HSF-IF.B.5

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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.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.*

76 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)

### Slope as a Rate of Change - Day 1 of 2

Algebra I »
Unit: Linear Functions

Algebra I »
Unit: Linear Functions

Big Idea:

#### This real-life application will help students develop the meaning of the slope concept.

Standards:

Favorites
(20)

Resources
(14)

### 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)

### Transformation of Polynomial Functions

Algebra II »
Unit: Polynomial Functions

Algebra II »
Unit: Polynomial Functions

Big Idea:

#### Models support conceptual understanding of function transformations. From cube to cubic!

Standards:

Resources
(30)

Reflections
(2)

Big Idea:

#### In many cases, polynomial functions are ideal mathematical models that support quantitative and abstract reasoning.

Standards:

Favorites
(3)

Resources
(12)

Reflections
(1)

### Discrete and Continuous Functions

Algebra I »
Unit: Linear Functions

Algebra I »
Unit: Linear Functions

Big Idea:

#### Discrete situations can be modeled by functions that are continuous. The domain and range help to determine how the graph of a function will appear.

Standards:

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(11)

Resources
(12)

Big Idea:

#### Understanding the domain of a piecewise function is essential to being able to graph it.

Standards:

Favorites
(4)

Resources
(15)

Reflections
(1)

### Using Points to Determine the Shape of a Graph

Algebra I »
Unit: Linear and Exponential Functions

Algebra I »
Unit: Linear and Exponential Functions

Big Idea:

#### In order to get a broad picture of functions and their graphs, we go a bit beyond just the linear and exponential functions that are the foci of this unit.

Standards:

Resources
(8)

Big Idea:

#### Now is the chance to show off what you know about functions.

Standards:

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(6)

Resources
(6)

Reflections
(1)

Big Idea:

#### Students who understand functions well can make connections between the graph of a function and the equation of the function.

Standards:

Favorites
(2)

Resources
(15)

Reflections
(1)

### Slope as a Rate of Change - Day 2 of 2

Algebra I »
Unit: Linear Functions

Algebra I »
Unit: Linear Functions

Big Idea:

#### Students debrief a lesson on slope as a rate of change by investigating each other's work.

Standards:

Favorites
(7)

Resources
(10)

### Running and the Domain of Middle Earth: Modeling a Run and a Hobbit's Journey through Piece-wise Functions

Algebra I »
Unit: Everything is Relative: Linear Functions

Algebra I »
Unit: Everything is Relative: Linear Functions

Big Idea:

#### Students model the many adventures of hobbit Frodo Baggins while exploring the concept of domain AND learning how to graph piece-wise functions!

Standards:

Favorites
(3)

Resources
(30)

Reflections
(3)

### Introduction to 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 use modeling and technology as tools to come to a deeper understanding of quadratic functions using real life contexts!

Standards:

Favorites
(46)

Resources
(25)

Reflections
(2)

### 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)

### Performance Task: Pulling It Together with Quadratics

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

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

Big Idea:

#### Students integrate concepts learned about quadratic equations and functions to analyze models and make recommendations for maximizing profit on the sale of smart phones.

Standards:

Favorites
(13)

Resources
(10)

Common Core Math

### Kindergarten

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### HS Algebra

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### HS Geometry

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### Fifth Grade

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### Ninth and Tenth Grade

### Kindergarten

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### 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