HSF-IF.C.8

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- HSF-IF.C.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
- HSF-IF.C.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- HSF-IF.C.9Compare 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.

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## HSF-IF.C.8

## Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

40 Lesson(s)

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### Patio Problem: Sequences and Functions

Algebra I »
Unit: Linear Functions

Algebra I »
Unit: Linear Functions

Big Idea:

#### Arithmetic sequences can be modeled by linear functions that both have the same common difference.

Standards:

Favorites
(25)

Resources
(9)

Reflections
(1)

### Quadratic Functions: Standard and Intercept Forms

Algebra II »
Unit: Polynomial Functions and Expressions

Algebra II »
Unit: Polynomial Functions and Expressions

Big Idea:

#### Quadratic functions are graphed as parabolas; how we go about creating the graph depends on which form the function is written in.

Standards:

Favorites
(10)

Resources
(21)

Reflections
(1)

### Operations with Polynomials Day 1 of 2

Algebra II »
Unit: Polynomials

Algebra II »
Unit: Polynomials

Big Idea:

#### Students get the opportunity to explore and make conclusions about operations with polynomials using graphing technology.

Standards:

Favorites
(8)

Resources
(20)

Reflections
(1)

### End of Unit Differentiated Problem Set

Algebra II »
Unit: Exponential and Logarithmic Functions

Algebra II »
Unit: Exponential and Logarithmic Functions

Big Idea:

#### This lesson allows the students to apply their mathematical knowledge in a real context.

Standards:

Favorites
(1)

Resources
(14)

### Elephant Tracks!

Algebra II »
Unit: Exponential and Logarithmic Functions

Algebra II »
Unit: Exponential and Logarithmic Functions

Big Idea:

#### This lesson teaches the students to use the natural logarithm function to find the age of an elephant!

Standards:

Favorites
(4)

Resources
(21)

Reflections
(3)

### Writing in Math Classroom, Part 1: Functions and Linear Functions

Algebra I »
Unit: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable

Algebra I »
Unit: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable

Big Idea:

#### Students score sample MCAS open responses in groups as an entry point to understanding and reflecting on their own writing!

Standards:

Favorites
(1)

Resources
(15)

### Quadratic Functions in Three Forms

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### An brief adventure in number theory provides some background knowledge for completing the square, then students get to practice manipulating quadratic expressions in different forms.

Standards:

Favorites
(8)

Resources
(24)

Reflections
(3)

Big Idea:

#### This review assignment will wrap up the functions unit and help students understand what they need to continue to study.

Standards:

Favorites
(2)

Resources
(8)

Reflections
(1)

### Comparing Investments

Algebra I »
Unit: Exponential Functions

Algebra I »
Unit: Exponential Functions

Big Idea:

#### To guide students in practice to develop meaning for each variable in either formula in order to make correct substitutions and evaluations.

Standards:

Favorites
(8)

Resources
(16)

Reflections
(1)

### Interpreting and Graphing Quadratic Functions

Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations

Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations

Big Idea:

#### Students interpret key features of quadratics in real-life contexts to see the value of modeling and power of quadratics!

Standards:

Favorites
(10)

Resources
(19)

Reflections
(3)

### Graphing Functions: Lines, Quadratics, Square and Cube Roots (and Absolute Values)

Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations

Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations

Big Idea:

#### Students learn to graph different types of functions AND compare and contrast key features of families of functions!

Standards:

Favorites
(7)

Resources
(16)

Reflections
(1)

### Building Quadratic Functions: f(x), kf(x) and f(kx)

Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations

Algebra I »
Unit: Interpret and Build Quadratic Functions and Equations

Big Idea:

#### Students use technology to construct their own understanding of different operations on the graph of quadratic functions!

Standards:

Favorites
(1)

Resources
(19)

Reflections
(1)

### Calculator Boot-Camp and Solving Exponential Equations

Algebra II »
Unit: Exponential and Logarithmic Functions

Algebra II »
Unit: Exponential and Logarithmic Functions

Big Idea:

#### This lesson places a high emphasis on teaching the students how to properly use a calculator when solving exponential/logarithmic equations.

Standards:

Favorites
(1)

Resources
(19)

Reflections
(1)

### Differentiated Problem Share Out - Unit Review

Algebra II »
Unit: Exponential and Logarithmic Functions

Algebra II »
Unit: Exponential and Logarithmic Functions

Big Idea:

#### This lesson allows the students to apply their mathematical knowledge in a real context.

Standards:

Resources
(16)

### Linear and Nonlinear Function Review and Portfolio

12th Grade Math »
Unit: Linear and Nonlinear Functions

12th Grade Math »
Unit: Linear and Nonlinear Functions

Big Idea:

#### Give students the chance to put all the pieces together. Give them the chance to make connections between the ideas and skills of the unit.

Standards:

Favorites
(1)

Resources
(8)

Common Core Math

### Kindergarten

### First Grade

### Second Grade

### Third Grade

### Fourth Grade

### Fifth Grade

### Sixth Grade

### Seventh Grade

### HS Number & Quantity

### HS Algebra

### HS Functions

### HS Geometry

### Kindergarten

### First Grade

### Second Grade

### Third Grade

### Fourth Grade

### Fifth Grade

### Sixth Grade

### Seventh Grade

### Eighth Grade

### Ninth and Tenth Grade

### Kindergarten

### First grade

### Second grade

### Third Grade

### Fourth grade

### Fifth grade

### Middle School

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

HS Number & Quantity

HS Algebra

HS Functions

HS Geometry

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

Eighth Grade

Ninth and Tenth Grade

Kindergarten

First grade

Second grade

Third Grade

Fourth grade

Fifth grade

Middle School