HSF-IF.B.4

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- HSF-IF.B.4For 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.*
- HSF-IF.B.5Relate 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.*
- HSF-IF.B.6Calculate 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.*

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## HSF-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.*

193 Lesson(s)

Big Idea:

#### Algebra is built on axioms and definitions and relies on proofs just as much as geometry.

Standards:

Favorites
(36)

Resources
(19)

Reflections
(2)

### Graphing Systems of Equations

Algebra I »
Unit: Making Informed Decisions with Systems of Equations

Algebra I »
Unit: Making Informed Decisions with Systems of Equations

Big Idea:

#### Students use technology to create and interpret systems of equations graphically!

Standards:

Favorites
(17)

Resources
(25)

Reflections
(1)

### Sketch Graphs I

8th Grade Math »
Unit: INTRODUCTION TO FUNCTIONS

8th Grade Math »
Unit: INTRODUCTION TO FUNCTIONS

Big Idea:

#### Use an engaging video to get kids to connect a verbal description with a concrete application and an abstract representation. It's a pretty cool video - check it out.

Standards:

Favorites
(19)

Resources
(13)

Big Idea:

#### Linear functions can be used to model how a changing quantity is represented in both the graph and equation of a function.

Standards:

Favorites
(10)

Resources
(16)

### Solving Systems by Graphing

Algebra I »
Unit: Systems of Equations

Algebra I »
Unit: Systems of Equations

Big Idea:

#### As students gain confidence in graphing - and interpreting the intersection points on - systems of equations, we continue to see how this skill relates to guess and check.

Standards:

Favorites
(7)

Resources
(21)

Reflections
(1)

### Ahoy again! What can you see now? Building Rational Functions

12th Grade Math »
Unit: Rational Functions and Equations

12th Grade Math »
Unit: Rational Functions and Equations

Big Idea:

#### Students use “spyglasses” again to build context around rational functions and begin to develop an understanding of how a rational function behaves.

Standards:

Favorites
(2)

Resources
(31)

Reflections
(1)

### Modeling With Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### This lesson allows students to make a connection between real-world phenomena and the average rate of change of a quadratic function.

Standards:

Favorites
(13)

Resources
(15)

### Review Workshop: Polynomial Functions and Expressions

Algebra II »
Unit: Polynomial Functions and Expressions

Algebra II »
Unit: Polynomial Functions and Expressions

Big Idea:

#### Tomorrow is the unit test on polynomial functions and expressions. In this lesson, we do more practice with word problems, solving equations, graphing parabolas, and rewriting quadratic functions.

Standards:

Favorites
(5)

Resources
(13)

Reflections
(1)

### Logs, Loans, and Life Lessons!

Algebra II »
Unit: Exponential and Logarithmic Functions

Algebra II »
Unit: Exponential and Logarithmic Functions

Big Idea:

#### This engaging lesson weaves together logarithms, loans, and life lessons!

Standards:

Favorites
(4)

Resources
(16)

### The Overtime Problem

12th Grade Math »
Unit: Piecewise Functions

12th Grade Math »
Unit: Piecewise Functions

Big Idea:

#### Get started thinking about inequalities by looking at real-world, every day examples. Represent these examples in as many different ways as possible.

Standards:

Favorites
(3)

Resources
(19)

Reflections
(1)

Big Idea:

#### Students finish up the Quadratic Functions Gallery Walk and begin to spot connections between where the roots and where the vertex are located.

Standards:

Favorites
(3)

Resources
(18)

Reflections
(1)

### Graphing and Writing Equations for Piecewise Functions

12th Grade Math »
Unit: Piecewise Functions

12th Grade Math »
Unit: Piecewise Functions

Big Idea:

#### Now that students have examined real-world examples, ask them to apply this knowledge to more abstract functions.

Standards:

Favorites
(3)

Resources
(11)

Reflections
(1)

### Can the Dog Reach the Bone? Determine whether a Point Lies within a Circle

12th Grade Math »
Unit: Circles

12th Grade Math »
Unit: Circles

Big Idea:

#### Will the dog be able to reach its bone? Students apply the definition of a circle, along with a method for determining whether or not a point lies on a circle.

Standards:

Favorites
(8)

Resources
(14)

Reflections
(1)

### Three Ways to Solve a Problem

Algebra I »
Unit: Systems of Equations

Algebra I »
Unit: Systems of Equations

Big Idea:

#### Over the course of today’s lesson, students will beg for an algebraic solution, understand on their own why it’s great that algebra was invented, and see the beauty of an elegant solution.

Standards:

Favorites
(3)

Resources
(19)

Reflections
(1)

### Write Absolute Value Functions as Piecewise Functions

12th Grade Math »
Unit: Piecewise Functions

12th Grade Math »
Unit: Piecewise Functions

Big Idea:

#### Use multiple representations to make connections between two different types of functions.

Standards:

Favorites
(2)

Resources
(12)

Common Core Math

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