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Thomas Jefferson - Author of The...

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Phonics Song 2 (new version)

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Other Resource Types ( 176 )

EngageNY

#### EngageNY Algebra I Curriculum

The Algebra 1 curriculum set is designed to help scholars develop fluency in
writing, interpreting, and solving linear equations, The 30 lessons in Module 1 are divided into four topics: An Introduction to Functions, the Structure of...

EngageNY

#### EngageNY Algebra II Module 3: Exponential and Logarithmic Functions

The 35 lessons in the Algebra II Module 3 collection are divided into five topics: Real Numbers, Logarithms, Exponential and Logarithmic Functions and their Graphs, Using Logarithms in Modeling situations, and Geometric series and...

EngageNY

#### EngageNY Algebra I Module 4: Polynomial and Quadratic Expressions, Equations, and Functions

The 26 lessons in the Algebra 1, Module 4 collection teach students how to use polynomial functions, as well as quadratic functions, square toot functions and cube root functions, to graph and interpret functions. All materials are copy...

EngageNY

#### EngageNY Algebra I Module 3: Linear and Exponential Functions

The Algebra 1, Module 3 collection focuses on linear and exponential functions. The module's 26 lessons are divided into four topics: Linear and Exponential Sequences, Functions and Their Graphs, Transformations of Functions, and Using...

Lesson Planet

#### Parent Functions and Transformations

Using parent functions, explore the different ways to move, flip, and stretch a function to a different position on the graph. Use this collection to introduce the idea, explore the rules, and practice the steps.

Lesson Planet

#### Geometric Transformations Applied to Function Families

Transform your life with functions! Learners explore geometric transformations of functions with group activities. Guided math journaling and individual practice ensure success with difficult concepts.

Lesson Planet

#### Math Exam 1 Review

Perfect as a review guide, this worksheet provides a range of questions focusing on functions. Topics include composing functions, transformations, domains, and polynomials. Also included are corresponding worksheets focusing on other...

Lesson Planet

#### Linear and Exponential Functions

This comprehensive unit on linear and exponential functions provides numerous clearly-written worksheets. Topics include graphing linear equations, solving systems of equations algebraically and by graphing, identifying the domain and...

Lesson Planet

#### Stretching the Quads

Scholars investigate transforming parabolas. In this transforming parabolas lesson plan, they take the parent graph y=x^2 and transform it by shifting left, right, up, and down and shrinking and stretching. The class finds maximums,...

Lesson Planet

#### Buying A Car

What is my monthly payment? Scholars research to find the perfect car for them to buy. Using the cost of the car, they determine a down payment and the amount of monthly payments using a zero interest loan. Finally, they investigate what...

Lesson Planet

#### Function Family Fun

It's time for a family reunion—function families, that is. Pupils first review different types of parent functions. They then see how to apply transformations to graphs and learn how to select the most appropriate type of function to...

Lesson Planet

#### Transformational Graphing in the Real World: Air Traffic Control

You're cleared to learn about absolute value functions. An interesting lesson has scholars investigate transformations of the graphs of absolute value functions. They look at air traffic control as an application of the concept.

Lesson Planet

#### Transformational Graphing in the Real World: Building Bridges

No suspension here, the resource is good to go. Using graphing calculators, scholars explore how transformations affect the graphs of quadratic functions. They consider how the changes relate to the context of suspension bridges.

Lesson Planet

#### Transformational Graphing in the Real World: Bacteria – Growth or Decay?

Grow—not decay—your knowledge of exponential functions. Young mathematicians graph exponential functions and explore how transformations affect the graphs. They decide whether the functions represent growth or decay in the context of...

Lesson Planet

#### College Algebra

Is there more to college algebra than this? Even though the eBook is designed for a college algebra course, there are several topics that align to Algebra II or Pre-calculus courses. Topics begin with linear equation and inequalities,...

Lesson Planet

#### Precalculus

Take a step beyond Algebra 2. Learners use the eBook to learn concepts from the typical Precalculus course. Content starts off with a short review of functions in general and moves on to the basic functions, finishing up with more...

Lesson Planet

#### Algebra and Trigonometry

Move on into trigonometry. An informative eBook takes the content of a College Algebra course and adds more relating to trigonometry and trigonometric functions. The content organization allows pupils to build upon their learning by...

Lesson Planet

#### Sine Solution

How many times can eager mathematicians catch the waves? Pupils find the solutions of three different trigonometric equations. They then determine the effect of the slope of a line that intersects a trigonometric function and the number...

Lesson Planet

#### Quadratic Reflections

Reflect upon the graphs of quadratic functions. Given a quadratic function to graph, pupils determine whether the graph after a horizontal and vertical reflection is still a function. The final two questions ask scholars to describe a...

Lesson Planet

#### Transformations of Graphs

Geometric transformations in algebra ... what? Given four transformations, the narrator explains how each affect the graph of the original function. The transformations involve translations and reflections, both horizontally and...

Lesson Planet

#### Determine If a Function Is Odd, Even, or Neither (Example 2)

A few more examples can't hurt. An informative video continues the examination of even and odd functions from a prior video. It looks at two additional examples of functions, one that is even and one that is neither even nor odd.

Lesson Planet

#### Determine If a Function Is Odd, Even, or Neither (Example 1)

Here's a hint: look at the exponents. Scholars watch a video that shows two examples of how to algebraically prove whether a function is even or odd. They then see how the exponents in a polynomial function relate to the determination.

Lesson Planet

#### Introduction to Odd and Even Functions

Even algebra beginners can understand even and odd functions. Viewers of a short video learn the definition of even and odd functions. The video investigates y = x^2 and y = x^3 using both algebraic and graphical methods.

Lesson Planet

#### Smarter Balanced Sample Items: High School Math – Claim 3

Communication is the key. A presentation provides 25 sample items for Claim 3, Communicating Reasoning, for the Smarter Balanced High School Math assessment. Items require pupils to answer the question and provide logical reasoning to...

Lesson Planet

#### Module 6: Modeling Periodic Behavior

Around and around we go ... again, and again, and again, and again! That's the nature of a periodic function. Young scholars learn how to model a periodic pattern with trigonometric functions. The nine-lesson unit explores the connection...

Lesson Planet

#### Module 4: Polynomial Functions

Bridge the gap between graphical and algebraic representations. Learners complete six lessons that begin by pointing out connections between the key features of a polynomial graph and its algebraic function. Later, pupils use the...

Lesson Planet

#### Symbolic Similarity

How many things does one transformation tell you? Learners compare and contrast the graphs of different parent functions with the same transformation. Using a rational and absolute value function, pupils identify key features of their...

Lesson Planet

#### Module 8: Modeling With Functions

Sometimes there just isn't a parent function that fits the situation. Help scholars learn to combine function types through operations and compositions. Learners first explore a new concept with an introductory activity and then follow...

Lesson Planet

#### Module 7: Trigonometric Functions, Equations, and Identities

Show your class that trigonometric functions have characteristics of their own. A resource explores the features of trigonometric functions. Learners then connect those concepts to inverse trigonometric functions and trigonometric...

Lesson Planet

#### Module 5: Rational Functions and Expressions

Where do those asymptotes come from? Learners graph, simplify, and solve rational functions in the fifth module of a 10-part series. Beginning with graphing, pupils determine the key characteristics of the graphs including an in-depth...

Lesson Planet

#### Module 7: Structure of Expressions

The structure of an expression is a descriptive feature. Learners build a solid understanding of quadratic functions using an analysis of expressions in different forms. The seventh module in a series of nine includes 12 lessons...

Lesson Planet

#### F.BF.B.3 and F.BF.B.5 Assessment Items

Transform questions into a formal assessment instrument. A set of five assessment items tests understanding of the Common Core math standards F-BF.3 and F-BF.5. Pupils identify transformations of functions and interpret parameters of...

Lesson Planet

#### Zombie Take-Over

The mathematical zombie apocalypse is near! Learners model the spread of zombies with a simulation activity. After collecting data, they graph everything and find a logistic model using a graphing calculator.

Lesson Planet

#### Transformers Parts 2-5 - Algebra 2 Parent Functions

Dive into an activity that may cause a little reflection! Building from the first lesson in the series of two, learners explore transformation using unfamiliar functions. The key takeaway is that applying transformations to any function...

Lesson Planet

#### Transformers Part 1 - Absolute Value and Quadratic Functions

Transform your instruction with an exploratory lesson! Young scholars manipulate absolute value and quadratic functions to look for transformation patterns. They use the patterns to write general rules of transformations.

Lesson Planet

#### Tidal Waves

Periodically ship the class a trigonometric application. Pupils model the level of water in a port. Using their models, learners determine the times that a ship can safely navigate into and out of the port, along with determining other...

Lesson Planet

#### Multi-Function Data Flyer

Explore different types of functions using an interactive lesson. Learners enter functions and view the accompanying graphs. They can choose to show key features or adjust the scale of the graph.

Lesson Planet

#### Linear Inequalities

An interactive lesson helps individuals learn to graph inequalities in two variables. Scholars can adjust the interactive to present the inequalities in standard or slope-intercept form.

Lesson Planet

#### Graphing Quadratic Equations

Sneak peek! Provide a first look at quadratic graphs using an introductory lesson of graphing quadratics that compares them to linear graphs. Pupils use graphing calculators to investigate the effects of changing the leading coefficient...

Lesson Planet

#### Functions, Graphs, and Symmetry...Oh My!

Can you determine a function's graph without actually graphing the function? Scholars learn to identify the shape of the graphs of different function types based solely on their equations. They also study the symmetry of graphs.

Lesson Planet

#### Write the Equations

What is the equation of the new absolute value function when it is moved? The assessment provides a graph of the parent absolute value function. Given three other graphs of a single transformation of a function, pupils determine the...

Lesson Planet

#### Transformations of Graphs: Translations

Explore translations of functions on both the graph and equation. Using a quadratic function, a video lesson shows how adding and subtracting values results in either a vertical or horizontal translation. The lesson compares and...

Lesson Planet

#### Creating a Polynomial Function to Fit a Table

Discover relationships between linear and nonlinear functions. Initially, a set of data seems linear, but upon further exploration, pupils realize the data can model an infinite number of functions. Scholars use multiple representations...

Lesson Planet

#### Algebra I: Model Falling Objects

Don't drop the ball on using a great resource. Scholars use provided data to graph the height of a dropped ball during one of its bounces. This graph and the data provide a means to create a quadratic equation for the relationship...

Lesson Planet

#### Families of Lines: Room in Perspective

Get a perspective of lines that share a point. The interactive displays a family of lines that share the same y-intercept. Individuals can find the equations of the lines by moving the line displayed and find what is common about all the...

Lesson Planet

#### Comparing Functions—Linear

Identify transformations of linear functions. Given the graph of the linear parent function, pupils compare the graphs of four other linear functions and determine how the graphs of each linear function relates to the graph of y = x.

Lesson Planet

#### Comparing Functions—Exponential

Observe what happens when individuals change the parameters of a simple exponential function. Pupils use graphing technology to compare exponential functions while changing one parameter. The scholars then make generalizations of the...

Lesson Planet

#### Connecting Algebra and Geometry

Connect algebra and geometry on the coordinate plane. The eighth unit in a nine-part integrated course has pupils develop the distance formula from the Pythagorean Theorem. Scholars prove geometric theorems using coordinates including...

Lesson Planet

#### Arch Project

Model real-life structures with mathematics. A project-based lesson presents a problem situation requiring classes to develop a function to model the St. Louis Arch and the Rainbow Bridge in Arizona. They create their models by...

Lesson Planet

#### Building an Explicit Quadratic Function by Composition

Use equivalent expressions to reveal information about their graphs. Pupils verify that two quadratic functions are equivalent. By comparing the two expressions, they determine the vertex, the zeros, the y-intercept, and the direction it...

Lesson Planet

#### Transformational Graphing

Find relationships between the structure of a function and its graph. An engaging lesson explores seven parent functions and their graphs. Learners match functions to their graphs and describe transformations.

Lesson Planet

#### Parabola Project

Class members select a picture that contains a parabola and construct a drawing of it using function graphs in the quadratic project. Individuals restrict the domains of the functions to create a more accurate drawing. They then submit a...

Lesson Planet

#### Modeling Motion: Rolling Cups

Connect the size of a rolling cup to the size of circle it makes. Pupils view videos of cups of different sizes rolling in a circle. Using the videos and additional data, they attempt to determine a relationship between cup measurements...

Lesson Planet

#### Identifying Even and Odd Functions

Is it even ... or odd? The task provides four functions to identify as being even, odd, or neither. Pupils use algebraic methods to make their decisions with select exponential, quadratic, and cubic functions.

Lesson Planet

#### Exploring Sinusoidal Functions

What effect does changing a parameter have on the graph of a trigonometric function? Pupils use a Desmos applet to explore the general sine graph. They experiment changing different parameters and record the resulting change of the...

Lesson Planet

#### Building a General Quadratic Function

Rewrite a quadratic function to easily see the transformations involved. The instructional task takes a general quadratic function and rewrites it into a form that shows the translations and scaling of the parent quadratic function. The...

Lesson Planet

#### Identifying Quadratic Functions (Vertex Form)

Pupils calculate the equation of a quadratic in vertex form from a specific graph and determine an equation that would fit the description of a parabola. The final question determines the individuals' understanding of the signs of the...

Lesson Planet

#### Medieval Archer

Class members determine the distance a video game character must move to shoot an arrow over a castle wall. Players determine the new equation to enter to represent the trajectory of the arrow and find all the distances the character can...

Lesson Planet

#### Para-Ball-A

Analyze the flight of a thrown ball. Learners determine the maximum height of a thrown ball and the time it takes to hit the ground given its initial speed. They continue to review different scenarios with different maximums or different...

Lesson Planet

#### Writing and Sketching Resource

Picture this—the class creates pictures using functions. Here, learners build functions to model specific graphic criteria. They use their knowledge of parent functions and transformations to create the perfect function.

EngageNY

#### End-of-Module Assessment Task - Algebra 2 (Module 3)

The last installment of a 35-part series is an assessment task that covers the entire module. It is a summative assessment, giving information on how well pupils understand the concepts in the module.

EngageNY

#### Transformations of the Graphs of Logarithmic and Exponential Functions

Transform your lesson on transformations. Scholars investigate transformations, with particular emphasis on translations and dilations of the graphs of logarithmic and exponential functions. As part of this investigation, they examine...

Lesson Planet

#### Module 7: Modeling with Functions

The sky's the limit of what you create when combining functions! The module begins with a review of transformations of parent functions and then moves to combining different function types using addition, subtraction, and multiplication....

Lesson Planet

#### Module 6: Trigonometric Functions

Create trigonometric functions from circles. The first lesson of the module begins by finding coordinates along a circular path created by a Ferris Wheel. As the lessons progress, pupils graph trigonometric functions and relate them to...

Lesson Planet

#### Module 4: Rational Functions

Time to study the most sensible function — rational functions! The seven-lesson unit develops the concept of a rational function through a connection to rational numbers and fractions. Scholars graph functions, solve equations, and...

Lesson Planet

#### Shifting Linear Equations in Function Notation

Time for a shift in thinking! Learners examine translations of linear functions. They use function notation to describe the translation and make connections to the graph.

Lesson Planet

#### Graphing Exponential Functions

Once you know how to graph y = b^x, the sky's the limit. Young mathematicians learn to graph basic exponential functions and identify key features, and then graph functions of the form f(x) = ab^(x – h) + k from the function f(x) = b^x.

Lesson Planet

#### Particle Motion

Derivatives are useful for many things — they can even keep track of particle motion. An informative lesson plan provides an introduction to the idea of the second derivative in particle motion. Class members determine the velocity...

Lesson Planet

#### Building Functions

Pupils determine equations that match the graphs of transformations and the parent quadratic function. The resource requires class members to attend to precision and think abstractly.

Lesson Planet

#### Dilations of Quadratic Graphs - Concept

Help learners recognize the characteristics of a quadratic graph and how changes affect them. An informative video uses a graphing calculator in order to find out what happens when the leading coefficient of a quadratic changes. The...

Lesson Planet

#### Identifying Quadratic Functions

Put your high schoolers to the test and see how well they know their quadratic functions. With excellent thought-provoking questions, learners use what they know about creating quadratic equations based off different pieces of...

Lesson Planet

#### Transforming the Graph of a Function

Function notation is like a code waiting to be cracked. Learners take the graph of an unknown equation and manipulate it based on three different transformation changes of the function equation. The final step is to look at three points...

Lesson Planet

#### Building a Quadratic Function Form

A simple tweak in the equation can mean big things for a quadratic graph. High school mathematicians look at the parent graph of a quadratic and incorporate three different changes to the function. The problems require explanations of...

Lesson Planet

#### Weightless Wonder

A video of the weightless wonder provides a setting for the math to follow. Groups analyze the graph of a quadratic function that models the path of the C-9 as it gives astronauts the experience of weightlessness. Using a graphing...

Lesson Planet

#### Describing Transformations Algebraically

Working with functions is transformational! An illustrative video explains the basics of the six algebraic transformations. The instructor uses function notation and provides an example of each.

Lesson Planet

#### Determining if a Function is Even, Odd, or Neither

Numbers are even and odd, but did you know functions can be too? The lesson shows the process of determining an even or odd function algebraically. It uses polynomial examples and shows an example of each type.

EngageNY

#### Modeling with Quadratic Functions (part 2)

How many points are needed to define a unique parabola? Individuals work with data to answer this question. Ultimately, they determine the quadratic model when given three points. The concept is applied to data from a dropped object,...

EngageNY

#### End-of-Module Assessment Task - Algebra 1 (Module 4)

Critical thinking is an important aspect of mathematics — it's time to put your brain to work! Use this assessment to challenge pupils and test their skills. Concepts assessed include function notation, factoring, completing the square,...

EngageNY

#### Modeling with Quadratic Functions (part 1)

Relevance is key! The resource applies quadratic modeling by incorporating application of physics and business. Pupils work through scenarios of projectile motion and revenue/profit relationships. By using the key features of the graph,...

EngageNY

#### Comparing Quadratic, Square Root, and Cube Root Functions Represented in Different Ways

Need a real scenario to compare functions? This lesson has it all! Through application, individuals model using different types of functions. They analyze each in terms of the context using the key features of the graphs.

EngageNY

#### Transformations of the Quadratic Parent Function

Efficiently graph a quadratic function using transformations! Pupils graph quadratic equations by completing the square to determine the transformations. They locate the vertex and determine more points from a stretch or shrink and...

EngageNY

#### Stretching and Shrinking Graphs of Functions

Why is that graph wider? Pupils learn about stretching and shrinking graphs of square root, absolute value, cubic, and quadratic functions. They study both vertical and horizontal stretches and shrinks in addition to reflections.

EngageNY

#### Translating Graphs of Functions

If you know one, you know them all! Parent functions all handle translations the same. This lesson examines the quadratic, absolute value, and square root functions. Pupils discover the similarities in the behavior of the graphs when...

EngageNY

#### Graphing Cubic, Square Root, and Cube Root Functions

Is there a relationship between powers and roots? Here is a lesson that asks individuals to examine the graphical relationship. Pupils create a table of values and then graph a square root and quadratic equation. They repeat the process...

EngageNY

#### Graphs Can Solve Equations Too

There are many equations Algebra I students are not ready to solve. Graphing to solve gives them a strategy to use when they are unsure of an algebraic approach to solve the problem. The instructional activity exposes learners to a wide...

EngageNY

#### Piecewise Functions

Show your class members that if they can graph a linear function, they can graph an absolute value function. Groups create an absolute value graph using a table, then entertain the idea of an absolute value function defined as two pieces...

EngageNY

#### End-of-Module Assessment Task - Algebra 1 (Module 3)

Looking for higher-level thinking questions? This assessment provides questions that challenge young mathematicians to think and analyze rather than simply memorize. Topics include piecewise functions, linear modeling, exponential...

Lesson Planet

#### Connecting Graphing and Solving Absolute Value Equations and Functions

Can you solve an equation graphically? Absolutely! This Algebra II lesson plan makes the connection between solving an absolute value equation and graphing two functions. Graphing absolute value functions is presented through the process...

Lesson Planet

#### Analytic Geometry Study Guide

Are you looking for a comprehensive review that addresses the Common Core standards for geometry? This is it! Instruction and practice problems built specifically for standards are included. The material includes geometry topics from...

Lesson Planet

#### Introduction to Logarithms

Build on pupils' understanding of inverse functions by connecting logarithmic functions to exponential functions. This activity allows individuals to see graphically the inverse relationship between an exponential and logarithmic...

Lesson Planet

#### Saxon Math: Algebra 2 (Section 12)

This final section of 12 Saxon Math units for algebra 2 wraps up the series with a strong showing of function summaries, trigonometric applications, and statistical analysis. Labs emphasize guided discovery learning of regression...

Lesson Planet

#### Saxon Math: Algebra 2 (Section 11)

As we approach the end of the Saxon math sections, the 11th of 12 units begins the process of summarizing and combining material from the previous lessons. The relationships between functions and their transformations are investigated,...

Lesson Planet

#### Function Families and Their Connections Including Vertical Shift of an Absolute Value Function

One of the strongest tools an algebra learner develops is the ability to quickly and accurately graph almost any given function. Often doing this quickly and accurately requires rigid transformations to a parent function, demonstrated in...

Lesson Planet

#### Function Families: Translations and Reflections

This comprehensive introduction to rigid transformation of functions does a fabulous job of breaking down translations and reflections into manageable concept chunks. Care is taken with horizontal translations, vertical translations,...

Lesson Planet

#### Module 7: Connecting Algebra and Geometry

The coordinate plane links key geometry and algebra concepts in this approachable but rigorous unit. The class starts by developing the distance formula from the Pythagorean Theorem, then moves to applications of slope. Activities...

Lesson Planet

#### End-of-Year Practice Test (Algebra II)

This complete multiple choice and grid-in practice end-of-year test for algebra II is a phenomenal resource to use as a whole or sprinkled throughout the curriculum. Useful for tracking progress or preparing the class for the format of...

Lesson Planet

#### End of Year Practice Test (Algebra I)

This complete multiple choice and short answer practice end-of-year test for algebra 1 offers a wealth of opportunities for customization. Offer it as a whole, to track progress or prepare the class for the format of the test, or...

Lesson Planet

#### Investigating Functions

Late in algebra 2 or early in pre-calculus, learners are developing a kind of functional intuition. This worksheet goes a long way toward training this skill by helping to expose patterns of transformations through both general and...

Lesson Planet

#### Going off on a Tangent Project

Slope of a curve is a seemingly paradoxical concept tackled in this step-by-step activity. Conversational in tone and approachable in its bite-sized attack, this lesson leads learners to develop the concept of tangential slopes...

Lesson Planet

#### Structures of Expressions

This comprehensive unit investigates transformations of quadratics, having learners follow "Optima" through the development and growth of her quilting business. Deftly weaving the story into the mathematical mechanics, the unit gives...

Lesson Planet

#### Symmetry & Odd/Even Functions

This straightforward activity provides learners with valuable practice in identifying different symmetries of functions. Brief, but thorough explication at the front of the activity guides and reminds learners of the techniques they...

Lesson Planet

#### Changing Functions

Your algebra 2 learners show what they can do in this assessment activity on shifting, reflecting, and stretching graphs. Given the graphs of various functions, they write the represented equation.

Lesson Planet

#### Building a General Quadratic Function

Learners rewrite a general quadratic function by completing the square to see a new form of the function that more easily identifies the x-coordinate of the vertex and the two roots of the function.

Lesson Planet

#### Building a Quadratic Function Form

Comparing the movement of graphs geometrically when small changes are made to the parent function motivates this collaborative discussion on the transformations of functions to their various forms. Vertical and horizontal shifts due to...

Lesson Planet

#### Transformations of Linear and Exponential Graphs

Your transformers will create and analyze graphs to discover which operations produce which transformations. Linear and exponential functions are used to model the transformations.

Lesson Planet

#### Exploring Exponential Graphs

Using a graphing calculator, your algebra 2 learners compare and contrast parent exponential graphs with their transformations. Range, horizontal asymptotes, y-intercepts and general graph changes are some of the characteristics the...

Lesson Planet

#### Transformation of Functions Exploration

Functions are on the move! This lesson plan provides an opportunity for learners to explore transformations of functions. The activity illustrates the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for both...

Lesson Planet

#### Transforming the graph of a function

This activity guides learners through an exploration of common transformations of the graph of a function. Given the graph of a function f(x), students generate the graphs of f(x + c), f(x) + c, and cf(x) for specific values of c. The...

Lesson Planet

#### Building an Explicit Quadratic Function by Composition

Use an activity to illustrate the different forms of a quadratic function. Here, the task asks learners to use composition of given functions to build an explicit function. The process emphasizes the impact of the order of composition...

Lesson Planet

#### Transforming Graphs of Quadratic Functions

In the activity on this webpage, learners use interactive graphing technology to investigate transformations of graphs. In the first part of the task, they look at the graph of a quadratic function with coordinates of a few points...

Lesson Planet

#### Representing Polynomials

Use this complete and very detailed lesson plan to assess your young scholars' understanding of two important behaviors of polynomials. The first is the relationship between the zeros of a polynomial function and the function's graph,...

Lesson Planet

#### Medieval Archer

This activity presents a problem about a computer game which uses functions to simulate the path of an arrow fired by an archer. Learners use the given function to determine where the archer must stand in order to fire an arrow that will...

Lesson Planet

#### Exploring Quadratic Data with Transformation Graphing

Using a data collection device to collect data regarding a bouncing ball, students use various features on graphing calculators to experiment with the parameters of the vertex form of the parabola and their effect on the shape of the...

Lesson Planet

#### Exploring Quadratic Data : Transformation Graphing

High schoolers analyze the vertex form of a parabola and find an approximate fit of a model. They explain the quadratic parabola function and its properties by developing quadratic models. They use translation and dilation to change the...

Lesson Planet

#### Equivalent or Not Equivalent?

Algebra learners look at equivalent expressions in the context of three different operations: division, squaring, and absolute value. In comparing these values, they will identity when expressions are equivalent.

Lesson Planet

#### IB Math SL 1 - Transformations and Combinations Worksheet

Study transformations and combinations with your advanced math class. They solve four graphing problems by graphing the transformations of a parent graph. They determine the equations to represent the given transformations of a parent...

Lesson Planet

#### End Behaviors of Polynomial Functions

Explore the concept of graphing polynomials with your class. Scholars graph polynomials and determine their end behavior. They use their calculator to determine the end behavior of linear, quadratic, and cubic equations.

Lesson Planet

#### Graphs of Rational Functions

Take your kids on a tour of graphing rational functions. Using this TI lesson, high schoolers identify the end behavior of their functions. They find the domain and range, describe end behavior, and look at asymptotes and restrictions of...

Lesson Planet

#### Applications of Exponential Functions

Exponential functions are the name of the game. Young mathematicians can work through each of the eight worksheets by evaluating functions, applying logarithms, completing logarithmic functions, and building inverse functions. This would...

Lesson Planet

#### Graphing Exponentials

Bring your Algebra class to the computer lab! Using materials created by Texas Instruments, they explore exponentiasl and graphs. Be sure to download the correct materials (on the right side of the webpage) before having them walk...

Lesson Planet

#### Stretching the Quads

Explore parabolas in this algebra lesson plan with the graphing calculator. The class investigates what effects the changing of the parameters of the vertex form of a quadrati have to its graph. They find the zeros of a quadratic...

Lesson Planet

#### Going Back to Your Roots

Investigate the Fundamental Theorem of Algebra and explore polynomial equations to determine the number of factors, the number of roots, and investigate multiplicity of roots.

Lesson Planet

#### Going Back to Your Roots

Who doesn't need to know the Fundamental Theorem of Algebra? Use the theorem to find the roots of a polynomial on a TI calculator. The class explores polynomials with one solution, no real solutions, and two solutions. This less lesson...

Lesson Planet

#### Exponential Reflections

High Schoolers explore the concept of exponential reflections. They use their Ti-Nspire to reflect the natural logarithm function over the line y=x. Students repeat the process using different exponential functions using a slider.

Lesson Planet

#### Exploring Expressions

Examine parts of an expression in this algebra lesson. Ninth graders identify the properties of the coefficient and their behavior to the graph. They graph the equation on a TI to see their results.

Lesson Planet

#### Comparing Functions—Quadratics

Square away any doubts about using this resource on quadratics. Scholars answer a set of questions on transformations of the graphs of quadratic functions. They determine how changes to the equation affect the graph.

Lesson Planet

#### Transformationally Speaking

Young mathematicians explore transformations of graphs by graphing sets of functions on the same pair of axes. They use their graphs to determine the effect that the values of a and b in y = ax + b have on the graph of y = x.

Lesson Planet

#### Transformation Investigation

Graph it! Investigate transformations with a graphing calculator. Pupils graph sets of linear functions on the same set of axes. They determine how changes in the equation of a linear function result in changes in the graph.

Lesson Planet

#### Student Exploration: Transformation of Functions

Pupils explore different types of function notation by creating their own function to input values. The directions aren't available but you can manipulate the document to either create your own functions for the class, or allow them to...

Lesson Planet

#### Unit Plan: Exponential and Logarithmic Functions

A six-day unit for algebra II on exponential and logarithmic functions builds upon Chapter 12 of Merrill Algebra II with Trigonometry; Applications and Connections. The text provides assistance in the depth of instruction and homework...

Lesson Planet

#### Identifying Even and Odd Functions

Use a worksheet to give learners practice in identifying even and odd functions. The problems on this page are also appropriate for use as assessment items, or you can use them with GeoGebra to interactively present concepts. The task is...

Lesson Planet

#### Making Connections Using Quadratic Functions

In this graphing worksheet, one completes 13 problem solving questions regarding quadratic functions and function notation. The emphasis is on understanding parent functions and transformations.

Lesson Planet

#### Exponential Transformations

Perform transformations on exponential functions! Teach your class how to perform dilation, compression, and translation. They graph exponential functions using the TI Calculator.

Lesson Planet

#### Exploring Transformations

Young scholars investigate functions and their transformations. They move absolute value functions around on the coordinate plane, and then define the transformation and plot the new graph. The table feature of the TI-calculator is used...

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#### Standard Form of Quadratic Functions

Students factor quadratic equations. In this algebra lesson, students identify the factors and use them to graph the parabola. They find the parameters and vertex of each graph.

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#### Polynomial Rollercoaster

Learners relate polynomials to a rollercoaster track as they translate a graph around on a coordinate plane. They differentiate between different forms of algebraic expressions.

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#### Points on a Line

How do you find slope? You use points on a line of course. slope. Teach your class how to calculate and differentiate between horizontal and vertical lines. They are sure to be pros at graphing lines on a coordinate plane by the end of...

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#### Characteristics of Exponential Functions

What can an upper grader do with an exponential function? They can solve and graph it, identify its important characteristic, and differentiate graphs based on shifts in graph bases that are greater or less than one. This 45 minute...

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#### Exploring Vertical Asymptotes

Scholars identify the domain of a rational function in this precalculus lesson. They identify the removable discontinuity and label what will make the denominator zero. Learners also describe properties of the graph as it relates to the...

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#### Graphic Designing with Transformed Functions

Teach your class how to transform a graph! By identifying the domain and range of the functions, students can observe the parabola and find the vertex of the transformed graph.

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#### Exploring Power Functions 1

Learners describe the end behavior of polynomial functions. Pupils relate the behavior of the graph to the exponent of the graph. They differentiate graphs with odd-exponent and graphs with even exponents.

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#### Logarithmic Transformations

Using the TI calculator to visualize and make predictions, students perform transformation vertically and horizontally on logarithmic graphs in order to solve problems.

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#### Introduction to Conic Sections

Learners slice cones and identify the different conics formed. They then derive the formula to solve problems involving cones. Pull out the TI calculators to visualize the slicing and the different parts and properties created.

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#### Rate of Change

Students observe and calculate slopes. In this algebra instructional activity, students graph equations and determine the pace at which the slope is changing. They use the navigator to see the change as they graph the lines around.

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#### Comparing Linear and Exponential Functions

Teach your class how to differentiate between linear and exponential functions. They use exponential properties to solve problems, graph them using the TI-Navigator, and make comparisons.

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#### Families of Functions

Learners use sliders to change the parameters of functions and examine how shifting parameters affects a graph. They identify the parameters of functions, find vertical and horizontal stretches, then calculate the scale factor and other...

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#### Parabolic Paths

Students investigate properties of parabolas. In this algebra lesson, students identify the different paths of a parabola. They use the navigator to make observations of the parabola.

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#### Torricelli's Law

Investigate velocity using Torricelli's Law! The class will have a blast solving problems involving velocity and their related equations. They create an equation to represent the flow of the water through a tank. Super helpful tips on...

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#### Variables and Expressions

Students solve equations by writing expressions. In this algebra lesson, students identify the different values for each variable. They use the navigator to see how to solve equations.

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#### Distributive Property

High schoolers solve problems using distribution. In this algebra lesson, students factor equations using the distributive property. They graph their solution on a graph.

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#### From Expressions to Equations

Learners differentiate between expression and equation by evaluating integers and observing the difference. They use the TI to see the steps to solve problems.

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#### Horizontal and Vertical Lines

Students solve equations and graph-their solutions. In this algebra lesson, students, identify the type of line using the slope of the equation. They graph and observe their lines.

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#### Transformations of Functions 1

Learn how to solve problems with transformation. High schoolers perform transformation on their graphs. Then, they use the TI to create a visual of the graph as it is moving along the graph.

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#### Transformations of Functions 2

Solving problems on the TI graphing calculator can be quite easy. Students observe the properties of transformation of functions and create a formula for the transformation.

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#### Domain and Range of Exponential Functions

Have your class find the domain and range for each function. Students graph equations using the TI. They find all the x and y values as they relate to the domain and range.

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#### Exponential Functions f(x) = abx

Students define exponential functions and graph the equation. For this algebra lesson, students discuss exponential growth and decay as they graph their functions. They differentiate between the base of growth and decay.

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#### Graphing Quadratic Functions

Pupils explore quadratic functions in this algebra lesson. They investigate transformation of quadratic functions using the TI calculator. They use the vertex form for this lesson.

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#### Exploring the Exponential Function

Learners collect and analyze data regarding exponential functions of the form y = abx. Students explore the affects of changing parameters on the graph of the function.

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#### Exponential Reflections

Explore the natural log function through the investigation of inverse of the exponential functions by plotting the inverse of the exponential solution points. Students examine the results to determine that the inverse is the natural log...

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#### Graphing the Absolute Vaule Function

Learners investigate the graph of the absolute value function and the relationship between the parameters of the equation and the graph of the function.

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#### Let's Play Ball with Families of Graphs

Learners explore quadratic equations in this Algebra II lesson. They investigate families of quadratic functions by graphing the parent function and family members on the same graph. Additionally, they write the equation of the parabola...

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#### Discriminating Against the Zero

Students explore the concept of quadratic equations. In this quadratic equations lesson, students find the roots or zeros of quadratic equations using the quadratic formula. Students give examples of functions with 2 real, rational...

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#### Exploring Quadratic Equations

By stretching and translating the parabola given and determining the effects on the equation, students explore finding the vertex and zeros of a parabola and relate them to the equation. Students also view the intercept form to determine...

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#### Complex Roots: A Graphical Solution

Using their Ti-Nspire to determine the solutions of parabolas, students explore the concept of complex roots. Students determine if parabolas have real or complex roots. Students determine the the axis of symmetry and the vertex given...

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#### Getting Triggy With It

The concept of sine and cosine is explored in this lesson where learners graph sine and cosine graphs using a transformation application on the graphing calculator. Students change the coefficients for the amplitude, period, frequency,...

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#### Exploring Complex Roots

In exploring the concept of complex roots, students find the axis of symmetry and roots of parabolas. Then, they discuss what makes a solution complex and how to identify functions with complex roots.

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#### Technology for Displaying Trigonometric Graph Behavior: Sine and Cosine

Students explore the concept of sine and cosine. In this sine and cosine activity, students work in groups to graph sine and cosine functions. Students examine how coefficients in various parts of each parent function shift the graph. ...

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#### I'm Lovin' It: Finding Area Between Curves

Students explore the concept of finding the area between two curves. In this finding the area between two curves instructional activity, students model the logos of McDonalds, Nike, and Motorola on grid paper. Students find functions to...

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#### Quadratic Function Investigations

Learners perform investigation of quadratic functions while taking part in the solving of various types of problems. They explore the changes in the coefficients on the quadratic function to observe the patterns. The lesson includes...

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#### Toothpicks and Transformations

Students investigate quadratic functions using geometric toothpick designs. They review transformations of quadratic functions-vertical and horizontal shifts, and stretches and shrinks. Students match the symbolic form of the function to...

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#### Vertex and Factored Form of Quadratic Functions

Students graph quadratic equations. In this algebra lesson, students solve quadratic equations by factoring. They identify the end behavior of the graph.

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#### Rose Curve

Arcsine will be better understood and applied through prediction the number of petals on a rose curve using polar equations. High schoolers relate rose curve to siusoidal functions using the Ti navigator.

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#### Trains in Motion

Students compare two object as they find the distance between them. In this geometry lesson, students create an equation describing the distance of time as a function. They use the navigator to observe the distance.

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#### Exploring Functions with CAS

Your mathematicians will examine several conjectures regarding even and odd functions and investigate a formal proof of the conjectures using CAS.

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#### Let's Play Some Ball!

Pupils review horizontal and vertical shifts of a parabola and how they effect a specific quadratic formula. They play a basketball review game in which they try to find the right quadratic equation for a given problem in order to earn...

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#### Explore the Transformations of Linear and Absolute Value Functions Using Graphing Utilities

Students explore the concept of transformations. For this transformation lesson, students use an applet that is an interactive absolute value graph applet. Students manipulate the applet to examine the change in the function and how it...