Algebra I Part A

Syllabus

Mr. Kea

ALGEBRA I Part B CURRICULUM PACING GUIDE

Algebra 1 Part B Course Outline

Expressions and Operations

A.1             The student will

1. represent verbal quantitative situations algebraically; and
2. evaluate algebraic expressions for given replacement values of the variables.

A.2             The student will perform operations on polynomials, including

1. a) applying the laws of exponents to perform operations on expressions;
2. adding, subtracting, multiplying, and dividing polynomials; and
3. c) factoring completely first- and second-degree binomials and trinomials in one variable.

A.3             The student will simplify

1. a)   square roots of whole numbers and monomial algebraic expressions square roots of whole numbers and monomial algebraic expressions;
2. b)   cube roots of integers; and
3. c)   numerical expressions containing square or cube roots.

Equations and Inequalities

A.4             The student will solve

1. multistep linear equations in one variable algebraically;
2. quadratic equations in one variable algebraically;
3. literal equations for a specified variable;
4. systems of two linear equations in two variables algebraically and graphically; and

1. practical problems involving equations and systems of equations.

A.5             The student will

1. solve multistep linear inequalities in one variable algebraically and represent the solution graphically;

1. represent the solution of linear inequalities in two variables graphically;
2. solve practical problems involving inequalities; and
3. represent the solution to a system of inequalities graphically.

A.6             The student will

1. a) determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line;
2. write the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line; and
3. graph linear equations in two variables.

Functions

A.7             The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including

1. a) determining whether a relation is a function;
2. domain and range;
3. c) zeros;
4. d) intercepts;
5. e) values of a function for elements in its domain; and
6. f) connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs.

Statistics

A.8             The student, given a data set or practical situation, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

A.9             The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear and quadratic functions.

Topic: Expressions and Operations

Standard A1.1, 3

• The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

Objectives:

• Translate verbal quantitative situations into algebraic expressions and vice versa.
• Model real-world situations with algebraic expressions in a variety of representations (concrete, pictorial, symbolic, verbal).
• Evaluate algebraic expressions for a given replacement set to include rational numbers.
• Evaluate expressions that contain absolute value, square roots, and cube roots.
• Express square roots of a whole number in simplest form.
• Express the cube root of a whole number in simplest form.
• Express the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have positive values.
• Topic: Equations and Inequalities
• Standard A1.4, 5
• The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
• Objectives:
• Solve a literal equation (formula) for a specified variable.
• Simplify expressions and solve equations, using the field properties of the real numbers and properties of equality to justify simplification and solution.
• Solve multistep linear equations in one variable.
• Confirm algebraic solutions to linear equations, using a graphing calculator.
• Solve multistep linear inequalities in one variable.
• Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers.
• Solve real-world problems involving equations and inequalities.
• Standard A1.6
• The student will graph linear equations and linear equations and inequalities in two variables, including
• Objectives:
• Use the parent function y = x and describe transformations defined by changes in the slope or y-intercept.
• Find the slope of the line, given the equation of a linear function.
• Find the slope of a line, given the coordinates of two points on the line.
• Find the slope of a line, given the graph of a line.
• Recognize and describe a line with a slope that is positive, negative, zero, or undefined.
• Use transformational graphing to investigate effects of changes in equation parameters on the graph of the equation.
• Write an equation of a line when given the graph of a line.
• Write an equation of a line when given two points on the line whose coordinates are integers.
• Write an equation of a line when given the slope and a point on the line whose coordinates are integers.
• Write an equation of a vertical line as x = a.  
• Write the equation of a horizontal line as y = c.
• Graph linear equations and inequalities in two variables, including those that arise from a variety of real-world situations.
• Standard A1.4, 5, 6
• Objectives:
• Given a system of two linear equations in two variables that has a unique solution, solve the system by substitution or elimination to find the ordered pair which satisfies both equations.
• Given a system of two linear equations in two variables that has a unique solution, solve the system graphically by identifying the point of intersection.
• Determine whether a system of two linear equations has one solution, no solution, or infinite solutions.
• Write a system of two linear equations that models a real-world situation.
• Interpret and determine the reasonableness of the algebraic or graphical solution of a system of two linear equations that models a real-world situation.
• Solve systems of linear inequalities algebraically and graphically.
• Topic: Functions
• Standard A1.7
• The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including
• Objectives:
• Determine whether a relation, represented by a set of ordered pairs, a table, or a graph is a function.
• Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.
• For each x in the domain of f, find f(x).
• Represent relations and functions using concrete, verbal, numeric, graphic, and algebraic forms. Given one representation, students will be able to represent the relation in another form.
• Detect patterns in data and represent arithmetic and geometric patterns algebraically.