
The Number System8.NS Know that there are numbers that are not rational, and approximate them by rational numbers.MGSE8.NS.1. Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.MGSE8.NS.2. Use rational approximation of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., estimate π^{2} to the nearest tenth).Show detailsExpressions & Equations8.EE Work with radicals and integer exponents.MGSE8.EE.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions.Show detailsMGSE8.EE.2. Use square root and cube root symbols to represent solutions to equations. Recognize that x^{2} = p (where p is a positive rational number and lxl ≤ has 2 solutions and x^{3} = p (where p is a negative or positive rational number and lxl ≤ 10) has one solution. Evaluate square roots of perfect squares ≤ 625 and cube roots of perfect cubes≥ 1000 and ≤ 1000.MGSE8.EE.3. Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other.Show detailsMGSE8.EE.4. Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Understand 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 (e.g. calculators).Geometry8.G Understand and apply the Pythagorean Theorem.MGSE8.G.6. Explain a proof of the Pythagorean Theorem and its converse.MGSE8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.MGSE8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.8.G Solve realworld and mathematical problems involving volume of cylinders, cones, and spheres.MGSE8.G.9. Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve realworld and mathematical problems.

Key Vocabulary Cube Root • Decimal Expansion • Exponent • Exponential Notation • Irrational • Like Terms • Multiplication Property of Equality • Multiplicative Inverses • Perfect Square • Radical • Rational • Scientific Notation • Significant Digits • Solution • Square Root • Radius • Radical • Rational Number • Right Triangle • Volume: Altitude of a Triangle • Base (of a Polygon) • Coordinate Plane • Coordinate Point of a Plane • Cone • Converse of Pythagorean Theorem • Cube Root • Cylinder • Deductive Reasoning • Diameter • Distance Formula • Geometric Solid • Height of Solids • Hypotenuse • Irrational • Leg of a Triangle • Perfect Squares • Perfect Cubes • Pythagorean Theorem • Pythagorean Triples • Sphere