EngageNY
Distance and Complex Numbers 2
Classmates apply midpoint concepts by leapfrogging around the complex plane. The 12th lesson in a 32 segment unit, asks pupils to apply distances and midpoints in relationship to two complex numbers. The class develops a formula to find...
EngageNY
Inverse Trigonometric Functions
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...
West Contra Costa Unified School District
Introduction to Inverse Functions
Ready to share the beauty of the inverse function with your classes? This algebra II instructional activity guides the discovery of an inverse function through a numerical, graphical, and an algebraic approach. Connections are made...
West Contra Costa Unified School District
Indefinite Integrals
The inverse of matter is anti-matter, so the inverse of a derivative is an antiderivative. The lesson introduces antiderivatives and indefinite integrals to the class along with the notation for integrals. Groups work together to find...
Virginia Department of Education
Circles in the Coordinate Plane
Make the connection between the distance formula and the equation of a circle. The teacher presents a lesson on how to use the distance formula to derive the equation of the circle. Pupils transform circles on the coordinate plane and...
Concord Consortium
Be Well
How much do you spend on healthcare each year? Data shows the expenditures in the US rise significantly each year. Young scholars use the data to calculate a rate of change over a 30-year period and look for—as well as provide— possible...
West Contra Costa Unified School District
Investigating the Discriminant
When is finding the discriminant enough? Using the quadratic formula helps find solutions to quadratic equations, but there are times when just using the discriminant is appropriate. Use this algebra II lesson to help classes see the...
West Contra Costa Unified School District
Derivative – Standard Definition
Making a clear connection to algebra concepts helps learners understand the definition of a derivative. The lesson begins with looking at limits of simple linear and rational functions, and leads to the definition of the derivative....
West Contra Costa Unified School District
The Extreme Value Theorem
Finding the critical numbers of a function can be extreme. The lesson introduces the Extreme Value Theorem to the class with a graph. Pupils then have an opportunity to practice determining the values using an algebraic function.
Curated OER
Rational and Irrational Numbers 2
Is the circumference of a circle always, sometimes, or never rational? Learners answer questions individually and also work in groups to look at sums and products of rational and irrational numbers. They must also be able to use the...
Curated OER
Modeling Conditional Probabilities 1: Lucky Dip
Check out this detailed lesson plan on conditional probability! Learners work individually and also collaboratively to analyze the fairness of a game and justify their reasoning. it includes detailed notes and many helpful suggestions...
Curated OER
Interpreting Algebraic Expressions
Interpreting algebraic expressions is a fundamental skill in beginning algebra. This lesson approaches the task in numerous ways. First, learners assess their understanding with a short worksheet on converting between words and...
Chicago Teachers Union Quest Center
Factored Form of a Quadratic Function
Build upon linear functions to learn about quadratics. The lesson introduces the concept of zeros for quadratic functions and makes the connection to the linear factors of the function. It presents quadratics in both graphical and...
Houghton Mifflin Harcourt
Simple and Compound Interest
Your learners will get lots of practice calculating simple and compound interest by the end of this lesson. Simple explanations and examples lead learners through the concepts and steps of calculating simple and compound interest...
EngageNY
Exploiting the Connection to Cartesian Coordinates
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...
Virginia Department of Education
Curve of Best Fit
Which function models the data best? Pupils work through several activities to model data with a variety of functions. Individuals begin by reviewing the shapes of the functions and finding functions that will fit plotted data points. By...
EngageNY
Wishful Thinking—Does Linearity Hold? (Part 1)
Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...
EngageNY
The Geometric Effect of Some Complex Arithmetic 2
The 10th instructional activity 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...
EngageNY
Representing Reflections with Transformations
In the 16th lesson in the series of 32 the class uses the concept of complex multiplication to build a transformation in order to reflect across a given line in the complex plane. The lesson breaks the process of reflecting across a line...
EngageNY
When Can We Reverse a Transformation? 2
The second lesson on finding inverse matrices asks class members to look for a pattern in the inverse matrix and test it to see if it works for all matrices. The teacher leads a discussion to refine the process in finding inverses, then...
EngageNY
When Can We Reverse a Transformation? 3
When working with matrix multiplication, it all comes back around. The 31st portion of the unit is the third instructional activity on inverse matrices. The resource reviews the concepts of inverses and how to find them from the previous...
EngageNY
Revisiting the Graphs of the Trigonometric Functions
Use the graphs of the trigonometric functions to set the stage to inverse functions. The lesson reviews the graphs of the basic trigonometric functions and their transformations. Pupils use their knowledge of graphing functions to model...
EngageNY
Properties of Trigonometric Functions
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 lesson connects them...
EngageNY
Getting a Handle on New Transformations 1
In the first of a two-day lesson on transformations with matrix notation the class transforms the unit square using general transformations, then calculates the area of the transformed image. They discover it is the same as finding the...
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