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Common Core: Math
Subject: Math
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 Grade 8 Module 2: The Concept of Congruence In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the...

 Grade 8 Module 3: Similarity In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the AngleAngle criterion for similar...

 Grade 8 Module 5: Examples of Functions from Geometry In the first topic of this 15 day module, students learn the concept of a function and why functions are necessary for describing geometric...

 Grade 8 Module 7: Introduction to Irrational Numbers Using Geometry Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented...

 Student Outcomes Students are introduced to vocabulary and notation related to rigid motions (e.g., transformation, image, and map). Students are introduced to transformations of the plane and learn...

 Student Outcomes Students perform translations of figures along a specific vector. Students label the image of the figure using appropriate notation. Students learn that a translation maps lines to...

 Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these...

 Student Outcomes Students will know the Pythagorean theorem and be shown an informal proof of the theorem. Students will use the Pythagorean theorem to find the length of the hypotenuse of a right...

 Student Outcomes Students learn that when lines are translated they are either parallel to the given line, or the lines coincide. Students learn that translations map parallel lines to parallel lines...

 Student Outcomes Students know the definition of congruence and related notation. Students know that to prove two figures are congruent there must be a sequence of rigid motions that maps one figure...

 Student Outcomes Students know that corresponding angles, alternate interior angles, and alternate exterior angles of parallel lines are equal. Students know that when these pairs of angles are...

 Student Outcomes Students learn the definition of dilation and why “same shape” is not good enough to say two figures are similar. Students know that dilations magnify and shrink figures.

 Student Outcomes Students know the definition of reflection and perform reflections across a line using a transparency. Students show that reflections share some of the same fundamental properties...

 Student Outcomes Students know the Angle Sum Theorem for triangles; the sum of the interior angles of a triangle is always 180 degrees. Students present informal arguments to draw conclusions about...

 In Topic C, on the definition and properties of congruence, students learn that congruence is just a sequence of basic rigid motions. The fundamental properties shared by all the basic rigid motions...

 Student Outcomes Students learn about the sequence of transformations (one move on the plane followed by another) and that a sequence of translations enjoy the same properties as a single translation...

 Student Outcomes Students know how to rotate a figure a given degree around a given center. Students know that rotations move lines to lines, rays to rays, segments to segments, and angles to angles...

 Student Outcomes Students learn that a rotation of 180 degrees moves a point on the coordinate plane (a, b), to (a, b). Students learn that a rotation of 180 degrees around a point, not on the line...

 Student Outcomes Students know a third informal proof of the angle sum theorem. Students know how to find missing interior and exterior angle measures of triangles and present informal arguments to...

 Student Outcomes Students learn that the reflection is its own inverse transformation. Students understand that a sequence of a reflection followed by a translation is not equal to a translation...

 Student Outcomes Students use the Pythagorean theorem to determine missing side lengths of right triangles.

 Student Outcomes Students learn that the reflection is its own inverse transformation. Students understand that a sequence of a reflection followed by a translation is not equal to a translation...

 Student Outcomes Students know the definition of similar and why dilation alone is not enough to determine similarity. Given two similar figures, students describe the sequence of a dilation and a...

 Topic B is a critical foundation to the understanding of congruence. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while...