Tenth graders investigate dilations and explore the dilation transformation before investigating the properties of a dilation using Cabri Jr. Students extend the concept of dilatation to the coordinate plane.

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...

Can you follow a composition of transformations, or better yet construct them? Young mathematicians analyze the composition of dilations, examining both the scale factor and centers of dilations. They discover relationships for both...

Does it matter how many points to dilate? The resource presents problems of dilating curved figures. Class members find out that not only do they need to dilate several points but the points need to be distributed about the entire curve...

The key to understanding is making connections. Scholars explore angle dilations using properties of parallel lines. At completion, pupils prove that angles of a dilation preserve their original measure. 

There are four activities in this extensive lesson covering the identity matrix and scaling, the linear representation of translations, the linear representation of rotations, and reflections. In small groups, they use the Cabri II...

Is that drawn to scale? Capture the artistry of geometry using the ratio method to create dilations. Mathematicians use a center and ratio to create a scaled drawing. They then use a ruler and protractor to verify measurements. 

Dilations from the origin have a multiplicative effect on the coordinates of a point. Pupils use the method of finding the image of a point on a ray after a dilation to find a short cut. Classmates determine the short cut of being...

Mathematicians compare triangles at different scales. In this geometry lesson, young scholars calculate the area and perimeter of triangles. They use the Ti to make observation of the change that takes place as the triangles are dilated.

Examine dilation with matrices with your class. Learners write a conjecture for how the scale factor determines the size of an image. They then use their conjecture to write a matrix multiplication problem for the illustrated...

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...

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...

Applying a learned technique to a new type of problem is an important skill in mathematics. The lesson asks scholars to apply their understanding to analyze dilations of different figures. They make conjectures and conclusions to...

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. 

Math whizzes explore dilations. They use matrices to perform dilations centered at the origins of triangles and investigate the effect of scale factor on the size relationship between the pre-image and the image of a polygon. A link to...

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,...

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.

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

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,...

How do dilated line segments relate? Lead the class in an activity to determine the relationship between line segments and their dilated images. In the fourth section in a unit of 16, pupils discover the dilated line...

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...

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...

Open up your pupils' eyes and minds on dilations. Scholars perform dilations on a trapezoid on the coordinate plane. They compare the image to the preimage and develop generalizations about dilations.

As they investigate scaling figures and calculate the resulting areas, groups determine the area of similar figures. They continue to investigate the results when the vertical and horizontal scales are not equal.