Download Secondary Algebra I Objectives

Secondary Algebra I Objectives
Chapter 1: Variables, Expressions, and Equations
Students will learn to identify patterns, represent real-world situations using
expressions and equations, and simplify expressions using the order of
operations
• Use constant differences to identify linear patterns in number sequences. (section 1.1)
• Use variables to represent unknown quantities. (section 1.2)
• Represent real world situations with linear equations and solve. (section 1.2)
• Apply the order of operations to algebraic expressions. (section 1.3)
Chapter 2: Operations in Algebra
Students will add, subtract, multiply, and divide rational numbers and algebraic
expressions and apply the commutative, associative, and distributive properties
when necessary.
• Simplify expressions involving opposites and absolute value. (section 2.1)
• Add, subtract, multiply, and divide rational expressions including real-world applications.
(sections 2.2-2.4)
• Apply and identify the Commutative, Associative, and Distributive Properties in multi-step
equations. (sections 2.5 – 2.7)
• Add, subtract, multiply, and divide algebraic expressions. (sections 2.6 and 2.7)
• Simplify expressions with several variables. (sections 2.6 and 2.7)
Chapter 3: Equations
Students will solve multi-step equations.
• Represent real world situations with linear equations and solve. (all sections)
• Solve equations with one variable by using addition, subtraction, multiplication, or division.
(sections 3.1-3.5)
• Solve multi-steps equations. (sections 3.4 and 3.5)
• Solve equations containing multiple variables for a specific variable (literal equations).
(section 3.6)
• Using formulas to solve equations in one and two variables. (section 3.6)
Chapter 4: Proportional Reasoning
Students will solve percent problems using proportional reasoning and by writing
an equation.
• Identify the means and extremes of a proportion. (section 4.1)
• Use proportions to solve problems. (section 4.1)
• Solve problems involving percents. (section 4.2)
• Sections 4.1 and 4.2 are the only sections covered in Chapter 4.
Chapter 5: Linear Functions
Students will write and graph linear equations.
• Graph lines in a coordinate plane. (If needed you may use 1.4 to review the coordinate
plane and graphing ordered pairs.
• Represent linear patterns with equations and graphs. (Make sure to incorporate section
1.5)
• Determine whether a relation is a function. (section 5.1)
• Identify the domain and range of relations. (section 5.1)
• Calculate the slope of a line using rise/run and the ratio of the differences of x- and
y coordinates. (section 5.2)
• Define, explain, and use the components of the slope-intercept equation. (section
5.4)
• Define, explain, and use the components of the standard form equation. (section
5.5)
• Identify parallel and perpendicular lines by comparing their slopes. (section 5.6)
• Write equations of lines that are parallel and perpendicular to given lines. (section
5.6)
• Finding the rate of change from a graph. (section 5.3)
• Solving and graphing direct variation equations. (section 5.3)
• Defining, explaining, and using the components of the point-slope form equation.
(section 5.5)
Chapter 6: Inequalities and Absolute Value
Students will solve various types of inequalities and graph their results on a
number line.
• Solve linear inequalities that involve addition, subtraction, multiplication, and
division. (section 6.1)
• State and apply the multiplication and division properties of inequality. (section 6.2)
• Solve multi-step inequalities in one variable. (section 6.2)
• Graph solution sets of compound inequalities. (section 6.3)
• Solve compound inequalities of the first degree. (section 6.3)
• Properties of the absolute value function. (section 6.4)
• Solving absolute value equations of the first degree. (section 6.5)
Chapter 7: Systems of Equations and Inequalities
Students will solve systems of equations by graphing, elimination and
substitution.
• Graph systems of linear equations (section 7.1)
• Solve systems of linear equations by inspecting a graph. (7.1)
• Find the exact solution to a system of linear equations with integer coefficients by
using the following methods: graphing, substitution, and elimination. (sections 7.1
– 7.3)
• Graph the solution to a system of linear inequalities with integer coefficients.
(section 7.5)
• Inconsistent and consistent, dependent and independent, systems. (section 7.4)
• Traditional math applications with one and two variables. (section 7.6)
Chapter 8: Exponents and Exponential Functions
Students will use laws of exponents to simplify expressions.
• Define exponents and bases. (section 8.1)
• Apply the Laws of Exponents on monomials including: power of a power, power of
a product, quotient of a power, power of a fraction. (sections 8.1-8.4)
• Find products of powers (section 8.2)
• Simplify products of monomials (sections 8.2-8.4)
Chapter 9: Polynomials and Factoring
Students will add, subtract, multiply and factor polynomials.
• Add and subtract polynomials (section 9.1)
• Find products of binomials by using the FOIL method. (section 9.3)
• Factor the polynomial by using the Greatest Common Factor. (section 9.5)
• Factor perfect square trinomials. (section 9.6)
• Factor the difference of squares. (section 9.6)
• Factor quadratic trinomials with leading coefficient of one. (section 9.7)
• Solve equations by factoring with leading coefficient of one. (section 9.8)
• Factoring the polynomial by using the binomial factor (grouping). (section 9.5)
• Factoring quadratic trinomials with leading coefficients other than one. (section 9.7)
• Solving equations by factoring with leading coefficients other than one. (section
9.8)
Chapter 10: Quadratic Functions
Students will solve equations using square roots and quadratic formula.
• Solve equations of the form ax2 = k. (section 10.2)
• Use the quadratic formula to find rational solutions to quadratic equations. (section
10.4)
• Relationships of the parent function y = x2 to related functions. (section 10.1)
• Graphing a quadratic function using the vertex form. (section 10.1)
• Using the quadratic formula to find the zeros of a quadratic function. (section 10.5)
• Graphing quadratic inequalities and testing solution regions. (section 10.6)
• Solving equations by multi-step factoring. (section 10.4)
• Identifying the appropriate factoring method for solving equations. (section 10.4)
Chapter 11: Rational Functions
Students will simplify and perform operations with rational expression and solve
rational equations.
• State the restrictions on the variable of a simplified rational expression. (section
11.2)
• Factor the numerator and denominator to simplify rational algebraic expressions.
The expressions in the numerator and denominator can be factored by GCF,
Special Factoring, or quadratic expressions with leading coefficient of 1. (section
11.3)
• Add, subtract, multiply and divide rational expressions including real-world
applications. (Adding and Subtracting will be with like denominators the
expressions in the numerator and denominator can be factored by GCF, Special
Factoring, or quadratic expressions with leading coefficient of 1. Real-world
applications will only be at an introductory level. (section 11.4)
• Solve rational equations by using the common-denominator method. (with
numerical denominators) (section 11.5)
• Defining and using two different forms of indirect variations to study real world
situations. (section 11.1)
• Adding, subtracting with unlike denominators, multiplying and dividing rational
expressions including real-world applications.(Adding and Subtracting with unlike
denominators) (section 11.4)
• Solving rational equations by using the common-denominator method. (Introduction
to variables in the denominator) (section 11.5)
Chapter 12: Radicals, Functions, and Coordinate Geometry
Students will apply simplifying techniques to write radical expressions and
solutions to equations in simplest radical form.
• Identify and estimate square roots. (section 12.1)
• Write numerical square roots in simplest radical form. (section 12.1)Perform
mathematical operations with radicals. (section 12.1)
• Solve simple equations containing square roots of the variable. (section 12.2)
• Find the side length of a right triangle given the lengths of its other two sides.
(section 12.3)
• Use the distance formula to find the distance between two points in a coordinate
plane. (section 12.4)
• Use the Pythagorean Theorem to understand the distance formula. (section 12.3)