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Common Core High School Functions Teaching and Learning Resources

Domain: BF: Building Functions

Common Core Math

Select the cluster for resources on this page:

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BF-A: Build a function that models a relationship between two quantities

Standards:

 

Technology-enhanced investigations:

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

arithmetic sequence explicit function geometric sequence model
composition exponent rules inverse function recursive formula for a sequence
explicit formula for a sequence function operations logarithm rules transformations

 

PhET Interactive Simulations: Function Builder. Aligns with BF-A.1 and BF-B.4.

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

Study.com: Algebra: Sequences and Series: This chapter contains seven video lessons, each of which includes sample problems and a short quiz.  Videos define sequences and series, how to find and classify arithmetic and geometric sequences, summation notation and mathematical series, and how to calculate arithmetic and geometric series with practice problems on these latter calculations provided.  There is a chapter multiple choice test following the last video.  Use all to address BF-A.2.

LearnZillion:

Southeast Comprehensive Center of SEDL: Video: Build a function that models a relationship between two quantities: This video aligns with standard BF-A.1.a.  View online or download.

MIT BLOSSOMS: Video lesson with additional teacher and learner resources.  Description is from the video summary. 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.

Purple Math:

Shodor Interactivate: Introduction to Arithmetic and Geometric Sequences: Lesson introduces learners to these concepts.  Sequencer is the virtual manipulative for students to explore further through producing sequences by varying the starting number, multiplier, and add-on.  The numbers in the sequence are displayed on a graph, and they are also listed below the graph.  Use with BF-A.2.

Teaching Channel Video: Ferris Wheel: Trigonometric Functions.  Lesson objectives: Model how a trigonometric function describes the relationship of a Ferris wheel rider as the wheel spins at a constant rate with relationship to the height of the rider from the ground.  Discern the relationship between the given measure and the period, phase, offset and amplitude of a cosine function.  Questions for learners to consider are included.  Use with BF-A.1.b, BF-B.3, and TF-A.1.

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

YouTube.com: Recognizing Patterns: Video to review arithmetic, geometric, powers, inductive reasoning patterns.  Use with BF-A.2.

Multiple Choice:

Study.com: Algebra: Sequences and Series chapter multiple choice test.  Learners should have completed the chapter  Sequences and Series with its seven video lessons prior to completing this test.  Use to address BF-A.2.

Constructed-response:

Algebra Lab:

Khan Academy: Practice questions with videos.

MATHguide.com:

Performance tasks:

Illustrative Mathematics: Functions:

Inside Mathematics: MARS Tasks:

Mathematics Assessment Project: Standards: High School: Functions:

Mathematics Vision Project, Secondary 1 Student Edition:

Mathematics Vision Project, Secondary 2 Student Edition:

Mathematics Vision Project, Secondary 3 Student Edition:

NCTM's Reasoning and Sense Making Task Library: Over the Hill includes the task overview, teacher notes for its use in the classroom, and student activity sheet.  Aligns with function standard BF-A.1b, algebra standards CED-A.2, REI-C.6, and mathematical practice standards 1, 4, 5, and 7.

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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BF-B: Build new functions from existing functions

Standards:

 

Technology-enhanced investigations:

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

PhET Interactive Simulations: Function Builder. Aligns with BF-A.1 and BF-B.4.

Study.com: Algebra: Functions: These are video lessons, each of which includes sample problems and a short quiz.  Use the following with BF-B.3 and BF-B.4:

Teaching Channel Video: Ferris Wheel: Trigonometric Functions.  Lesson objectives: Model how a trigonometric function describes the relationship of a Ferris wheel rider as the wheel spins at a constant rate with relationship to the height of the rider from the ground.  Discern the relationship between the given measure and the period, phase, offset and amplitude of a cosine function.  Questions for learners to consider are included.  Use with BF-A.1.b, BF-B.3, and TF-A.1.

LearnZillion:

Saltire Software: Common Core Nuggets: There are four applets addressing vertical and horizontal translations and dilations in graphing, which align with BF-B.3.

Study.com: Algebra: Exponentials and Logarithms: There are eight video lessons in this chapter, each of which includes sample problems and a short quiz.  Videos address the basic definitions of exponentials and logarithms, exponential growth and decay, how to evaluate logarithms, logarithm properties and practice problems for those properties, and how to solve exponential and logarithmic equations.  There is a chapter multiple choice test following the last video  Use all the videos with BF-B.5.

A. Dendane: Analyze Math:  Select the following:

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

Thinking Mathematics:

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

National Library of Virtual Manipulatives: Scroll down to Algebra (9-12) and select Function Transformations: Explore how simple transformations affect the graph of a function.

Purple Math: Use with BF-B.

Shodor Interactivate: Function Flyer: This activity allows the manipulation of the constants and coefficients in any function thereby encouraging the user to explore the effects on the graph of the function by changing those numbers.  Good for studying about translations and dilations.

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

Multiple Choice:

Khan Academy: Practice questions with videos.

MathsIsFun.com: Tutorial on the Inverse Functions.  Examples are shown.  Learners then complete 10 multiple choice problems.  Aligns with BF-B.4.

Wolfram Demonstrations Project:

Study.com: Algebra: Exponentials and Logarithms chapter multiple choice test.  Learners should have completed the eight video lessons in this chapter on Exponentials and Logarithms prior to taking this test.  Use with BF-B.5.

Constructed-response:

Algebra Lab: Inverse Functions: Lesson and practice problems finding inverse functions and verifying that two functions are inverses of each other.

Khan Academy: Practice questions with videos.

Zweigmedia.com: Algebra Review Tutorials and examples using multiple choice and fill-in to test understanding.  Learners can also choose to do game versions of some topics.  Use with BF-B.5: Logarithms.

Performance tasks:

Georgia Standards of Excellence Framework: Pre-Calculus Unit 2: Trigonometric Functions.  This unit contains two tasks: Right Triangles and the Unit Circle, and Inverse Trigonometric Functions.  Tasks align to BF-B.4, BF-B.4.d, TF-A.3, TF-A.4, TF-B.6, TF-B.7 and are also related to TF-A.2, TF-B.5, and IF-C.7.e.

Illustrative Mathematics: Functions:

Inside Mathematics MARS Tasks:

Mathematics Assessment Project: Standards: High School: Functions:

Mathematics Vision Project, Secondary 1 Student Edition:

Mathematics Vision Project, Secondary 2 Student Edition:

Mathematics Vision Project, Secondary 3 Student Edition:

NCTM's Reasoning and Sense Making Task Library: Tidal Waves includes the task overview, teacher notes for its use in the classroom, and student activity sheet.  Aligns with BF-B.3, TF-B.5 and mathematical practice standards 1 and 7.

 

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