Appendix On Implementing District Standards
This curriculum unit was developed to implements California Common Core State Standards for Mathematics, which are also the academic standards of the East Side Union High School District.
California Common Core State Standards for Mathematics
The three mathematical domains being used throughout this curriculum unit in connection to geometry (G) are congruence (CO), geometric measurements and dimensions (GMD), and similarity, right triangles, and trigonometry (SRT).
G.CO.2 - Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
G.CO.3 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G.CO.4 - Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.5 - Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
G.CO.6 - Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
G.GMD.4 - Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
G.SRT.1 - Verify experimentally the properties of dilations given by a center and a scale factor: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
G.SRT.2 - Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.3 - Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.
G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Standards for Mathematical Practices
The following Standards for Mathematical Practices (SMP) are used in particular lessons and activities within this curriculum unit:
SMP 1: Make Sense of Problems and Persevere in Solving Them
This practice is used in Lesson 3 of this curriculum unit when students develop similarity statements that contain information about congruent angels and proportional sides. Also, this practice is used when students draw similar triangles to have the same orientation to make relationships clear.
SMP 7: Look for and make use of structure
This practice is used in Lesson 2 of this curriculum unit when students are asked to describe changing signs of coordinates based on location within coordinate plane and relate the translation vector to rules applied to coordinates.
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