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. 

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...

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...

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...

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...

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...

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. 

To commute or not to commute, that is the question. The 26th segment in a 32-segment lesson plan focuses on the effect of performing one transformation after another one. The pupils develop the procedure in order to multiply two 2 X 2...

Class members make a real connection to matrices in the 25th part of a series of 32 by looking at the identity matrix and making the connection to the multiplicative identity in the real numbers. Pupils explore different...

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...

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...

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...

The coordinate plane is a popular place! Identify rotations, reflections, and dilations on the coordinate plane. Pupils work in small groups to match transformations of a figure with the description of the transformation....

Create a personal tree. By visiting an exhibit at the National Museum of Mathematics, the resource introduces the idea of fractals. The exhibit takes an image of the person and creates a tree by repeating scaled images on the shoulders...

Double the dimensions, quadruple the surface area. Pairs build similar prisms and compare the ratios of their surface areas and volumes to the ratio of the heights. Given two similar cones, partners determine the ratios of the lateral...

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...

How do you find the lengths of items that cannot be directly measured? The 13th installment in a series of 16 has pupils use the similarity content learned in an earlier resource to solve real-world problems. Class members determine...

Use 2x2 matrices to move along a line. The second day of a two-day lesson 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...

What does it take to show two triangles are similar? The 11th segment in a series of 16 introduces the AA Criterion for Similarity. A discussion provides an informal proof of the theorem. Exercises and problems require scholars to apply...

Determine whether two triangles are similar. The lesson presents opportunities for pupils to find the criterion needed to show that two triangles are similar. Scholars use the definition of similarity to find any missing side...