Course Objectives

Algebra 1A Objectives

Unit 1:  Introduction to Algebra

Lesson 1:  Symbols in Algebra

• Read, write, and understand algebraic expressions.
• Evaluate algebraic expressions by substituting a value for the variable(s) in the expression.
• Use the order of operations to simplify numerical expressions that involve grouping symbols, multiplication, division, addition and subtraction.
• Evaluate a number raised to a power.
• Use the order of operations to evaluate expressions.
• Use the order of operations to evaluate algebraic expressions for given values of the variable(s).

Lesson 2:  Properties and Sentences

• Recognize the Commutative and Associative Properties.
• Use the Commutative and Associative Properties to evaluate expressions.
• Recognize the Distributive Property.
• Use the Distributive Property to evaluate expressions.
• Simplify algebraic expressions by combining like terms.

Lesson 3:  Real Number and the Number Line

• Recognize and graph real numbers on a number line.
• Compare and recognize the elements of the sets of whole numbers, integers, natural numbers, and rational numbers.
• Find the absolute value of a number, and understand absolute value as the distance from zero on the number line.
• Graph numbers on the number line.
• Find the greater or lesser of two numbers.
• Find the opposite of a number.
• Add and subtract real numbers.
• Use the Zero Property of Multiplication.
• Multiply real numbers.
• Evaluate expressions with exponents that involve positive and negative real numbers.
• Simplify expressions that include addition, subtraction, multiplication, and division with positive and negative real numbers.

Unit 2:  Introduction to Equations

Lesson 1:  Combined Operations

• Simplify algebraic expressions by combining like terms.
• Evaluate algebraic expressions by substituting a value for the variable by combining like terms first.
• Use the Distributive Property to simplify algebraic expressions.
• Evaluate algebraic expressions using the Distributive Property.
• Simplify algebraic expressions.
• Evaluate algebraic expressions by substituting for a variable or variables.
• Write algebraic expressions to fit application problems.
• Solve geometric problems involving perimeter and area.

Lesson 2:  Introduction to Function and Equations

• Graph points on the coordinate plane.
• Identify the quadrants in the coordinate plane.
• Write functions using function notation.
• Understand the meaning of domain and range.
• Find ordered pairs of a function.
• Find ordered pairs for two variable equations given one coordinate.
• Graph linear equations by finding ordered pairs.
• Graph horizontal and vertical lines.
• Use graphing to solve systems of linear equations in which one equation is a constant function.

Lesson 3:  Solving Equations Analytically

• Solve one-step equations using addition or subtraction, including integers, decimals, and fractions.
• Solve one-step equations with multiplication and division, including equations with fractions and decimals.
• Solve equations by combining like terms, and using addition, subtraction, multiplication, and division.

Unit 3:  Solving Equations

Lesson 1:  Equations and Problem-Solving

• Solve absolute value equations with absolute values on both sides of the equation.
• Solve equations that require using the Distributive Property to remove parentheses.
• Solve equations with fractions by using the least common multiple (LCM) of the denominators in the equation.
• Solve equations by using multiplication to remove any decimals.
• Solve complicated equations that involve fractions and decimals by using multiplication to remove decimals and fractions.

Lesson 2:  Percents

• Write and simplify ratios.
• Solve word problems involving ratios.
• Convert between fractions, decimals, and percents.
• Find a percent of a number.
• Solve problems with percents including sale price, tax, profit, and commission problems

Unit 4:  Inequalities and Absolute Value

Lesson 1:  Inequalities

• Solve and graph the solutions of inequalities by using the addition and subtraction properties of inequalities.
• Solve inequality word problems that use the addition and subtraction properties of inequalities.
• Solve and graph the solutions of inequalities using the addition and subtraction properties of inequality.
• Write and solve inequalities that model real-life situations using the addition and subtraction properties of inequality.
• Solve and graph the solutions of inequalities using the multiplication and division properties of inequality.
• Write and solve inequalities that model real life situations using the multiplication and division properties of inequality.
• Write and graph compound inequality statements, including both conjunctions and disjunctions.

Lesson 2:  Absolute Value

• Solve equations with absolute values.
• Solve inequalities with absolute values.

Unit 5:  Polynomials

Lesson 1:  Monomials

• Multiply monomials using the Product Rule.
• Simplify monomials using the Power of a Power Rule and the Power of a Product Rule.
• Simplify monomials with positive or negative exponents using the Quotient Rule, the Zero Power Rule, the Negative Exponent Rule, and the Power of a Quotient Rule.
• Determine whether or not numbers are written correctly in scientific notation.
• Convert between standard notation and scientific notation.
• Multiply and divide numbers written in scientific notation.

Lesson 2:  Combining

• Add and subtract polynomials, including adding polynomials to find the perimeter of a polygon.
• Use the Distributive Property to find the product of a monomial and a polynomial.
• Multiply two binomials, including special products.
• Multiply a binomial by a trinomial.

Lesson 3:  Factoring

• Factor a polynomial by factoring out the greatest common factor (GCF) of the terms.
• Factor trinomials in which the leading coefficient is 1.
• Factor trinomials in which the leading coefficient is not equal to 1 and in which the terms have no common factors.
• Factor trinomials that are binomial squares, or the sum or difference of squares.
• Factor trinomials in which the terms have a common factor.
• Factor trinomials by grouping.