Do you view proofs as an essential geometric skill? The resource builds on an understanding of dilations by proving the Dilation Theorem of Segments. Pupils learn to question and verify rather than make assumptions. 

Class members perform complex operations on a plane in the 17th segment in the 32-part series. Learners first verify that multiplication by the reciprocal does the same geometrically as it does algebraically. The class then circles back...

Investigate dilations to learn more about them. The second segment in a series of 16 provides a discussion of properties of dilations by going through examples. The problem set provides opportunities for scholars to construct dilations.

Circles are the foundation of many geometric concepts and extensions - a point that is thoroughly driven home in this extensive unit. Fundamental properties of circles are investigated (including sector area, angle measure, and...

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...

Challenge the class to prove that the dilation properties always hold. The activity develops an informal proof of the properties of dilations through a discussion. Two of the proofs are verified with each class member performing the...

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

Develop a more precise definition of similar. The lesson plan begins with an informal definition of similar figures and develops the need to be more precise. The class learns about dilations and uses that knowledge to arrive at a...

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...

Are you searching for a purpose for geometric constructions? Use an engaging approach to explore dilations. Scholars create dilations using a construction method of their choice. As they build their constructed dilation, they...

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....

The 10th lesson 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 number, and another...

Can you prove it? Lead your class through the development of the Side Splitter Theorem through proofs. Individuals connect the ratio and parallel method of dilation through an exploration of two proofs. After completing the proofs,...

Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...

Is it bigger, or is it smaller—or maybe it's the same size? Individuals learn to describe enlargements and reductions and quantify the result. Lesson five in the series connects the creation of a dilated image to the result. Pupils...

Proving triangles are similar is often an exercise in applying one of the many theorems young geometers memorize, like the AA similarity criteria. But proving that the criteria themselves are valid from basic principles is a great...

Apply, apply, apply! A measurement lesson applies a number of concepts to help learn a new construction. Scholars learn to divide a segment into n equal parts using a method that uses the Side Splitter Theorem and a method that...

One is chance, two is a coincidence, three's a pattern. Scholars must determine similarities and differences of a regular hexagon undergoing dilation. They look at lengths, angles, areas, and symmetry.

Class members investigate the effect of a negative scale factor dilation on coordinate shapes as they watch a short video that shows an example of a geometric figure undergoing a dilation with a negative scale factor. Learners then try a...

Individuals show what they know about the geometric representations of complex numbers and linearity. Seventeen questions challenge them to demonstrate their knowledge of moduli and operations with complex numbers. The assessment is...

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...

Circles, circles, everywhere! Pupils learn all about circles, central angles, inscribed angles, circle theorems, arc length, area of sectors, and radian measure using a set of 12 lessons. They then discover volume formulas through...

Understanding how functions transform is a key concept in mathematics. This introductory instructional activity makes a strong connection between the function, table, and graph when exploring transformations. While the resource uses...

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