Translating complex numbers is as simple as adding 1, 2, 3. In the ninth lesson in a 32-part series, the class takes a deeper look at the geometric effect of adding and subtracting complex numbers. The resource leads pupils into what it...

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...

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...

Learn how to increase the probability of success. The 19th installment of a 21-part module teaches future mathematicians how to use probability to analyze decisions. They determine strategies to maximize the chances of a desired outcome.

Your classes become video game designers for a day! They utilize their matrices, vectors, and transformation skills to create and design their own game images. The complex task requires learners to apply multiple concepts to create their...

Examine the meaning and purpose of vectors. Use the lesson to teach your classes how find the magnitude of a vector and what it represents graphically. Your pupils will also combine vectors to find a resultant vector and interpret its...

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,...

Should matrices be allowed to commute when they are being multiplied? Learners analyze this question to determine if the commutative property applies to matrices. They connect their exploration to transformations, vectors, and complex...

Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...

Teach how graphic designers can use mathematics to represent three-dimensional movement on a two-dimensional television surface. Pupils use matrices, vectors, and transformations to model rotational movement. Their exploration involves...

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,...

Learners discover that multiplying transformation matrices produces a composition of transformations. Using software, they map the transformations and relate their findings to the matrices. 

Wait, let's start over — teach your class how to return to the beginning. The first lesson looking at inverse matrices introduces the concept of being able to undo a matrix transformation. Learners work with matrices with a determinant...

When working with matrix multiplication, it all comes back around. The 31st portion of the unit is the third lesson on inverse matrices. The resource reviews the concepts of inverses and how to find them from the previous two lessons....

How do vectors help make problem solving more efficient? Math scholars use vectors to represent different phenomenon and calculate resultant vectors to answer questions. Problems vary from modeling airplane motion to the path of a...

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...

The matrix — it's not just a movie. The instructional activity introduces the concept of 2 x 2 matrix multiplication as a way to represent linear transformations. Class members determine when a linear transformation represented as...

Conjugating in the math classroom — and we're not talking verbs! The seventh instructional activity in a series of 32 introduces the class to the building blocks of complex number division. During the instruction, the class learns to...

The 14th lesson in the unit has the class prove the nine general cases of the geometric representation of complex number multiplication. Class members determine the modulus of the product and hypothesize the relationship for the...

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...