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Lesson Plan
EngageNY

Using Permutations and Combinations to Compute Probabilities

For Teachers 11th - 12th Standards
Now that we know about permutations and combinations, we can finally solve probability problems. The fourth installment of a 21-part module has future mathematicians analyzing word problems to determine whether permutations or...
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Lesson Plan
EngageNY

Modeling Video Game Motion with Matrices 2

For Teachers 11th - 12th Standards
The second day of a two-part lesson on motion introduces the class to circular motion. Pupils learn how to incorporate a time parameter into the rotational matrix transformations they already know. The 24th installment in the 32-part...
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Lesson Plan
EngageNY

Complex Numbers as Vectors

For Teachers 11th - 12th Standards
Show your math class how to use vectors in adding complex numbers. Vectors represent complex numbers as opposed to points in the coordinate plane. The class uses the geometric representation to add and subtract complex numbers and...
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Lesson Plan
EngageNY

The Geometric Effect of Some Complex Arithmetic 2

For Teachers 11th - 12th Standards
The 10th lesson in a series of 32, continues with the geometry of arithmetic of complex numbers focusing on multiplication. Class members find the effects of multiplying a complex number by a real number, an imaginary number, and another...
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Lesson Plan
EngageNY

Exploiting the Connection to Trigonometry 1

For Teachers 11th - 12th Standards
Class members use the powers of multiplication in the 19th installment of the 32-part unit has individuals to utilize what they know about the multiplication of complex numbers to calculate the integral powers of a complex number. Groups...
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Lesson Plan
EngageNY

Getting a Handle on New Transformations 2

For Teachers 11th - 12th Standards
Use 2x2 matrices to move along a line. The second day of a two-day lesson plan is the 28th installment in a 32-part unit. Pupils work together to create and solve systems of equations that will map a transformation to a given point. The...
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Lesson Plan
EngageNY

Exploiting the Connection to Cartesian Coordinates

For Teachers 11th - 12th Standards
Multiplication in polar form is nice and neat—that is not the case for coordinate representation. Multiplication by a complex number results in a dilation and a rotation in the plane. The formulas to show the dilation and rotation are...
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Lesson Plan
EngageNY

Why Are Vectors Useful? 2

For Teachers 11th - 12th Standards
Investigate the application of vector transformations applied to linear systems. Individuals use vectors to transform a linear system translating the solution to the origin. They apply their understanding of vectors, matrices,...
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Lesson Plan
EngageNY

An Area Formula for Triangles

For Teachers 11th - 12th Standards
Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....
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Lesson Plan
EngageNY

Inverse Trigonometric Functions

For Teachers 11th - 12th Standards
Build on the understanding of finding angles using trigonometric ratios. Pupils develop the definitions of inverse trigonometric functions by restricting their domains in the 13th lesson of a 16-part series. They use inverse functional...
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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

Precalculus: Function Models for Real-Life Situations

For Teachers 10th - 12th
Young scholars use calculators and "by hand" techniques to compare models of real-life data situations, determine the best model for a situation, and use their models to make predictions.
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Lesson Plan
EngageNY

Does Every Complex Number Have a Square Root?

For Teachers 11th - 12th Standards
Help the class find a better way. Pupils recall finding nth roots or a complex number in polar form from a previous module to find the square root of a complex number. Using the second installment in a series of 23, scholars discover it...
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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
EngageNY

Horizontal and Vertical Asymptotes of Graphs of Rational Functions

For Teachers 11th - 12th Standards
Get close to your favorite line. Scholars use end behavior to help find horizontal asymptotes. With the understanding of domains of rational functions, learners find vertical asymptotes and then use graphing calculators to verify the...
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Lesson Plan
Curated OER

Exercise Set 1.5: Inverse Functions

For Teachers 11th - Higher Ed
In this inverse functions worksheet, students review inverse functions. They solve 66 questions. Problems cover a wide variety of types. Students graph functions and their inverses, they identify one-to-one functions and the domains and...
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Lesson Plan
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Curated OER

Graphing at all Levels: It's a Beautiful Thing!

For Teachers 8th - 12th Standards
Mixing math and art is done in this lesson by applying graphing knowledge to create a unique piece of art. This lesson varies acording to the graphing knowledge of the artist. First, learners identify and review various types of graphing...
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Lesson Plan
EngageNY

Linear Systems in Three Variables

For Students 10th - 12th Standards
Put all that algebra learning to use! Using algebraic strategies, learners solve three-variable systems. They then use the three-variable systems to write a quadratic equation given three points on the parabola.
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Lesson Plan
1
1
Curated OER

Sum of Infinite Geometric Series

For Teachers 9th - 12th Standards
Your mathematicians solve problems using geometric series in this pre-calculus lesson. They divide a unit square into very small pieces and identify the reasoning behind the sum of a series being less than one.
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Lesson Plan
Curated OER

Some More Trigonometry

For Teachers 9th - 10th
Students define the law of cosine and its correct usage. In this trigonometry lesson, students define the law of Heron's area formula and use it to solve problems. They review other trigonometric values and identify the identities.
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Lesson Plan
West Contra Costa Unified School District

Average Rate of Change

For Teachers 9th - 12th Standards
The concept of slope gets an approachable, yet theoretical, treatment in a comprehensive algebra lesson. The use of functional notation and problem-solving techniques keep the material rigorous, but detailed teaching notes and lots of...
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Lesson Plan
EngageNY

Complex Number Division 1

For Teachers 11th - 12th Standards
Conjugating in the math classroom — and we're not talking verbs! The seventh lesson in a series of 32 introduces the class to the building blocks of complex number division. During the instruction, the class learns to find the...
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Lesson Plan
EngageNY

Matrix Multiplication Is Distributive and Associative

For Teachers 11th - 12th Standards
Learn the ins and outs of matrix multiplication. After discovering the commutative property does not apply to matrix multiplication in a previous lesson plan in the series, pupils now test the associative and distributive properties. The...
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Lesson Plan
EngageNY

Properties of Trigonometric Functions

For Teachers 11th - 12th Standards
Given a value of one trigonometric function, it is easy to determine others. Learners use the periodicity of trigonometric functions to develop properties. After studying the graphs of sine, cosine, and tangent, the instructional...