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Lesson Plan
EngageNY

Solutions to Polynomial Equations

For Teachers 11th - 12th Standards
Take a step back to Algebra II. The first lesson in a series of 23 asks scholars to remember working with quadratic equations with complex solutions. Pupils apply polynomial identities to complex numbers and work examples that show how...
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Lesson Plan
Curated OER

Going Back to Your Roots

For Teachers 9th - Higher Ed Standards
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.
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Lesson Plan
Curated OER

Graphical Analysis

For Teachers 9th - 12th Standards
Get out your TI-nspire graphing calculator and explore polynomials. Learners determine where a given polynomial are increasing or decreasing, find maximums, minimums, and zeros of polynomials, and discuss end behavior of polynomials....
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Lesson Plan
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Curated OER

Going Back to Your Roots

For Teachers 9th - 12th Standards
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...
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Lesson Plan
EngageNY

Roots of Unity

For Teachers 11th - 12th Standards
Visualize the nth roots of unity. Pupils calculate the nth roots of unity and find all n roots. Learners plot the solutions in the complex plane and observe that they are the vertices of a regular n-gon inscribed in the unit circle....
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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.
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Lesson Plan
Curated OER

Eighty-Six Various Polynomial Function Problems

For Teachers 11th - Higher Ed
In this polynomial functions worksheet, students solve eight-six various problems concerned with the degree, graph, intercepts, end behavior, and transformations of polynomial functions. Some of the problems are algebraic work and some...
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Lesson Plan
EngageNY

End Behavior of Rational Functions

For Teachers 11th - 12th Standards
Connect end behavior to previous learning. Pupils connect finding the end behavior of rational functions to finding end behavior of polynomial functions. The 13th segment in a 23-part unit starts with finding the end behavior or power...
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Lesson Plan
EngageNY

Rational Functions

For Teachers 11th - 12th Standards
Make a connection between rational expressions and rational functions. Pupils review simplifying and performing operations on rational expressions and recall what it means for two rational expressions to be equivalent based on their...
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Lesson Plan
Curated OER

End Behavior of Polynomial Functions

For Teachers 9th - 10th
Students identify the end behavior of polynomial functions. In this algebra lesson, students graph different polynomials functions and find a correlation between exponents and function behavior. They identify the effect the leading...
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Lesson Plan
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Curated OER

Multiplicity of Zeros of Functions

For Teachers 9th - 12th Standards
Pupils identify the multiplicity of exponents as they graph polynomials. They write equations for a function given the zeros of the function and work backwards from solving equations.
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Lesson Plan
Curated OER

Exploring Vertical Asymptotes

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

Crossing the Asymptote

For Teachers 9th - 11th
Young scholars investigate graphs and their asymptotes. In this precalculus lesson, students examine the numerator and denominator of their rational functions. This helps them identify where and when the graph will cross its asymptote.
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Lesson Plan
EngageNY

Exploiting the Connection to Trigonometry 2

For Teachers 11th - 12th Standards
The class checks to see if the formula for finding powers of a complex number works to find the roots too.  Pupils review the previous day's work and graph on the polar grid. The discussion leads the class to think about how to reverse...
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Lesson Plan
Curated OER

Finite Differences

For Teachers 9th - 12th Standards
Young mathematicians solve problems with polynomials. As they graph and analyze polynomial functions, learners define constant and finite, and determine the relationship between the constant set of differences and the slope of a linear...
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Lesson Plan
EngageNY

The Structure of Rational Expressions

For Teachers 11th - 12th Standards
Find out when rational expressions are closed. Pupils review adding, subtracting, multiplying, and dividing with rational numbers to make the connections to operations with rational expressions. Using specific examples, learners notice...
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Lesson Plan
EngageNY

Wishful Thinking—Does Linearity Hold? (Part 1)

For Teachers 11th - 12th Standards
Not all linear functions are linear transformations — show your class the difference. The first activity in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...
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Lesson Plan
EngageNY

Wishful Thinking—Does Linearity Hold? (Part 2)

For Teachers 11th - 12th Standards
Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...
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Lesson Plan
Curated OER

Discriminating Against the Zero

For Teachers 9th - 12th Standards
Students explore the concept of quadratic equations.  For 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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Lesson Plan
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Curated OER

Dog Pen Problem

For Teachers 9th - 12th Standards
Teach your class about various approaches to solving the problem of maximizing the area of a rectangle space with a fixed perimeter in the context of a farmer's dog pen. Then, they complete a worksheet independently to summarize the...
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Lesson Plan
Curated OER

Linear and Quadratic Functions

For Teachers 11th
In this algebra worksheet, 11th graders solve quadratic functions using the quadratic formula. They take the square roots of both side of each equation then graph both the linear and quadratic functions. There are a total of 84 problems...
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Lesson Plan
Curated OER

Products of Linear Functions

For Teachers 8th - 10th
Students investigate the horizontal intercepts of functions. In this algebra lesson, students identify whether the factor of two functions results in a quadratic equation or not. They compare and contrast linear equations and higher...
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Lesson Plan
Curated OER

The football and Braking Distance; Model Data with Quadratic Functions

For Teachers 8th - 10th
Students use the quadratic formula to solve application problems. The first problem relates to the path of a football thrown from the top of the bleachers. Students compute the time it will take the football to reach certain heights. In...
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Lesson Plan
Curated OER

Model Data with Quadratic Functions

For Teachers 8th - 11th
Students model data using quadratic equations. In this algebra lesson, students simplify and factor quadratic equations. They graph the function using collected data and analyze the parabola.