Unit 1: Number Sense-Squares, Square Roots, Cubes & Cube Roots - 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 rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
Unit 2: The Real Number System Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Attend to precision.
Unit 3 :Properties of Exponents
Know and apply the properties of integer exponents to generate equivalent numerical expressions. Construct viable arguments and critique the reasoning of others. Model with mathematics. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning Essential Vocabulary:
Base
Dividing Powers with the Same Base Property
Exponent
Exponential Form
Laws of Exponents
Multiplication Property of Exponents
Perfect Cube
Perfect Square
Power
Raising a Power to a Power Property
Raising a Product to a Power Property
Raising a Quotient to a Power Property
Zero Exponent
UNIT 4 : Scientific Notation
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 x 3-3= 3-3= 1/33 = 1/27. 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 x 108 and the population of the world as 7 x 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. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational nu Make sense of problems and persevere in solving them. Reason abstractly and quantitatively.
UNIT 5: Solving Equation 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 is irrational. Solve linear equations in one variable.
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Attend to precision.
Unit 6: Geometric Properties
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Students will understand that…
parallel lines cut by a transversal create congruent and supplementary angle pairs
they can use the angle relationships in parallel lines cut by a transversal to find missing angle measurements using algebraic reasoning
the interior angles of a triangle add up to 180
the exterior angle of a triangle is congruent to the sum of the two remote interior angles
they can use the geometric properties of interior and exterior angles of a triangle to find missing measurements using algebraic reasoning
similar figures have congruent corresponding angles and proportional corresponding side lengths and use this to find missing measurements
Essential Vocabulary:
Adjacent Angles
Alternate Exterior Angles
Alternate Interior Angles
Angle-Angle Criterion
Angle Sum Theorem
Angle-Angle Similarity Postulate
Complimentary Angles
Congruent
Congruent Angles
Corresponding Angles
Corresponding Sides
Deductive Reasoning
Exterior Angle
Interior Angle
Nonadjacent Angles
Parallel Lines
Remote Interior Angles
Same Side Interior Angles
Scale Factor
Similar Polygons
Similarity
Supplementary Angles
Transversal
Triangle
Triangle Exterior Angle Theorem
Triangle Sum Theorem
Vertical Angles
Unit:7 PYTHAGOREAN THEOREM
Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a rational number. Explain a proof of the Pythagorean Theorem and its converse. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Make sense of problems and persevere in solving them.
Unit:8 Volume of Cylinders, Cones & Spheres Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a rational number. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Reason abstractly and quantitatively. Use appropriate tools strategically. Look for and express regularity in repeated reasoning. Make sense of problems and persevere in solving them.
Unit 9:Identifying Functions
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.