Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Assessment Limits : Items may require the student to be familiar with using the algebraic description for a translation, and for a dilation when given the center of dilation. Items may require the student to be familiar with the algebraic description for a 90-degree rotation about the origin, , for a 180-degree rotation about the origin, , and for a 270-degree rotation about the origin, . Items that use more than one transformation may ask the student to write a series of algebraic descriptions.
Clarification : Students will explain using properties of similarity transformations why the AA criterion is sufficient to show that two triangles are similar.
Students will use triangle similarity to prove theorems about triangles.
Students will prove the Pythagorean theorem using similarity.
Stimulus Attributes : Items may be set in a real-world or mathematical context.
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.