
Unit 1  Transformations, Congruence and Similarity

Unit 2 Exponents
OVERVIEW of Unit 2 Exponents and Equations
In this unit student will:
 distinguish between rational and irrational numbers and show the
 recognize that every rational number has a decimal representation that either terminates or repeats;
 recognize that irrational numbers must have decimal representations that neither terminate nor repeat;
 understand that the value of a square root can be approximated between integers and that non–perfect square roots are irrational;
 locate rational and irrational numbers on a number line diagram;
 use the properties of exponents to extend the meaning beyond countingnumber exponents;
 recognize perfect squares and cubes, understanding that nonperfect squares and nonperfect cubes are irrational;
 recognize that squaring a number and taking the square root of a number are inverse operations; likewise, cubing a number and taking the cube root are inverse operations;
 express numbers in scientific notation;
 compare numbers, where one is given in scientific notation and the other is given in standard notation;
 compare and interpret scientific notation quantities in the context of the situation;
 use laws of exponents to add, subtract, multiply and divide numbers written in scientific notation;
 solve onevariable equations with the variables being on both sides of the equals sign, including equations with rational numbers, the distributive property, and combining like terms; and
 analyze and represent contextual situations with equations, identify whether there is one, none, or many solutions, and then solve to prove conjectures about the solutions.
 distinguish between rational and irrational numbers and show the

Unit 3 Geometric Applications of Exponents
In this unit students will:• determine the relationship between the hypotenuse and legs of a right triangle;• use deductive reasoning to prove the Pythagorean Theorem and its converse;• apply the Pythagorean Theorem to find the distance between two points in a coordinate system; and• solve problems involving the Pythagorean Theorem including diagonals of 3 dimensional figures.

Unit 4 Functions
• recognize a relationship as a function when each input is assigned to exactly one unique output;• reason from a context, a graph, or a table, after first being clear which quantity is considered the input and which is the output;• produce a counterexample: an “input value” with at least two “output values” when a relationship is not a function;• explain how to verify that for each input there is exactly one output; and• translate functions numerically, graphically, verbally, and algebraically.“Function machine” representations are useful for helping students imagine input and output values, with a rule inside the machine by which the output value is determined from the input. Notice that the standards explicitly call for exploring functions numerically, graphically, verbally, and algebraically (symbolically, with letters). This is sometimes called the “rule of four.

UNIT 5 Linear Functions
In this unit students will:• graph proportional relationships;• interpret unit rate as the slope;• compare two different proportional relationships represented in different ways;• use similar triangles to explain why the slope is the same between any two points on a nonvertical line;• derive the equation y = mx for a line through the origin;• derive the equation y = mx + b for a line intercepting the vertical axis at b; and• interpret equations in y = mx + b form as linear functions.In this unit, distance time problems serve the purpose of illustrating how the rates of two objects can be represented, analyzed, and described in different ways: graphically and algebraically. Students create representative graphs and the meaning of various points. They then compare the same information when represented in an equation.By using coordinate grids and various sets of three similar triangles, students prove that the slopes of the corresponding sides are equal, thus making the unit rate of change equal. After proving with multiple sets of triangles, students generalize the slope to y = mx for a line through the origin and y = mx + b for a line through the vertical axis at b.In Grade 8, the focus is on linear functions, and students begin to recognize a linear function from its form y = mx + b. Students also need experiences with nonlinear functions, including functions given by graphs, tables, or verbal descriptions but for which there is no formula for the rule, such as a girl’s height as a function of her age. Students learn that proportional relationships are part of a broader group of linear functions, and they are able to identify whether a relationship is linear. Nonlinear functions are included for comparison.

Unit 6 Solving Systems of Equations
Two way tables  relative frequencies
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