain: IF: Interpreting Functions

Common Core Math

Select the cluster for resources on this page:

  • IF-A: Understand the concept of a function and use function notation

  • IF-B: Interpret functions that arise in applications in terms of the context

  • IF-C: Analyze functions using different representations

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IF-A: Interpret the structure of expressions.

Standards:

  • IF-A.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  • IF-A.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • IF-A.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

 

Technology-enhanced investigations:

Mathwords.com: Math Dictionary: Key vocabulary for this domain.  Use with IF-A, IF-B, IF-C:

amplitude exponential function maximum of a function recursive formula for a sequence
asymptote exponential growth minimum of a function step function
average rate of change extremum period of a periodic function symmetric
domain function piecewise function x-intercept
end behavior function operations range y-intercept
exponential decay increasing function and decreasing function rational function zero of a function

 

CK-12: Algebra: Concepts, videos, and practice problems for learners to complete.

Ron Blond: Mathematics Glossary: Select grades 10-12 and keyword: function. Multiple means of representation to explain concepts.  JAVA applets are included.  Use with IF-A.1.

Studygeek.org: Domain and Range Calculator Online, powered by Wolfram Alpha.  Students benefit from seeing the use of function notation in the answer and seeing the graph of the function.  Use with IF-A.1.

Study.com: Algebra: Functions: These are video lessons, each of which includes sample problems and a short quiz.  Use the following with IF-A.1 and IF-A.2:

LearnZillion:

  • Lesson set: Identify functions and find domain and range.  This is a series five video lessons: Identify functions given sets, mappings, and real world scenarios, identify functions using tables and graphs, identify functions using algebra, find the domain and range of a function, understand graphs of f(x).  Aligns with IF-A.1.
  • Lesson set: Use and interpret function notation; evaluate functions.  This is a series  of four video lessons: Understand function notation, evaluate functions written in function notation, understand restrictions on functions in terms of domain and range, evaluate mathematical situations by analyzing the domain and range of functions.  Aligns with IF-A.2.
  • Lesson set: Evaluate functions, use function notation, and interpret statements that use function notation.  This is a series of five video lessons: Understand functions in terms of inputs and outputs, understand f(x), evaluate a function given an input value, put restrictions on a domain, interpret functions in context.  Aligns with IF-A.2.
  • Lesson set: Understand sequences.  This is a series of seven video lessons: Represent an arithmetic sequence as an explicit rule, represent explicit rules as linear functions, use explicit rules to write sequences recursively, explore the Fibonacci sequence as an example of a recursive sequence, represent a geometric sequence as an explicit rule, represent an explicit rule as an exponential function, write a geometric sequence recursively.  Aligns with IF-A.3.
  • Lesson set: Recognize that sequences are functions and identify their features.  This is a series of four video lessons: Understand sequences as functions, create a recursive formula, create an explicit formula, apply recursive and explicit formulas.  Aligns with IF-A.3.

Math Open Reference: Graphical Function Explorer: Graph up to three functions on the same set of axes using this free online graphing tool.

McDougal Littell ClassZone, Algebra 2, 2011: Select resources in Ch. 2 Linear Equations and Functions for interactive practice: Animations (Virtual manipulatives, including Exploring Functions and Relations), Games/Vocabulary Flashcards, and PowerPoint lesson examples, and interactive problems within the eWorkbook. See multiple choice below for related sections to use within the eWorkbook (Do section 2.1).  Use with IF-A.1.

Purplemath: Functions versus Relations, including domain and range.  Use with IF-A.1.

Shodor Interactivate:

  • Vertical Line Test: This test helps to determine if the graph of an equation is that of a function.
  • Graphit: Create graphs of functions and sets of ordered pairs on the same coordinate plane. This is like a graphing calculator with advanced viewing options.

National Library of Virtual Manipulatives: Scroll down to Algebra (9-12) and select the following:

  • Function Machine: Explore the concept of functions.  Input a value into the machine and observe the output.
  • Grapher: A tool for graphing and exploring functions.

NCTM E-Examples from Principles and Standards for School Mathematics: 7.2 Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body.  This is a three-part investigation with three applets for learners to manipulate parameters as they investigate the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body.

NCTM Illuminations: Counting the Trains: In this unit, students will investigate a relationship between recursive functions and exponential functions.

MIT BLOSSOMS: Video lessons with additional teacher and learner resources.  Descriptions are from the video summaries.

  • Amazing Problems: Arithmetic and Geometric Sequences: "This lesson aims to introduce arithmetic sequences and geometric sequences to secondary school students. It uses two wonderful problems to do that and it explains the laws of those two kinds of sequences."  Aligns with IF-A.3, BF-A.1.a, and BF-A.2.
  • The Power of Exponentials, Big and Small: "Exponential growth is keenly applicable to a variety of different fields ranging from cell growth in biology, nuclear chain reactions in physics to computational complexity in computer science. In this lesson, through various examples and activities, [the presenters] have tried to compare exponential growth to polynomial growth and to develop an insight about how quickly the number can grow or decay in exponentials."  Aligns with Algebra standards SSE-B.3.c and CED-A.2 and Function standards IF-A.3, IF-C.7.(a, c, e), IF-C.8.b, and LE-A.1.(a, c).

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives:

Zweigmedia.com:  Tutorials and examples using fill-in or multiple choice to test understanding.  Learners can also choose to do game versions of some topics.  Use with IF-A.1 and IF-A.2: Functions from the Numerical, Algebraic, and Geometric Viewpoints

Multiple Choice:

Glencoe Online Learning Center, Algebra 2 (2010) self-check quizzes:

Khan Academy: See Algebra I: Functions and Precalculus: Sequences, Series, and Induction: Practice questions with videos.

McDougal Littell ClassZone, Algebra 2, 2011: Ch. 2.1 Quiz: Represent Relations and Functions: Use with IF-A.1.

OpenEd:

Constructed-response:

Khan Academy: See Algebra I: Functions, Algebra 2 (includes several sections on functions): Practice questions with videos.

Louisiana Department of Education: Multiple choice and constructed response Sample Test Items: Algebra 1 (from 2016-2017): Constructed Response samples: Falling Rock Function aligns with IF-A.2; Water Spray aligns with IF-B.4; and Solving Quadratics aligns with algebra standard REI-B.4.

Math Warehouse: Algebra: Relations, Functions, Domain, Range etc.  The section includes lessons, interactive demonstrations, and practice problems and also includes evaluating functions, inverse of a function (including an applet), vertical line test, one-to-one functions, composition of functions, operations (add, subtract, multiply) functions, and recursive sequences/functions.  Aligns with IF-A.1, IF-A.2, and IF-A.3.

Performance tasks:

Illustrative Mathematics: Functions:

Inside Mathematics: MARS task: Printing Tickets: This task aligns with standards IF-A.2, IF-B.4, and IF-C.9

Mathematics Assessment Project: Standards: High School: Functions: http://map.mathshell.org/stds.php?standardid=1448

Mathematics Vision Project, Secondary 1 Student Edition:

  • Module 4: Linear and Exponential Functions: This module contains 10 classroom tasks.  Function standards addressed in Module 3 include IF-A.3, IF-C.7, LE-A.1, LE-A.2, LE-A.3, LE-B.5, and BF-A.1, BF-A.2.  Task 1: Connecting the Dots aligns with function standard IF-A.3.
  • Module 5: Features of Functions: This module contains nine classroom tasks.  Function standards addressed in Module 4 include IF-A.1, IF-A.2, IF-A.3, and IF-B.4, IF-B.5, IF-C.7, and BF-A.1.  Complete the following:
  • Task 7: A Water Function aligns with IF-A.1
  • Task 8: To Function or Not to Function aligns with standards IF-A.1 and IF-A.3.
  • Task 4: Water Park; Task 5: Pooling it Together; Task 6: Interpreting Functions; and Task 9: Match That Function align with IF-A.2.

WeTeachNYC, developed by the New York City Department of Education: High School Algebra: Aussie Fir Tree: Unit Overview: “The Aussie Fir Tree task is a culminating task for a 2-3 week unit on algebra that uses the investigation of growing patterns as a vehicle to teach students to visualize, identify and describe real world mathematical relationships. Students who demonstrate mastery of the unit are able to solve the Aussie Fir Tree task in one class period.” Function standards addressed include IF-A.3, BF-A.1 and BF-A.1.a.  Algebra standards include CED-A.1, REI-B.4 and REI-B.4.a.  Mathematical Practices standards include MP.1, MP.3, MP.4, MP.6, and MP.7.

 

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IF-B: Interpret functions that arise in applications in terms of the context

Standards:

  • IF-B.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
  • IF-B.5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
  • IF-B.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Technology-enhanced investigations:

Graphing Calculator is free from Desmos.com and compatible with any computer or tablet.  Examples of graphs possible are also at Chrome.Google, where you can also launch the app.

Concord Consortium STEM resources: Mathematics:  Each of the following includes an applet, student activity, teacher lesson plan, and student assessment.

  • Graphing Quadratic Equations: Aligns with IF-B.4, IF-C.7.a, and IF-C.8.a.
  • Quadratic Equations in Vertex Form: Aligns with IF-B.4, IF-C.7.a, and IF-C.8.a.
  • Quadratic Word Problems Part 1: Students solve two problems involving the motion of projectile objects, modeling the motion using quadratic equations.  Students graph parabolas and use the graphs to answer questions about projectile objects. Students identify the maximum heights of the moving objects and discover how long each object is in the air before hitting the ground.  Aligns with IF-B.4, and IF-C.7.a.
  • Quadratic Word Problems Part 2: Students solve two problems involving the motion of projectile objects, modeling the motion using quadratic equations.  One problem involves profits from a business and the other, water draining from a bathtub.  Aligns with IF-B.4, and IF-C.7.a.

A. Dendane: Analyze Math: Periodic Functions: Applet to explore and understand what it means to be a periodic function.  Aligns with IF-B.4.

LearnZillion:

Math Open Reference: Graphical Function Explorer: Graph up to three functions on the same set of axes using this free online graphing tool.

MIT BLOSSOMS: Video lessons with additional teacher and learner resources.  Descriptions are from the video summaries.

  • The Quadratic Equation: It’s Hip to Be Squared: "The lesson begins with three quadratics and their graphs (three parabolas):  y = x2 - 2x + (0 or 1 or 2). The prerequisite or co-requisite is some working experience with algebra, like factoring x2 -2x into x(x-2). The objective is to connect four things: the formula for y, the graph of y (a parabola), the roots of y and the minimum or maximum of y."  Aligns with Algebra standards SSE-B.3.a, CED-A.2, and REI-B.4.b and Function standards IF-B.4, IF-C.7.a, IF-C.8.a, BF-B.3.
  • Tragedy of the Commons: "This lesson introduces students to the “Tragedy of the Commons,” an extended metaphor for problems of shared environmental or man-made resources that are overused and eventually depleted. In this metaphor, shared resources are compared to a common grazing pasture, or “commons,” on which any dairy farmer can graze as many cows as he/she wishes. If too many cows are added to the commons, they will overeat the grass in the pasture and the shared resource will become depleted – a disadvantage to everyone. In this lesson, students will be inspired to think about possible solutions to this problem."  Aligns with Algebra standard SSE-B.3.c and Function standards IF-B.4, IF-C.8.b, LE-A.1.a, LE-A.3, and LE-B.5.
  • Free Fall: "This video lesson is an example of "teaching for understanding" in lieu of providing students with formulas for determining the height of a dropped (or projected) object at any time during its fall. The concept presented here of creating a chart to organize and analyze data collected in a simple experiment is broadly useful."  Aligns with Algebra standard CED-A.2 and Function standards IF-B.6, IF-C.7.a, and LE-A.1.a.

Shodor Interactivate:

  • Graphit: Create graphs of functions and sets of ordered pairs on the same coordinate plane. This is like a graphing calculator with advanced viewing options.
  • Derivate: View the graph and the equation of the line tangent to any function at any point on the function.  This manipulative can be used with IF-B.6.
  • Incline: "This activity demonstrates the relationship between dependent and independent variables by allowing students to explore a real life example. After adjusting the biker's path and the initial velocity, the user can analyze the resulting speed vs. position graph."  Use with IF-B, and Algebra strand CED-A, SSE-A.

NCTM Illuminations:

  • Domain Representations: In this lesson, students use graphs, tables, number lines, verbal descriptions, and symbols to represent the domain of a function.
  • Drug Filtering: In this lesson, students observe a model of exponential decay on how kidneys filter blood and after performing calculations of the amount of a drug left in the body over time, they make and analyze a graphical representation of the exponential function.
  • Growth Rate: In this lesson, “Given growth charts for the heights of girls and boys, students will use slope to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.”

Purplemath: Meaning of Slope and Y-Intercept

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.

Multiple-choice:

Khan Academy: See Algebra I: Functions: Graphing Functions, Domain and Range, and Analyzing Linear Functions, and Algebra 2 (includes several sections on functions): Practice questions with videos.

Constructed-response:

Louisiana Department of Education: Multiple choice and constructed response Sample Test Items: Algebra 1 (from 2016-2017): Constructed Response samples: Falling Rock Function aligns with IF-A.2; Water Spray aligns with IF-B.4; and Solving Quadratics aligns with algebra standard REI-B.4.

Khan Academy: See Algebra I: Functions: Practice questions with videos. Range of a function: Aligns with IF-B.5.

OpenEd:

Performance tasks:

Illustrative Mathematics: Functions:

Inside Mathematics: MARS Tasks:

  • Quadratic: Students work with a quadratic function in various forms. This task aligns with function standards IF-B.4, IF-C.7, IF-C.8 and algebra standard REI-B.4.
  • Graphs (2007): Students work with linear and quadratic functions, their graphs and equations.  This task aligns with function standards IF-B.4, IF-B.5, IF-C.7 and IF-C.9.

Mathematics Assessment Project: Standards: High School: Functions: http://map.mathshell.org/stds.php?standardid=1448 Task 430: Functions and Everyday Situations

Mathematics Common Core Toolbox: PARCC Prototype Project:  Under High School Tasks, select:

  • Isabella's credit card: Students see a page resembling a spreadsheet.  They "consider a financial context requiring multiple calculations for each month ... Students create a recursive process for calculating values within the context." They "calculate values and complete the table for the second and third months. ... the task allows for the use of either the recursive process or a description of steps that lead to a solution." Finally, they "extend their use of the recursive process or sequence of steps to find additional values. They identify the important values and interpret those values within the context to answer the questions." This three-part task aligns with function standards BF-A.1, IF-B.4, and mathematical practice standards MP.2, MP.4 and MP.5.

Mathematics Vision Project, Secondary 1 Student Edition:

  • Module 4: Linear and Exponential Functions: This module contains 10 classroom tasks.  Task 2: Sorting Out the Change; and Task 3: Where’s My Change? align with function standard IF-B.6.  Other function standards addressed in Module 3 include IF-A.3, IF-C.7, LE-A.1, LE-A.2, LE-A.3, LE-B.5, and BF-A.1, BF-A.2.
  • Module 5: Features of Functions: This module contains nine classroom tasks.  Function standards addressed in Module 4 include IF-A.1, IF-A.2, IF-A.3, and IF-B.4, IF-B.5, IF-C.7, and BF-A.1. Task 1: Getting Ready for a Pool Party; Task 2: Floating Down the River; Task 3: Features of Functions; Task 4: Water Park; Task 5: Pooling it Together; Task 6: Interpreting Functions; and Task 9: Match That Function align with both IF-B.4 and IF-B.5.

Mathematics Vision Project, Secondary 2 Student Edition:

  • Module 4: More Functions, More Features: This module contains 7 classroom tasks.  Function standards addressed in Module 4 include IF-C.7b within tasks 1-4; BF-B.4 in tasks 5-6; and IF-B.4 in task 7.

Mathematics Vision Project, Secondary 3 Student Edition:

  • Module 3: Polynomial Functions: This module contains 8 classroom tasks.  Task 2 and task 6 align to function standard IF-B.4; task 3 includes standard IF-B.6.
  • Module 4: Rational Functions: This module contains 7 classroom tasks.  Multiple standards are addressed. Standards IF-B.4, IF-B.5, IF-B.6 are among those found in tasks 1-2, 4-7.

 

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IF-C: Analyze functions using different representations

Standards:

  • IF-C.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
    • IF-C.7.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
    • IF-C.7.b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
    • IF-C.7.c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
    • (+) IF-C.7.d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
    • IF-C.7.e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
  • IF-C.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
    • IF-C.8.a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
    • IF-C.8.b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
  • IF-C.9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

 

Technology-enhanced investigations:

Concord Consortium STEM resources: Mathematics:  Each of the following includes an applet, student activity, teacher lesson plan, and student assessment.

  • Graphing Quadratic Equations: Aligns with IF-B.4, IF-C.7.a, and IF-C.8.a.
  • Quadratic Functions in Vertex Form: Aligns with IF-B.4, IF-C.7.a, and IF-C.8.a.
  • Quadratic Word Problems Part 1: Students solve two problems involving the motion of projectile objects, modeling the motion using quadratic equations.  Students graph parabolas and use the graphs to answer questions about projectile objects. Students identify the maximum heights of the moving objects and discover how long each object is in the air before hitting the ground.  Aligns with IF-B.4, and IF-C.7.a.
  • Quadratic Word Problems Part 2: Students solve two problems involving the motion of projectile objects, modeling the motion using quadratic equations.  One problem involves profits from a business and the other, water draining from a bathtub.  Aligns with IF-B.4, and IF-C.7.a.
  • Graphing Exponential Equations: Learn about exponential functions by graphing various equations representing exponential growth and decay. Graph these functions by connecting ordered pairs on x-y axes.  Aligns with IF-C.7.e, IF-C.8.b and BF-B.3.
  • Exponential Growth: Learn about exponential growth in real-world situations. Problems involve the application of compound interest and exponential population growth.  Aligns with IF-C.7.e, IF-C.8.b and BF-B.3.
  • Exponential Decay: Learn to use exponential decay equations and interpret graphs of real-world situations.  Problems involve the application of depreciation of an asset and radioactive decay.  Aligns with IF-C.7.e, IF-C.8.b and BF-B.3.

Ohio Resource Center on YouTube: Tutorials for High School Mathematics.  Select the following, which align with IF-C.7:

Study.com: Algebra: Matrices and Absolute Value:  This is a series of eight video lessons, six of which are on absolute value.  Each video also includes sample problems and a short quiz.  Absolute value videos begin with the question, What is Absolute Value? and then include how to evaluate, solve, and graph absolute value equations.  Graphing also includes transformations, dilations, and reflections of absolute value equations.  Aligns with IF-C.7.

LearnZillion:

Thinking Mathematics:

A. Dendane: Analyze Math:  Select the following, which align with IF-C.7:

  • Graphs of Quadratic Functions: A video showing the use of an applet to explain the effects of parameters a, b and c included in the definition of a quadratic function of the form f(x) = a x2 + b x + c on the properties of graph, which is a parabola, of the function such opening up or down, the vertex and the range of values.
  • Explore Quadratic Functions: HTML5 applet for learners to explore the properties of the quadratic equation of the form f(x) = a x2 + b x + c by changing the parameters a, b, and c.
  • Find the Domain of Rational Functions: A video using examples to demonstrate how to find the domain of rational functions.
  • Graphs of Rational Functions: A video showing the use of an applet to explain the effects of parameters a, b, c and d included in the definition of a rational function of the form f(x) = (a x + b) / (c x + d) on the properties of graph of the function such as horizontal and vertical asymptotes.
  • Rational Functions: Applet for learners to explore rational functions and the properties of their graphs such as domain, vertical and horizontal asymptotes, x and y intercepts
  • Exponential Functions: HTML5 applet to explore the graphs of exponential functions.  Learners change parameters a, b, c, d, and B in equations of the form f(x)= a(Bb(x+c))+ d.
  • Logarithm Functions: HTML5 applet to explore graphs of logarithms of the form f(x)= a logB( b( x + c) ) + d by changing parameters a, b, c, d, and base B.
  • Square Root Functions: Interactive applet to explore graphs of square root functions of the form f(x) = a SQRT(x-c) + d.  Learners change parameters a, c, and d and can also determine characteristics of graphs such as domain, range, x intercept, y intercept.  There is access to a tutorial with examples of square root graphs, including square roots of quadratics.
  • Cube Root Functions: Interactive applet to explore graphs of square root functions of the form f(x) = a (x-c)1/3 + d.  Learners change parameters a, c, and d and can also determine characteristics of graphs such as domain, range, x intercept, y intercept.

Math Open Reference: Graphical Function Explorer: Graph up to three functions on the same set of axes using this free online graphing tool.

MIT BLOSSOMS: Video lessons with additional teacher and learner resources.  Descriptions are from the video summaries.

  • The Quadratic Equation: It’s Hip to Be Squared: "The lesson begins with three quadratics and their graphs (three parabolas):  y = x2 - 2x + (0 or 1 or 2). The prerequisite or co-requisite is some working experience with algebra, like factoring x2 -2x into x(x-2). The objective is to connect four things: the formula for y, the graph of y (a parabola), the roots of y and the minimum or maximum of y."  Aligns with Algebra standards SSE-B.3.a, CED-A.2, and REI-B.4.b and Function standards IF-B.4, IF-C.7.a, IF-C.8.a, BF-B.3.
  • Free Fall: "This video lesson is an example of "teaching for understanding" in lieu of providing students with formulas for determining the height of a dropped (or projected) object at any time during its fall. The concept presented here of creating a chart to organize and analyze data collected in a simple experiment is broadly useful."  Aligns with Function standards IF-B.6, IF-C.7.a, LE-A.1.a, and Algebra standard CED-A.2.
  • The Power of Exponentials, Big and Small: "Exponential growth is keenly applicable to a variety of different fields ranging from cell growth in biology, nuclear chain reactions in physics to computational complexity in computer science. In this lesson, through various examples and activities, [the presenters] have tried to compare exponential growth to polynomial growth and to develop an insight about how quickly the number can grow or decay in exponentials."  Aligns with Algebra standards SSE-B.3.c and CED-A.2 and Function standards IF-A.3, IF-C.7.(a, c, e), IF-C.8.b, and LE-A.1.(a, c).
  • Flu Math Games: "This video lesson shows students that math can play a role in understanding how an infectious disease spreads and how it can be controlled."  Additional simulations are included.  Aligns with Algebra standards SSE-B.3.c and REI-A.1; Function standards IF-C.8.b, BF-B.4.a, and LE-A-1.(a, c); and Statistics and Probability standards ID-B.6.a, IC-A.1, IC-B.4, CP-A.2, and MD-A.1.
  • The Towers of Hanoi: Experiential Recursive Thinking: "This lesson is about the Towers of Hanoi problem, a classic famous problem involving recursive thinking to reduce what appears to be a very large and difficult problem into a series of simpler ones.  The learning objective is for students to begin to understand recursive logic and thinking, relevant to computer scientists, mathematicians and engineers."  Aligns with Algebra standard SSE-B.3.c, and Function standards IF-C.8.b and LE-A.1.a.
  • Tragedy of the Commons: "This lesson introduces students to the “Tragedy of the Commons,” an extended metaphor for problems of shared environmental or man-made resources that are overused and eventually depleted. In this metaphor, shared resources are compared to a common grazing pasture, or “commons,” on which any dairy farmer can graze as many cows as he/she wishes. If too many cows are added to the commons, they will overeat the grass in the pasture and the shared resource will become depleted – a disadvantage to everyone. In this lesson, students will be inspired to think about possible solutions to this problem."  Aligns with Algebra standard SSE-B.3.c and Function standards IF-B.4, IF-C.8.b, LE-A.1.a, LE-A.3, and LE-B.5.

Purple Math:

Teacher Tube videos:

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 94 manipulatives addressing IF-C.7, 26 manipulatives for IF-C.8, and 2 manipulatives for IF-C.9.  Among those:

Multiple-choice:

A. Dendane: Analyze Math: Graphs of Rational Functions: Self-check quiz.  Learners are given an equation of a function and select the correct graph of it.  Learners need to write down their answers and then check from answers provided.

CK-12: Analysis of Rational Functions: Finding restrictions, vertical asymptotes, breaks, end behavior, and intercepts: Practice questions with review content and video.  Aligns with IF-C.7.d.

Glencoe Online Learning Center, Algebra 2 (2010) self-check quizzes:

Khan Academy: See Algebra 1: Functions; Algebra 2 (includes several sections on functions): Practice questions with videos.

McDougal Littell ClassZone, Algebra 2, 2011:

OpenEd:

  • Graphs of functions: 5 questions that combine multiple choice and free response.  Includes related review resources.  Aligns with IF-C.7.
  • Equivalent forms of functions: 5 questions that combine multiple choice and free response.  Includes related review resources.  Aligns with IF-C.8.
  • Comparing functions: 5 questions that combine multiple choice and free response.  Includes related review resources.  Aligns with IF-C.9.

Constructed-response:

Khan Academy: Practice questions with videos.

Math Warehouse: Converting the Equation of a Parabola: Vertex and Standard Forms: Tutorial and Practice Problems converting vertex form to standard form, and standard form to vertex form using completing the square method.  Aligns with IF-C.8.

Performance tasks:

Exponential functions on the Web: This site contains links to several lessons on the web with specific examples of exponential functions in real world scenarios.

Illustrative Mathematics: Functions:

Inside Mathematics: MARS Tasks:

  • Functions (pdf) or see all MARS Tasks: Functions & Relations: Course 1 Algebra: Scroll down the page to select Functions: Learners work with graphs of linear and non-linear functions.  This task aligns with function standards IF-C.7, IF-C.9 and LE-A.3.
  • Sorting Functions (pdf) or see all MARS Tasks: Functions & Relations: Course 1 Algebra: Scroll down the page to select Sorting Functions: Learners match graphs of four functions with their equations, tables, and rules.  This task aligns with function standard IF-C.7 and algebra standard CED-A.2.
  • Quadratic: Students work with a quadratic function in various forms.  This task aligns with function standards IF-B.4, IF-C.7, IF-C.8 and algebra standard REI-B.4.
  • Graphs (2007): Students work with linear and quadratic functions, their graphs and equations.  This task aligns with function standards IF-B.4, IF-B.5, IF-C.7 and IF-C.9.

Mathematics Assessment Project: Standards: High School: Functions: http://map.mathshell.org/stds.php?standardid=1448

Mathematics Vision Project, Secondary 1 Student Edition:

  • Module 4: Linear and Exponential Functions: This module contains 10 classroom tasks.  Task 5: Getting Down to Business; and Task 9:  Up a Little, Down a Little align with function standard IF-C.7.  Other function standards addressed in Module 3 include IF-A.3, IF-C.7, LE-A.1, LE-A.2, LE-A.3, LE-B.5, and BF-A.1, BF-A.2.
  • Module 5: Features of Functions: This module contains nine classroom tasks.  Function standards addressed in Module 4 include IF-A.1, IF-A.2, IF-A.3, and IF-B.4, IF-B.5, IF-C.7, and BF-A.1. Task 4: Water Park; Task 5: Pooling it Together; Task 6: Interpreting Functions; and Task 9: Match that Function align with IF-C.7.
  • Module 7: Connecting Algebra and Geometry: This module contains six classroom tasks.  Task 4: Training Day; Task 5: Training Day Part II; and Task 6: Shifting Functions each address the function standards BF-A.1, BF-B.3, and IF-C.9.  The other three tasks address geometry standards GPE-B.4, GPE-B.5, and GPE-B.7.

Mathematics Vision Project, Secondary 2 Student Edition:

Mathematics Vision Project, Secondary 3 Student Edition:

 

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