Cluster 1: Understand similarity in terms of similarity transformations. (Geometry - Major Cluster)Archived

Students are asked to graph the image of three points on a line after a dilation using a center not on the line and to generalize about dilations of lines when the line does not contain the center.

Type: Formative Assessment

Students are asked to graph the image of three points on a line after a dilation using a center not on the line and to generalize about dilations of lines when the line does not contain the center.

Type: Formative Assessment

Students are asked to dilate a line segment and describe the relationship between the original segment and its image.

Type: Formative Assessment

Students are asked to justify statements of a proof of the AA Similarity Theorem.

Type: Formative Assessment

Students will indicate a complete proof of the AA Theorem for triangle similarity.

Type: Formative Assessment

Students are asked to graph the image of two points on a line after a dilation using a center on the line and to generalize about dilations of lines when the line contains the center.

Type: Formative Assessment

Students are asked to describe the AA Similarity Theorem.

Type: Formative Assessment

Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two quadrilaterals are similar.

Type: Formative Assessment

Students are given the definition of similarity in terms of similarity transformations and are asked to explain how this definition ensures the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Type: Formative Assessment

Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two triangles are similar.

Type: Formative Assessment

This set of geometry challenges focuses on using transformations to show similarity and congruence of polygons and circles. Students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Using non-rigid motions (dilations), students learn how to show that two polygons are similar. Students will write coordinate proofs confirming that two figures are similar.

Type: Lesson Plan

Students determine the minimum amount of information needed to prove that two triangles are similar.

Type: Lesson Plan

Students will learn the difference between congruence and similarity of classes of figures (such as circles, parallelograms) in terms of the number of variable lengths in the class. A third category will allow not only rigid motions and dilations, but also a single one-dimensional stretch, allowing more classes of figures to share sufficient common features to belong.

Type: Lesson Plan

This resource is designed to allow students to discover the effects of dilations on geometric objects using the free online tools in GeoGebra.

Type: Lesson Plan

Students identify dilations, verify that polygons are similar, and use the dilation rule to map dilations. Task cards are provided for independent practice. The PowerPoint also includes detailed illustrations for constructing a dilation using a compass and a straight edge.

Type: Lesson Plan

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties:

• Solving problems by determining the lengths of the sides in right triangles.
• Finding the measurements of shapes by decomposing complex shapes into simpler ones.

The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

Type: Lesson Plan

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties solving problems by determining the lengths of the sides in right triangles and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

Type: Lesson Plan

This lesson is designed to introduce students to the idea of finding patterns in the generation of several different types of fractals. This lesson provides links to discussions and activities related to patterns and fractals as well as suggested ways to work them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Lesson Plan

Don't be a shrinking violet. Learn how uniform scaling is important for candy production.

Type: Perspectives Video: Professional/Enthusiast

The "machine" generates 5000 points based upon a random selection of points. Each point is chosen iteratively to be a particular fraction of the way from a current point to a randomly chosen vertex. For carefully chose fractions, the results are intriguing fractal patterns, belying the intuition that randomness must produce random-looking outputs.

Type: Problem-Solving Task

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other, using the definition of similarity in terms of similarity transformations.

Type: Problem-Solving Task

This task asks students to make deductions about a line after it has been dilated by a factor of 2.

Type: Problem-Solving Task

This informational text resource is intended to support reading in the content area. The article indicates that traditional geometry does not suffice in describing many natural phenomena. The use of computers to implement repeated iterations can generate better models. Offered by IBM, this text can be used in a high school geometry class to demonstrate applications of similarity and to illustrate important ways that geometry can be used to model a wide range of scientific phenomena.

Type: Text Resource

In this tutorial, students will use a scale factor to dilate one line onto another.

Type: Tutorial

This is an interactive model that demonstrates how different light levels effect the size of the pupil of the eye. Move the slider to change the light level and see how the pupil changes.

Type: Virtual Manipulative

Students will analyze the perimeters of stages of the Koch Snowflake and note that the perimeter grows by a factor of 4/3 from one stage to the next. This means that the perimeter of this figure grows without bound even though its area is bounded. This effect was noted in the late 1800's and has been called the Coastline Paradox.

Type: Worksheet