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. 

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 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.

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 instructional activity develops an informal proof of the properties of dilations through a discussion. Two of the proofs are verified with each class member...

Translating complex numbers is as simple as adding 1, 2, 3. In the ninth lesson plan 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...

Geometric transformations are explored by high schoolers. They will create a set of instructions for plotting coordinates representing an original transformation of a real-world figure. These instructions are shared with middle...

Develop a more precise definition of similar. The lesson 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...

Students solve problems of dilation and velocity. In this geometry instructional activity, students apply the Pythagorean Theorem to solve problems and relate it to time and velocity.

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 plan on inverse matrices. The resource reviews the concepts of inverses and how to find them from the previous two...

Students investigate the rigid motions of reflection, rotation, translation, and dilation. This investigation be accomplished through classroom instruction and exploration using Geometer's Sketchpad.

Tenth graders identidy and define various geometry terms, Students create exact replicas of a shape that is either smaller or larger than the original shape. Students prove that their entire shapes are larger or smaller in the same...

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,...

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 plan 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...

Learners examine images and preimages of a mapping and identify isometry. They view images by M.C. Escher, observe teacher demonstrations, and create a translation image, a rotation image, and a dilation.

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...

Double, toil ,and double linear dimensions. Learners first complete an assessment investigating how doubling linear dimensions affects the area of pizzas and the volume of popcorn containers. They then complete an activity investigating...

High schoolers perform dilation on various geometric shapes. They also discuss pros and cons of dilation and employ the Frayer Model to study the vocabulary words in this section.