A: Linear Equations and Inequalities

A.1: To solve linear equations in one variable containing:

A.1.a: variables on both sides

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side

A.1.c: fraction or decimal coefficients

Solving Algebraic Equations II

A.2: To solve a formula for an indicated variable.

Area of Triangles
Solving Formulas for any Variable

A.3: To solve, graph, and verify linear inequalities of one variable.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

A.4: To translate English phrases into mathematical terms and vice-versa.

Linear Functions
Systems of Linear Inequalities (Slope-intercept form)

B: Relations, Linear Functions, and Variation

B.1: To define the following terms: relation, ordered pair, abscissa, ordinate.

Introduction to Functions
Point-Slope Form of a Line
Points, Lines, and Equations

B.3, B.4: To graph ordered pairs in the Cartesian coordinate plane, and to graph real-world relations in the Cartesian coordinate plane.

Linear Functions
Point-Slope Form of a Line
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

B.1.b: To define the following terms: function, linear function, slope, x-intercept, y-intercept, ration, proportion, direct variation, partial variation.

Arithmetic Sequences
Compound Interest
Point-Slope Form of a Line
Points, Lines, and Equations

B.6: To identify, graph, and interpret examples of linear functions describing real-world situations.

Absolute Value with Linear Functions
Compound Interest
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

B.7: To graph a linear function using a table of values.

Absolute Value with Linear Functions
Compound Interest
Exponential Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

B.8: To determine if a relation is a function by employing the vertical line test.

Linear Functions

B.10: To determine if an ordered pair is a solution to the linear equation.

Points, Lines, and Equations

B.11: To calculate the slope of a line:

B.11.a: graphically (m = rise/run)

Cat and Mouse (Modeling with Linear Systems) - Metric
Distance-Time and Velocity-Time Graphs - Metric
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

B.11.b: algebraically

Cat and Mouse (Modeling with Linear Systems) - Metric
Distance-Time and Velocity-Time Graphs - Metric
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

B.11.c: from the equation (y = mx+ b)

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Slope-Intercept Form of a Line

B.12: To determine the slope of horizontal, vertical, parallel, and perpendicular lines.

Cat and Mouse (Modeling with Linear Systems) - Metric
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

B.12.b: To write linear equations in:

B.12.b.a: slope-intercept form

Linear Inequalities in Two Variables
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

B.12.b.b: standard form

Standard Form of a Line

B.13 & B.14.a: x and y intercepts

Cat and Mouse (Modeling with Linear Systems) - Metric
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

B.13 & B.14.b: the slope and an ordered pair

Cat and Mouse (Modeling with Linear Systems) - Metric
Point-Slope Form of a Line
Slope-Intercept Form of a Line

B.13 & B.14.c: the slope and y-intercept (y = mx + b)

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

B.15, B.16: To write the equation of a line when given:

B.15, B.16.a: slope and y-intercept

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

B.15, B.16.b: slope and one point on the line

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

B.15, B.16.c: the graph of the line

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

B.15, B.16.d: two points on the line

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

B.17: To construct scatterplots from real-world data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

B.18: To interpret and critically analyze these scatterplots.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

B.19: To identify, describe, and interpret examples of direct variation in real-world situations.

Determining a Spring Constant
Direct and Inverse Variation

B.20: To solve proportions involving direct variation.

Direct and Inverse Variation

B.21: To solve problems involving direct variation.

Determining a Spring Constant
Direct and Inverse Variation

B.22: To identify partial variation.

Direct and Inverse Variation

B.23: To solve problems involving partial variation.

Direct and Inverse Variation

B.24: To define, illustrate, and identify an arithmetic sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

B.25: To determine the nth term of an arithmetic sequence.

Arithmetic Sequences

D: Lines and Line Segments

D.1: To define line segment, ray, line, bisector, median, perpendicular line, perpendicular bisector, transversal, alternate interior angles, corresponding angles, same-side interior angles.

Congruence in Right Triangles
Proving Triangles Congruent
Similar Figures

D.2: To identify and calculate the measures of corresponding angles, alternate interior angles, and same-side interior angles formed by parallel lines.

Similar Figures
Triangle Angle Sum

D.4, D.5, D.6, D.7: Informally and formally construct:

D.4, D.5, D.6, D.7.a: congruent segments;

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines

D.4, D.5, D.6, D.7.b: the perpendicular bisector of a line segment;

Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

D.4, D.5, D.6, D.7.c: a line perpendicular to a given line from a point not on the line;

Constructing Parallel and Perpendicular Lines

D.4, D.5, D.6, D.7.d: a line perpendicular to a given line from a point on the line; and,

Constructing Parallel and Perpendicular Lines

D.4, D.5, D.6, D.7.e: a line parallel to a given line through a point not on the line.

Constructing Parallel and Perpendicular Lines

E: Angles and Polygons

E.1: To define and illustrate by drawing the following: acute angle, right angle, obtuse angle, straight angle, reflex angle, complementary angles, supplementary angles, adjacent angles, vertically opposite angles, congruent angles, central angles of a regular polygon.

Investigating Angle Theorems

E.3.a: To define and illustrate the following polygons: convex, non-convex, regular, triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid.

Area of Parallelograms
Classifying Quadrilaterals
Concurrent Lines, Medians, and Altitudes
Perimeter and Area of Rectangles
Special Parallelograms
Square Roots
Triangle Angle Sum
Triangle Inequalities

E.3.b: To define and illustrate the following triangles: scalene, isosceles, equilateral, acute, right, obtuse.

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Triangle Inequalities

E.4: To classify quadrilaterals as trapezoids, isosceles trapezoids, parallelogram, rectangles, rhombuses, and squares.

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

E.6: To state and apply the properties of parallelograms:

E.6.a: opposite sides are parallel

Classifying Quadrilaterals
Special Parallelograms

E.6.b: opposite sides are congruent

Parallelogram Conditions
Special Parallelograms

E.6.c: opposite angles are congruent

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

E.6.d: the diagonals bisect each other.

Parallelogram Conditions

E.9: To determine the measures of the interior and exterior angles of regular n-gons.

Polygon Angle Sum

E.10: To determine the number of diagonals in a polygon of n sides.

Polygon Angle Sum

E.13: To determine if a triangle is a right triangle by using the converse of the Pythagorean Theorem.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

E.14: To determine the value of the three primary trigonometric ratios by using a calculator.

Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine

E.15: To determine the measure of an angle given the value of one trigonometric ratio of the angle using a calculator.

Sine, Cosine, and Tangent Ratios

E.16: To calculate the measure of an angle or the length of a side of a right triangle using the tangent, sine, and cosine ratios.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine
Tangent Function

E.17: To solve problems that involve trigonometric ratios, using a calculator.

Sine, Cosine, and Tangent Ratios

F: Review of Algebraic Skills

F.2.d: To write numbers in scientific notation and vice versa.

Unit Conversions 2 - Scientific Notation and Significant Digits

F.3.a: To add and subtract polynomials.

Addition and Subtraction of Functions
Addition of Polynomials

F.3.b: To multiply: a monomial by a monomial

Multiplying Exponential Expressions

F.3.d: To multiply: a binomial by a binomial

Modeling the Factorization of x²+bx+c

F.3.e: To divide: a monomial divisor

Dividing Polynomials Using Synthetic Division

F.3.f: To divide: a polynomial by a monomial

Dividing Polynomials Using Synthetic Division