EngageNY
First Consequences of FTS
Challenge the young mathematicians to find the exact coordinates of a dilated point. The fifth segment in a 16-part series introduces the class to the converse of the Fundamental Theorem of Similarity. Scholars use the theorem to find...
EngageNY
Similarity
Use the coordinate plane to show two figures are similar. The lesson incorporates congruence transformations and dilations to move a figure on to another figure. Pupils determine that if a similarity transformation exists between two...
Charleston School District
Review Unit 2: Congruence and Similarity
Review for the test with a comprehensive list of terms and concepts for the unit on congruence and similarity. It divides divides the sections in the order of the lessons presented during the unit.
EngageNY
Exploiting the Connection to Cartesian Coordinates
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...
Virginia Department of Education
Transformations
Geometry in life-sized dimensions! Using enlarged graph paper, pupils perform a series of transformations. By recording the initial and final placement of the images, they are able to analyze the patterns in the coordinates during a...
EngageNY
Scale Factors
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...
EngageNY
Making Scale Drawings Using the Parallel Method
How many ways can you create a dilation? Many! Individuals strengthen their understanding of dilations by using various methods to create them. The new technique builds on pupils' understanding of the ratio method. Using the ratio,...
EngageNY
Mid-Module Assessment Task - Geometry (Module 2)
Challenge: create an assessment that features higher level thinking from beginning to end. A ready-made test assesses knowledge of dilations using performance tasks. Every question requires a developed written response.
EngageNY
Dividing the King’s Foot into 12 Equal Pieces
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 that...
EngageNY
Justifying the Geometric Effect of Complex Multiplication
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...
EngageNY
The Geometric Effect of Multiplying by a Reciprocal
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...
Illustrative Mathematics
Similar Circles
Young geometers flex their transformation muscles in this brief but powerful exercise using dilations and translations to develop the similarity of circles. The plan provides guidelines to help learners navigate a pair of deceptively...
EngageNY
End-of-Module Assessment Task — Precalculus (Module 1)
A transformational assessment determines how far pupils are advancing toward mastering complex and matrix standards. The assessment checks the learners' understanding of linear transformations, complex numbers and the complex plane,...
Mathed Up!
Negative Scale Factor
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...
EngageNY
The Geometric Effect of Some Complex Arithmetic 2
The 10th activity 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...
Massachusetts Department of Education
Similarity through Transformations
Create the ultimate miniature golf course. The 93-page model curriculum unit from the Massachusetts Department of Elementary and Secondary Education contains nine lessons on understanding similarity in terms of both Euclidean geometry...
Willow Tree
Transformations
How does something go from here to there? Describe it with a transformation. Young mathematicians learn how to translate, reflect, rotate, and dilate an image.
EngageNY
Modeling Video Game Motion with Matrices 1
Video game characters move straight with matrices. The first day of a two-day lesson introduces the class to linear transformations that produce straight line motion. The 23rd part in a 32-part series has pupils determine the...
EngageNY
Four Interesting Transformations of Functions (Part 3)
Continue the study of transformations with an examination of horizontal stretches, shrinks, and reflections. Individuals use the same process used in parts one and two of this series to examine horizontal changes. The resource also...
EngageNY
Stretching and Shrinking Graphs of Functions
Why is that graph wider? Pupils learn about stretching and shrinking graphs of square root, absolute value, cubic, and quadratic functions. They study both vertical and horizontal stretches and shrinks in addition to reflections.
University of Utah
Geometry: Transformations, Congruence, and Similarity
Rigid motions are to congruence as what are to similarity? Investigate properties of rigid motions and define congruence in terms of rigid motions with the ninth chapter of a 10-part eighth grade workbook series. The lesson then prompts...
EngageNY
Getting a Handle on New Transformations 2
Use 2x2 matrices to move along a line. The second day of a two-day lesson plan is the 28th installment in a 32-part unit. Pupils work together to create and solve systems of equations that will map a transformation to a given point. The...
Mathematics Vision Project
Module 4: Similarity and Right Triangle Trigonometry
Right you are to use a great resource. Starting with a lesson on dilations, scholars learn about similarity transformations and similar triangles. They use the knowledge to develop an understanding of right triangle trigonometry in later...
EngageNY
Linear Transformations as Matrices
Don't stop with two-dimensional learning, go to the next dimension! Learners verify that 3x3 matrices represent linear transformations in the third dimension. Additionally, they verify the algebraic properties that extend to vector...