ALGEBRA

TOPICS OF INSTRUCTION

Steve Murphy—NorthFond du LacHigh School

2005-2006

Sets

  • Sets and Venn Diagrams

Objective: Comprehend the vocabulary and symbols of terms and concepts associated with sets.

Objective: Interpret Venn diagrams.

Objective: Construct Venn diagrams.

Objective: Comprehend the classifications of “Real Numbers” sets.

Probability and Statistics

  • Mean, Median, Mode, and Range

Objective: Compute the mean of a data set.

Objective: Compute the median of a data set.

Objective: Compute the mode of a data set.

Objective: Compute the range of a data set.

  • Statistical Graphs

Objective: Interpret picture graphs.

Objective: Interpret line graphs.

Objective: Construct line graphs.

Objective: Interpret bar graphs.

Objective: Construct bar graphs.

Objective: Interpret circle graphs.

Objective: Construct circle graphs.

Objective: Interpret frequency distributions.

Objective: Construct frequency distributions.

Objective: Interpret histograms.

Objective: Construct stem-and-leaf plots.

Objective: Interpret stem-and-leaf plots.

Objective: Construct box-and-whisker plots.

Objective: Interpret box-and-whisker plots.

  • Probability

Objective: Comprehend the vocabulary and symbols of terms and concepts associated with probability.

Objective: Compute theoretical probability.

Objective: Compute experimental probability.

Objective: Differentiate between dependent and independent events.

Objective: Compute probability of dependent events.

Objective: Compute probability of independent events.

Objective: Compute using the multiplicative “counting principle.”

Real Numbers

  • Real numbers and the number line

Objective: Identify and graph real numbers and their opposites.

Objective: Determine the absolute value of real numbers.

  • Addition and subtraction of real numbers

Objective: Add real numbers.

Objective: Subtract real numbers.

Objective: Identify and apply properties of real numbers.

  • Multiplication and division of real numbers

Objective: Multiply and divide real numbers.

Objective: Use multiplication properties for real numbers.

  • Order of operations

Objective: Simplify numeric expressions using the “order of operations.”

  • Exponents

Objective: Simplify numeric expressions using exponents.

Objective: Properly use the rules of exponents to simplify algebraic expressions.

  • The distributive property

Objective: Use the distributive property expressions with grouping symbols.

  • The real number system

Objective: Express a rational number as the quotient of two integers.

Objective: Identify the subsets of the real number system.

Objective: Find the principal square root of a number.

  • The order of real numbers

Objective: Express a list of real numbers in order from least to greatest.

  • Properties of equality

Objective: Use and identify properties of equality.

  • Patterns

Objective: Recognize patterns in given numerical sequences.

Objective: Determine missing numbers in given numerical sequences.

Formulas

  • Use literal equations and formulas

Objective: Work with literal equations and formulas.

  • Right triangles and the Pythagorean theorem

Objective: Solve problems involving sides of right triangles using the Pythagorean theorem.

Objective: Solve problems involving special right triangles (45-45-90 and 30-60-90).

  • The distance formula

Objective: Use the distance formula to find the distance between two points in the coordinate plane.

Objective: Find the distance between two points on a number line.

Objective: Use the distance formula to find the distance between two points in the coordinate plane.

Objective: Solve problems involving the rate times time equals distance formula.

  • The midpoint formula

Objective: Use the midpoint formula to find the midpoint between two points in the coordinate plane.

  • The slope formula

Objective: Use the slope formula to find the slope between two points on the coordinate plane.

  • Simple and compound interest

Objective: Solve equations using the simple interest formula.

Objective: Solve equations using the compound interest formula.

  • The Quadratic Formula

Objective: Solve quadratic equations by using the quadratic formula.

Objective: Solve quadratic equations by using the completing the square formula.

  • Direct variation

Objective: Identify relationships that represent direct variations.

Objective: Use direct variation to solve word problems.

  • Inverse variation

Objective: Identify relationships that represent inverse variations.

Objective: Use inverse variation to solve word problems.

  • Joint and combined variation

Objective: Use joint variation and/or combined variation to solve word problems.

  • Geometric Formulas

Objective: Solve problems involving area formulas.

Objective: Solve problems involving perimeter formulas.

Objective: Solve problems involving circumference formulas.

Objective: Solve problems involving volume formulas.

Objective: Solve problems involving surface area formulas.

Objective: Solve problems involving polygon angle formulas.

Objective: Solve problems involving combination and permutation formulas.

Objective: Solve problems involving perimeter formulas.

Functions

  • Terminology

Objective: Comprehend vocabulary and notational symbols associated with functions.

  • Relations and functions

Objective: Identify tables and ordered pairs that represent functions.

Objective: Evaluate functions.

Objective: Identify the domain and range of functions.

Objective: Determine whether a relation is a function.

Equations

  • Terminology

Objective: Comprehend vocabulary associated with equations.

  • Variables and Expressions

Objective: Comprehend vocabulary associated with variables and expressions.

Objective: Write, evaluate, and simplify algebraic expressions.

  • Equation solving with mental math and estimation

Objective: Use mental math, estimation, or number lines to solve linear equations.

  • Equation solving with addition and subtraction

Objective: Use the addition and subtraction properties of equality to solve linear equations.

  • Equation solving with multiplication and division

Objective: Use the multiplication and division properties of equality to solve linear equations.

  • Equation solving using two or more operations

Objective: Use two or more operations to solve linear equations.

  • Equation solving with variables on both sides

Objective: Solve linear equations with variables on both sides of the “equals” symbol.

  • Word problems involving equations

Objective: Translate word phrases into variable and numerical expressions.

Objective: Solve given word problems involving equations.

  • Forms of equations

Objective: Express an equation in standard form.

Objective: Express an equation in point-slope form.

Objective: Express an equation in slope-intercept form.

Objective: Determine the equation of a line with given components.

  • Ratios and proportions

Objective: Solve equations using ratios and proportions.

  • Complex rational expressions

Objective: Convert mixed expressions to rational expressions.

Objective: Simplify complex rational expressions.

  • Rational equations

Objective: Solve rational equations.

Objective: Solve motion and work problems.

  • Mixture problems

Objective: Use tables and equations to solve mixture problems.

  • Absolute value equations

Objective: Solve absolute value equations algebraically.

  • Absolute value equation graphs

Objective: Graph equations involving absolute value.

Inequalities

  • Terminology

Objective: Comprehend vocabulary associated with inequalities.

  • Inequalities on the number line

Objective: Determine whether real numbers are solutions of inequalities.

Objective: Graph solutions of inequalities on the number line.

  • Solve inequalities using one operation

Objective: Solve inequalities using one operation.

  • Solve inequalities using two or more operations

Objective: Solve inequalities using two or more operations.

  • Solve compound inequalities

Objective: Solve and graph compound inequalities.

  • Absolute value inequalities

Objective: Solve absolute value inequalities algebraically.

Systems of Equations

  • Solve systems of linear equations by substitution

Objective: Use substitution to find solutions that satisfy two linear equations.

  • Solve systems of linear equations by the elimination method

Objective: Use the elimination method to find solutions that satisfy two linear equations.

  • Solve systems of linear equations by graphing

Objective: Find solutions that satisfy two linear equations by graphing the equations.

  • Solve quadratic equations using square roots

Objective: Use the square root method of solving quadratic equations of the form .

  • The quadratic formula

Objective: Solve quadratic equations of the form using the quadratic formula.

Objective: Use the ”discriminant” to determine the number of real solutions of quadratic equations.

  • Determinants

Objective: Compute the numerical values of determinants.

  • Cramer’s rule

Objective: Use Cramer’s rule to determine solutions to systems of equations.

Triangles and Trigonometry

  • Triangles

Objective: Classify triangles according to side lengths and angle measures.

Objective: Solve problems involving sides and angles of triangles.

  • Triangle trigonometry with sine, cosine, and tangent

Objective: Determine trigonometric ratios for acute angles in a right triangle, given side lengths.

Objective: Determine measures for acute angles, given side lengths or the values of trigonometric ratios.

Objective: Use trigonometric ratios to measure indirectly.

Graphing

  • Terminology

Objective: Comprehend vocabulary associated with the coordinate plane.

Objective: Comprehend vocabulary associated with graphing.

  • The coordinate plane and graphs of functions

Objective: Graph ordered pairs on the coordinate plane.

Objective: Identify graphs that represent functions.

  • Linear functions

Objective: Recognize and graph linear functions from tables or ordered pairs.

  • Nonlinear functions

Objective: Graph nonlinear functions using ordered pairs.

Objective: Identify coordinates of points on graphs on nonlinear functions.

  • Solve equations by graphing

Objective: Use graphing to solve linear equations.

  • The slope of a line

Objective: Determine the slope of a line that passes through given points.

  • The slope – intercept form of a linear equation

Objective: Write an equation in slope – intercept form.

Objective: Use the slope and y – intercept of graphs to write an equation.

  • Parallel and perpendicular lines

Objective: Use equations to determine whether lines are parallel, perpendicular, or neither.

  • The point - slope form of a linear equation

Objective: Use the slope and one point to write an equation.

Objective: Use two points to write an equation.

  • The standard form of a linear equation

Objective: Write the standard form of a linear equation.

Objective: Graph equations written in standard.

  • Graph linear inequalities in two variables

Objective: Identify solutions of linear inequalities.

Objective: Graph linear inequalities.

  • Solve systems of linear inequalities by graphing

Objective: Determine solutions of systems of linear inequalities by graphing.

  • Graph absolute value functions

Objective: Graph absolute value functions using a table of values.

  • Graphs of quadratic functions

Objective: Graph quadratic equations of the form .

  • Solve quadratic equations by graphing

Objective: Use graphing to solve quadratic equations.

Objective: Determine the number of real solutions of quadratic equations.

Polynomials

  • Terminology

Objective: Comprehend vocabulary associated with polynomials.

Objective: Represent given polynomials in standard form.

  • Addition and subtraction of polynomials

Objective: Determine the degree of a polynomial.

Objective: Add polynomials.

Objective: Subtract polynomials.

  • Multiplying monomials

Objective: Multiply monomials using properties of exponents.

  • Dividing monomials

Objective: Divide monomials using properties of exponents.

Objective: Simplify expressions using negative and zero exponents.

  • Multiplying polynomials

Objective: Multiply polynomials.

  • Dividing polynomials

Objective: Divide one polynomial by another polynomial.

  • Simplifying rational expressions

Objective: Simplify rational expressions.

  • Determining variable restrictions

Objective: Determine the values of the variable for which a rational expression is undefined.

  • Addition and subtraction of rational expressions

Objective: Add rational expressions.

Objective: Subtract rational expressions.

  • Multiplication and division of rational expressions

Objective: Multiply rational expressions.

Objective: Divide rational expressions.

Factoring and Multiples

  • Terminology

Objective: Comprehend vocabulary associated with factoring and multiples.

  • Divisibility testing

Objective: Utilize the rules of divisibility.

  • Prime factorization

Objective: Express a given number in terms of multiples using it’s prime factors.

  • Factoring polynomials

Objective: Factor polynomials whose terms have a common monomial factor.

Objective: Factor trinomials with integral quadratic coefficients.

  • Greatest common factor

Objective: Determine the greatest common factor between given numbers.

Objective: Determine the greatest common factor between given algebraic monomials.

  • Least common multiple

Objective: Determine the least common multiple between given numbers.

Objective: Determine the least common multiple between given algebraic monomials.

  • Factoring special products

Objective: Use patterns to factor the difference of two squares polynomials.

Objective: Use patterns to factor perfect square trinomials.

  • Factoring by grouping

Objective: Use the distributive property to factor polynomials by grouping.

  • Factoring completely

Objective: Factor polynomials completely using multiple steps.

  • Solving quadratic equations by factoring

Objective: Solve quadratic equations by factoring.

Radicals

  • Terminology

Objective: Comprehend vocabulary associated with radicals.

  • Simplification of radicals

Objective: Simplify terms and expressions containing radicals.

  • Multiplication and division of radicals

Objective: Multiply terms and expressions containing radicals.

Objective: Divide terms and expressions containing radicals.

  • Addition and subtraction of radicals

Objective: Add terms and expressions containing radicals.

Objective: Subtract terms and expressions containing radicals.

  • Solving radical equations

Objective: Solve equations containing radical terms and expressions.

Fractions, Decimals, and Percents

  • Terminology

Objective: Comprehend vocabulary associated with fractions, decimals, and percents.

Objective: Identify terminating, non-terminating, and repeating decimals.

  • Operations with decimals

Objective: Add decimal expressions.

Objective: Subtract decimal expressions.

Objective: Multiply decimal expressions.

Objective: Divide decimal expressions.

Objective: Convert decimals to fractions.

Objective: Convert decimals to percents.

Objective: Solve word problems involving decimals.

  • Operations with fractions

Objective: Add rational expressions.

Objective: Subtract rational expressions.

Objective: Multiply rational expressions.

Objective: Divide rational expressions.

Objective: Convert numbers from improper fractions to mixed numbers and vice versa.

Objective: Simplify given fractions.

Objective: Convert fractions to decimals.

Objective: Convert fractions to percents.

Objective: Solve word problems involving fractions.

  • Scientific notation

Objective: Write numbers in scientific notation.

Objective: Simplify expressions containing numbers written in scientific notation.

  • Operations with percents

Objective: Convert percents to fractions.

Objective: Convert percents to decimals.

Objective: Solve word problems involving percents.

Objective: Solve problems involving percent increase or percent decrease.

Objective: Use proportions and other equations to solve percent problems.