Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.
Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology
In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. 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 properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.
Topic A: Definitions and Properties of the Basic Rigid Motions (8.G.A.1)
Lesson 1: Why Move Things Around?
Lesson 2: Definition of Translation and Three Basic Properties
Lesson 3: Translating Lines
Lesson 4: Definition of Reflection and Basic Properties
Lesson 5: Definition of Rotation and Basic Properties
Lesson 6: Rotations of 180 Degrees
Topic B: Sequencing the Basic Rigid Motions (8.G.A.2)0
Lesson 7: Sequencing Translations
Lesson 8: Sequencing Reflections and Translations
Lesson 9: Sequencing Rotations
Lesson 10: Sequences of Rigid Motions
Topic C: Congruence and Angle Relationships (8.G.A.2, 8.G.A.5)
Lesson 11: Definition of Congruence and Some Basic Properties
Lesson 12: Angles Associated with Parallel Lines
Lesson 13: Angle Sum of a Triangle
Lesson 14: More on the Angles of a Triangle
Topic D: The Pythagorean Theorem (8.G.B.6, 8.G.B.7)
Lesson 15: Informal Proof of the Pythagorean Theorem
Lesson 16: Applications of the Pythagorean Theorem