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Buying a Car
Future car owners use geometric sums to calculate payments for a car loan in the 31st installment of a 35-part module. These same concepts provide the basis for calculating annuity payments.
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Buying a House
There's no place like home. Future home owners investigate the cost of buying a house in the 33rd installment of a 35-part module. They come to realize that the calculations are simply a variation of previous formulas involving car loans...
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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...
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An Appearance of Complex Numbers 2
Help the class visualize operations with complex numbers with a lesson that formally introduces complex numbers and reviews the visualization of complex numbers on the complex plane. The fifth installment of a 32-part series reviews the...
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Distance and Complex Numbers 1
To work through the complexity of coordinate geometry pupils make the connection between the coordinate plane and the complex plane as they plot complex numbers in the 11th part of a series of 32. Making the connection between the two...
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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...
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Introduction to Networks
Watch as matrices break networks down into rows and columns! Individuals learn how a network can be represented as a matrix. They also identify the notation of matrices.
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Coordinates of Points in Space
Combine vectors and matrices to describe transformations in space. Class members create visual representations of the addition of ordered pairs to discover the resulting parallelogram. They also examine the graphical representation of...
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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...
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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...
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Vectors and the Equation of a Line
Represent linear equations in both two and three dimensions using parametric equations. Learners write parametric equations for linear equations in both two and three variables. They graph and convert the parametric equations to...
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Solving Equations Involving Linear Transformations of the Coordinate Plane
How can matrices help us solve linear systems? Learners explore this question as they apply their understanding of transformation matrices to linear systems. They discover the inverse matrix and use it to solve the matrix equation...
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Solving General Systems of Linear Equations
Examine the usefulness of matrices when solving linear systems of higher dimensions. The lesson asks learners to write and solve systems of linear equations in four and five variables. Using matrices, pupils solve the systems and apply...
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Matrix Addition Is Commutative
Explore properties of addition as they relate to matrices. Using graphical representations of vector matrices, scholars test the commutative and associative properties of addition. They determine if the properties are consistent for...
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Matrix Multiplication Is Distributive and Associative
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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Completing the Square (part 1)
Avoid the trap of memorizing steps when completing the square with a resources that provides a conceptual approach to completing the square. Learners that are able to recognize a perfect square trinomial are ready to complete the square.
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The General Multiplication Rule
In the first installment of a 21-part module, scholars build on previous understandings of probability to develop the multiplication rule for independent and dependent events. They use the rule to solve contextual problems.
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Discrete Random Variables
You don't need to be discreet about using the resource on discrete variables. In the fifth installment of a 21-part module, scholars explore random variables and learn to distinguish between discrete and continuous random variables. They...
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Estimating Probability Distributions Empirically 1
What if you don't have theoretical probabilities with which to create probability distributions? The 11th installment of a 21-part module has scholars collecting data through a survey. The results of the survey provide empirical data to...
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Fair Games
What constitutes a fair game? Scholars learn about fair games and analyze some to see if they are fair. They extend this idea to warranties and other contexts.
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Special Triangles and the Unit Circle
Calculate exact trigonometric values using the angles of special right triangles. Beginning with a review of the unit circle and trigonometric functions, class members use their knowledge of special right triangles to find the value of...
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Addition and Subtraction Formulas 2
Knowing the addition formulas allows for the calculations of double and half formulas. The fourth installment of 16 has the class use the addition formula to develop the double angle trigonometric formulas. Using the double formula,...
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Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
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Modeling with Inverse Trigonometric Functions 2
Use inverse trigonometric functions to work with ramps, rabbits, and Talladega. The class models real-world situations with trigonometric functions and solves them using inverses in the 15th installment of a 16-part series. Pupils solve...