Class members make a real connection to matrices in the 25th part of a series of 32 by looking at the identity matrix and making the connection to the multiplicative identity in the real numbers. Pupils explore different...

Explore methods for solving linear systems with your classes and introduce learners to using matrices as a viable method. Scholars are able to recognize situations where matrices are the efficient method of solving. Application...

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...

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,...

Help the class visualize operations with complex numbers with a activity that formally introduces complex numbers and reviews the visualization of complex numbers on the complex plane. The fifth installment of a 32-part series...

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...

Matrix multiplication can seem random to pupils. Here's a instructional activity that uses a real-life example situation to reinforce the purpose of matrix multiplication. Learners discover how to multiply matrices and relate the process...

Time for matrices and complex numbers to come together. Individuals use matrices to add and multiply complex numbers by a scalar. The instructional activity makes a strong connection between the operations and graphical transformations.

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...

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,...

Data encryption is an important security measure for sensitive data stored on computers. Pupils learn how to utilize matrices for creating code. They also get a great review of matrix multiplication, inverse matrices, and the identity...

There's a strong chance that class members enjoy learning math through engaging games. Scholars analyze games of chance to determine long-term behavior. They learn to calculate expected value to help with this assessment.

Discover the extension of parametric equations to model linear transformations. Scholars first write parametric equations to model lines through two points. They then find the parametric equations that represent a linear transformation.

Does complex number multiplication have the class spinning? Here's a resource that helps pupils explore and discover the geometric effect of multiplying complex numbers. In the 14th installment in the 32-part unit groups look at the unit...

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 plan...

Discover how mathematics can be useful in comparing strategies. Scholars develop probability distributions for situations and calculate expected value. They use their results to identify the best strategy for the situation.

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.

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...

Complex solutions are not always simple to find. In the fourth lesson of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the first lesson....

What do you get when you combine a matrix and a cube? Well that depends on the matrix! Pupils use online software to graph various transformations of a cube. Ultimately, they are able to describe the matrix that is responsible for a...

Assess your classes' knowledge using questions that require high-level thinking and explanation. Learners use matrices to answer application questions. They also demonstrate their understanding of matrix operations.

Investigate expected value as a long-run average. The eighth installment of a 21-part module has scholars rolling pairs of dice to determine the average sum. They find aggregate data by working in groups and interpret expected value as...

Challenge scholars to show what they know about properties and addition and subtraction formulas for trigonometric functions. The resource provides a mid-unit check on the progress toward mastery of trigonometric concepts. The areas...

Not all linear functions are linear transformations, only those that go through the origin. The third lesson in the 32-part unit proves that linear transformations are of the form f(x) = ax. The lesson plan takes another look at examples...