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...

Count the benefits of using the resource. The second installment of a 21-part module focuses on the fundamental counting principle to determine the number of outcomes in a sample space. It formalizes concepts of permutations and...

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...

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,...

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...

How do graphic designers project three-dimensional images onto two-dimensional spaces? Scholars connect their learning of matrix transformations to graphic design. They understand how to apply matrix transformations to make...

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...

Assess pupil understanding of the relationship between matrices, vectors, linear transformations, and parametric equations. Questions range from recall to more complex levels of thinking. Problems represent topics learned throughout the...

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.

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...

Discover the connection between vectors and translations. Through the lesson, learners see the strong relationship between vectors, matrices, and translations. Their inquiries begin in the two-dimensional plane and then progress to the...

Investigate the components of vectors and vector addition through geometric representations. Pupils learn the parallelogram rule for adding vectors and demonstrate their understanding graphically. They utilize the correct notation and...

What does it take to build a stable arch? Pupils apply vectors and physics as they examine arched bridges and their structural integrity. They use vectors to represent the forces acting on the stone sections and make conclusions based on...

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...

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...

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.

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...

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...

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...

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...

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...

Learn the ins and outs of matrix multiplication. After discovering the commutative property does not apply to matrix multiplication in a previous instructional activity in the series, pupils now test the associative and distributive...

Have you hit a wall when trying to create performance task questions? Several open-ended response questions require a deep level of thinking. Topics include triangle congruence, quadrilaterals, special segments, constructions, and...

Allow your pupils to become the mathematicians! Individuals explore the properties of a midsegment of a triangle through construction and measurement. Once they figure out the properties, learners use them to draw conclusions.