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Mathematics Vision Project

Module 3: Polynomial Functions

For Students 9th - 12th Standards
An informative module highlights eight polynomial concepts. Learners work with polynomial functions, expressions, and equations through graphing, simplifying, and solving. 
Lesson Plan
Curated OER

Graphing Polynomials

For Teachers 9th - 11th
Students graph polynomial equations using different methods. In this algebra instructional activity, students identify the different ways the x and y values relate in a graph. They solve for x by finding the zero's of the polynomials.
Lesson Plan
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EngageNY

The Special Role of Zero in Factoring

For Students 10th - 12th Standards
Use everything you know about quadratic equations to solve polynomial equations! Learners apply the Zero Product Property to factor and solve polynomial equations. They make a direct connection to methods they have used with quadratic...
Lesson Plan
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Curated OER

Polynomials: Factors, Roots and Zeroes

For Teachers 9th - 12th Standards
Students factor polynomial equations. In this algebra lesson plan, students identify the zeros of the equations. They use algebra to rewrite word problems using symbols.
Lesson Plan
EngageNY

Graphing Quadratic Functions from Factored Form

For Students 9th - 10th Standards
How do you graph a quadratic function efficiently? Explore graphing quadratic functions by writing in intercept form with a lesson that makes a strong connection to the symmetry of the graph and its key features before individuals write...
Lesson Plan
EngageNY

Creating and Solving Quadratic Equations in One Variable

For Students 9th - 10th Standards
Give your classes practice at modeling using quadratic models with a resource that uses area and integer problems to allow individuals to create second degree polynomials. Young mathematicians solve equations using factoring and then...
Lesson Plan
Curated OER

Polynomials Functions

For Teachers 9th - 12th
High schoolers factor polynomials and linear functions and apply concepts of the fundamental theorem of algebra to solve problems. They graph their solutions and analyze the graph.
Lesson Plan
Curated OER

Quadratic Equations and Functions

For Teachers 8th - 11th
This comprehensive lesson plan reviews solving and graphing quadratic functions and functions of higher degree.  Using the vertex form of a quadratic functions, one finds the vertex, minimum or maximum, and axis of symmetry. A few...
Lesson Plan
EngageNY

Modeling with Polynomials—An Introduction (part 2)

For Students 10th - 12th Standards
Linear, quadratic, and now cubic functions can model real-life patterns. High schoolers create cubic regression equations to model different scenarios. They then use the regression equations to make predictions.
Lesson Plan
EngageNY

Obstacles Resolved—A Surprising Result

For Students 10th - 12th Standards
The greater the degree, the more solutions to find! Individuals find the real solutions from a graph and use the Fundamental Theorem of Algebra to find the remaining factors. 
Lesson Plan
Curated OER

Quadratic Formula

For Teachers 9th - 12th Standards
Mathematicians determine the solutions of a quadratic function by looking at a graph. They use the quadratic formula to solve quadratic functions on their Ti-Nspire.
Lesson Plan
Curated OER

The Quest for Roots of Higher Order Equations

For Teachers 9th - 12th Standards
Young mathematicians explore the concept of solutions to higher order equations as they find roots of polynomials of degree three or higher. They also use the zero function on the Ti-83 to locate zeros of polynomials on a graph.
Lesson Plan
Curated OER

Discovering Different Types of Functions

For Teachers 10th - 12th
Graph polynomials and identify the end behavior of each polynomial function. The class differentiates between linear, quadratic, and other polynomial equations.
Lesson Plan
Curated OER

Exploring Quadratic Equations

For Teachers 11th
Eleventh graders explore quadratic equations.  In this Algebra II lesson, 11th graders use Geometer’s Sketchpad to explore the properties of quadratics and the connections with polynomials and linear equations.  The lesson is...
Lesson Plan
K20 LEARN

Awesometh Degree of a Function

For Teachers 10th - 11th Standards
Build up a polynomial. Learners use printed cards to create polynomials. Using a graphing utility, pupils make comparisons between the polynomials they built. To further cement the concept, they build upon their algebraic vocabulary as...
Lesson Plan
Curated OER

Another Way of Factoring

For Teachers 8th - 10th Standards
Focusing on this algebra instructional activity, learners relate quadratic equations in factored form to their solutions and their graph from a number of different aspects. In some problems, one starts with the original equation and...
Lesson Plan
Curated OER

Polynomial Rollercoaster

For Teachers 9th - 12th Standards
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.
Lesson Plan
Curated OER

Parabolas

For Teachers 9th - 12th
Students investigate parabolas and their equations.  In this parabolas and their equations lesson, students graph quadratic equations on their graphing calculator.  Students find the axis of symmetry of a parabola. ...
Lesson Plan
Curated OER

Taylor Polynomial Examples

For Teachers 9th - 12th Standards
Learners graph Taylor polynomials. In this calculus lesson, students relate accuracy of a Taylor polynomial to the degree of the equation. They graph their polynomials using the TI calculator.
Lesson Plan
Curated OER

Cost Calculations Lesson Plan

For Teachers 10th - 11th
Students analyze data using graphs and equations. In this algebra lesson, students calculate the cost of lumber, convert price per foot to price per piece, solve equations using addition and subtraction and give exact answer when needed....
Lesson Plan
EngageNY

Factoring Extended to the Complex Realm

For Students 10th - 12th Standards
A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...
Lesson Plan
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EngageNY

Overcoming a Third Obstacle to Factoring— What If There Are No Real Number Solutions?

For Students 10th - 12th Standards
Time for pupils to use their imagination! Learners examine the relationship between a system with no real solution and its graph. They then verify their discoveries with algebra. 
Assessment
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Balanced Assessment

Alcohol Level

For Students 9th - 12th Standards
How long does it take alcohol to leave your system? Individuals explore this question by examining a polynomial function. They draw conclusions by analyzing the key features of the given polynomial function.
Lesson Plan
Curated OER

Adding and Subtracting Polynomials Using Algebra Tiles

For Teachers 9th - 11th
Students add and subtract polynomials. In this algebra lesson, students use algebra tiles to perform operation of polynomials. They model their problems and understand how to combine like terms using tiles.