Topics and Objectives
1. Chapter 1 - Integers
— Determine opposite numbers, compare integers, and the absolute value of given integers
— Using the rules of addition, subtraction, multiplication, and division provided simplify all integer problems
— Use Order of Operations to simplify numerical expressions
— Organize the real number system in a graphic organizer and determine whether it is closed under various operations
— Recognize the Properties of Equality and how it is applied in solving basic arithmetic
2. Chapter 2 - Algebraic Expressions
— Translate word phrases into numerical or algebraic expressions
— Simplify expressions by combining like terms and using the distributive property
— Simplify exponential expressions using the product, quotient, or power rules
3. Chapter 3 - Equations & Inequalities
— Solve basic one and two step linear equations and inequalities by addition, subtraction, multiplication, and division
— Solve multi-step equations and inequalities with variables on one side or both sides
— Determine and understand how an equation can have one solution, no solution, or infinitely many solutions
— Translate word phrases into numerical or algebraic equations/inequalities
— Create and apply equations to real-world examples and scenarios
4. Chapter 4 - Ratios, Proportions, & Percents
— Understand the concept of a ratio and learn the various ways that it can be written
— Calculate the unit rates when given real-world applications
— Find the missing measurement value of rate when given the unit rate
— Determine whether figures are similar and solve any missing measurements when giving a scale drawing, model, or similar figure
— Solve percent proportions and use/create percent equations to determine the value of a discount, mark-up, sales tax, and tip
— Calculate the simple interest as well as the rate, time, or principal when already given the interest value
5. Chapter 5 - Functions & Linear Representations
— Understand that a function is a rule that assigns to each input exactly one output
— Interpret the equation y=mx+b as defining a linear function, whose graph is straight line
— Graph proportional relationships, interpreting the unit rate as the slope of the graph
— Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane
— Construct a function to model a linear relationship between two quantities
— Determine the rate of change and initial value of the function from a description of a relationship or from two ordered pair values, including reading these from a table, graph, or formula
6. Chapter 6 - System of Equations
— Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously
— Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations
— Solve real-world and mathematical problems leading to linear equations in two variables
7. Chapter 7 - Geometry
— Use informal arguments to establish facts about the angle sum and exterior angle of triangles, and the angle-angle criterion for similarity of triangles
— Explain the congruence of various angles when parallel lines are cut by a transversal
— 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
— Understand the angle congruency and side similarities of similar quadrilaterals
— Memorize quadrilateral rules
8. Chapter 8 - Transformations
— Verify experimentally the properties of rotations, reflections and translations
— Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations
— Describe a sequence between two similar two-dimensions figures that exhibits the similarity between them
— Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates
9. Chapter 9 - Measurement (Area & Volume)
— Know the formulas for the perimeter and area of triangles, rectangles, squares, quadrilaterals, trapezoids, and circles
— Solve the area and perimeter of composite figures and figures of shaded regions
— Know the formulas for the volume and surface area of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems
— Identifying and classify a three-dimensional figure by its proper name
— Identify the perimeter/area/volume of a figure with specific measurements per side
10. Chapter 10 - Probability & Statistics
— Understand the various forms of probability (theoretical and experimental) using the vocabulary conjunctions "and" or "or"
— Create mathematical expressions when given an independent or dependent event (compound probability) in a real-world scenario
— Determine which measures of center (mean, median, and mode) would best represent the set of data
— Calculate mean, median, mode and range
— Construct and interpret scatter plots using the measurement data given
— Investigate patterns of association between two quantities on a scatter plot
— Create a two-way frequency table when given a set of data of a real-world scenario