Syllabus for Algebra 1

FIRST NINE WEEK

 

Chapter 0 Preparing for Algebra

Lessons:

  0-2 Real Numbers

   0-3 Operations with Integers

   0-4 Adding and Subtracting Rational Numbers

   0-5 Multiplying and Dividing Rational Numbers

   0-11 Simple Probability and Odds

   0-12 Measures of Center and Variation

   0-13 Representing Data

SPI 3102.2.3 Describe and/or order a given set of real numbers including both rational and irrational numbers.

3102.2.8 Use multiple strategies to approximate the value of an irrational number including irrational square roots and including location on the real number line.

3102.2.7 Identify the subsets in the real number system and understand their relationships.

3102.2.4 Operate efficiently with both rational and irrational numbers.

3102.5.12 Use techniques to identify the possible outcomes of an experiment or sample space and compute the probability of an event.

3102.5.2 Identify the effect on mean, median, mode, and range when values in the data set are changed.

3102.5.3 When a set of data is changed, identify the effects on measures of central tendency, range, and inter-quartile range.

3102.5.4 Explore quartiles, deciles, and percentiles of a distribution.

3102.5.1 Interpret displays of data to answer questions about the data set(s).

3102.5.2 Develop a meaning for and identify outliers in a data set and verify.

3102.5.5 Construct and interpret various forms of data representations.

Chapter 1 Expressions, Equations, and Functions

Lessons:

   1-2 Order of Operations

   1-3 Properties of Numbers

   1-4 The Distributive Property

   1-5 Equations

   1-6 Relations

   1-7 Functions

SPI 3102.1.3 Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems.

3102.1.9 Identify and use properties of the real numbers.

3102.2.1 Recognize and use like terms to simplify expressions.

3102.3.6 Interpret various relations in multiple representations.

3102.3.7 Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.

3102.1.4 Translate between representations of functions that depict real-world situations.

3102.3.7 Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.

3102.3.16 Determine if a relations is a functions from its graph or from a set of ordered pairs.

3102.3.25 Find functions values using f(x) notation or graphs.

Chapter 2 Linear Equations

Lessons:

   2-1 Writing Equations

   2-2 Solving One-Step Equations

   2-3 Solving Multi-Step Equations

   2-4 Solving Equations with the Variable on Each Side

   2-5 Solving Equations Involving Absolute Value

   2-6 Ratios and Proportions

   2-7 Extension Lesson Quartiles, Deciles, and Percentiles

   2-8 Literal Equations and Dimensional Analysis

SPI 3102.1.2 Write and equation symbolically to express a contextual problem.

3102.1.9 Identify and use properties of the real numbers.

3102.3.11 Solve multi-step linear equations with one variable.

3102.3.5 Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value.

3102.3.14 Solve absolute value equations and inequalities with one variable and graph their solutions on a number line.

3102.1.2 Use the terminology of mathematics correctly.

3102.1.5 Use formulas, equations, and inequalities to solve real-world problems including time/rate/distance, percent increase/decrease, ratio/proportion, and mixture problems.

3102.4.4 Convert rates and measurements.

3102.4.5 Use dimensional analysis to convert rates and measurements both within a system and between systems and check the appropriateness of a solution.

Chapter 3 Linear Functions

Lessons:

3-1 Graphing Linear Equations

3-3 Rate of Change and Slope

3-5 Arithmetic Sequences as Linear Functions

3-6 Proportional and Non-proportional Relationships

SPI 3102.3.8 Determine the equation of a line and/or graph a linear equation.

3102.1.16 Understand and express the meaning of the slope and y-intercept of linear functions in real-world contexts.

3102.3.23 Determine the graph of a linear equation including those that depict contextual situations.

3102.1.1 Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation.

3102.3.1 Express a generalization of a pattern in various representations including algebraic and function notation.

3102.3.2 Explore patterns including Pascal's Triangles and the Fibonacci sequence.

3102.1.4 Write a rule with variables that expresses a pattern.

 

SECOND NINE WEEK

 

Chapter 4  Linear Functions and Relations & 6.1

Lessons:

       4-1 Graphing Equations in Slope-Intercept Form

       6-1  Graphing Systems of Equations

       4-2 Writing Equations in Slope-Intercept Form

       4-4  Parallel and Perpendicular Lines

       4-5  Scatter Plots and Lines of Fit

SPI 3102.3.8 Determine the equation of a line and/or graph a linear equation.

3102.1.5 Recognize and express the effect of changing constants and/or coefficients in problem solving.

3102.3.22 Express the equation of a line in standard form, slope-intercept, and point-slope form.

3102.3.23 Determine the graph of a linear equation including those that depict contextual situations.

3102.3.24 Interpret the changes in the slope-intercept form and graph of a linear equation by looking at different values of the parameters, m and b.

3102.3.9 Solve systems of linear equation/inequalities in two variables.

3102.3.27 Determine the number of solutions for a system of linear equations (0, 1, or infinitely many solutions).

3102.3.28 Solve systems of linear equations graphically, algebraically, and with technology.

3102.3.17 Recognize "families" of functions.

3102.3.18 Analyze the characteristics of graphs of basic linear relations and linear functions including constant function, direct variation, identity function, vertical lines, absolute value of linear functions. Use technology where appropriate.

3102.1.2 Write an equation symbolically to express a contextual problem.

3102.3.8 Determine the equation of a line and/or graph a linear equation.

3102.3.21 Determine the equation of a line using given information including a point and slope, two points, a point and a line parallel or perpendicular, graph, intercepts.

3102.5.1 Interpret displays of data to answer questions about the data set(s) (e.g., identify pattern, trends, and/or outliers in a data set).

3102.5.3 Using a scatter-plot, determine if a linear relationship exists and describe the association between variables.

3102.5.4 Generate the equation of a line that fits linear data and use it to make a prediction.

3102.5.6 Draw qualitative graphs of functions and describe a general trend or shape.

3102.5.7 Compare two data sets using graphs and descriptive statistics.

Chapter 5 – Linear Inequalities & 6-8

Lessons:

     5-1  Solving Inequalities by Addition and Subtraction

     5-2 – Solving Inequalities by Multiplication and Division

     5-3  Solving Multi-Step Inequalities

     5-4  Solving Compound Inequalities

     5-5  Inequalities Involving Absolute Value

     5-6  Graphing Inequalities in Two Variables

     6-8  Systems of Inequalities

SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value.

3102.3.13 Solve multi-step linear inequalities with one variable and graph the solution on a number line.

3102.3.14 Solve absolute value equations and inequalities (including compound inequalities) with one variable and graph their solutions on a number line.

3102.3.26 Graph linear inequalities on the coordinate plane and identify regions of the graph containing ordered pairs in the solution.

3102.3.29 Solve contextual problems involving systems of linear equations or inequalities and interpret solutions in context.

Chapter 7 – Polynomials

    7-1 Multiplying Monomials

    7-2 Dividing Monomials

    7-3 Scientific Notation

    7-4 Polynomials

    7-5 Adding and Subtracting Polynomials

    7-6 Multiplying a Polynomial by a Monomial

    7-7 Multiplying Polynomials

    7-8 Special Products

SPI 3102.3.4 Simplify expressions using exponent rules including negative exponents and zero exponents.

3102.2.2 Multiply, divide, and square numbers expressed in scientific notation.

3102.2.5 Perform operations with numbers in scientific notation (multiply, divide, powers).

3102.2.6 Use appropriate technologies to apply scientific notation to real-world problems.

3102.3.5 Add, subtract, and multiply polynomials including squaring a binomial.

3102.3.2 Operate with polynomials and simplify results.

3102.3.5 Add, subtract, and multiply polynomials including squaring a binomial.

 

THIRD NINE WEEK

 

Chapter 8 Factoring and Quadratic Equations

   Lessons:

     8-1 Monomials and Factoring

     8-2 Using the Distributive Property

     8-3 Quadratic Equations: x2 + bx + c = 0

     8-4 Quadratic Equations: ax2 + bx + c = 0

     8-5 Quadratic Equations: Differences of Squares

     8-6 Quadratic Equations: Perfect Squares

SPI 3102.3.3 Factoring polynomials.

3102.3.8 Find the GCF of the terms in a polynomial.

3102.3.9 Find two binomial factors of a quadratic expression.

3102.3.10 Find the solution of a quadratic equation and/or zeros of quadratic function.

3102.3.32 Recognize the connection among factors, solutions (roots), zeros of related functions, and x-intercepts in equations that arise from quadratic functions.

3102.3.9 Find two binomial factor of a quadratic expression.

3102.3.10 Find the solution of a quadratic equation and/or zeros of quadratic function.

Chapter 11 Rational Functions and Equations

    Lessons:

      11-2 Rational Functions

      11-3 Simplifying Rational Functions

      11-4 Multiplying and Dividing Rational Expressions

SPI 3102.3.4Operate with, evaluate, and simplify rational expressions including determining restrictions on the domain of the variables.

3102.3.7 Construct and solve systems of linear equations and inequalities in two variables by various

Chapter 9 Quadratic and Exponential Functions

   Lessons:

     9-1 Graphing Quadratic Functions

     9-2 Solving Quadratic Equations by Graphing

     9-5 Solving Quadratic Equations by Using Quadratic Formula

     9-6 Exponential Functions

SPI 3102.3.11 Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.

3102.3.10 Find the solution of a quadratic equation and/or zeros of a quadratic function.

3102.3.8 Find the GCF of the terms in a polynomial.

3102.3.11 Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.

3102.3.34 Graph exponential functions in the form of y = a(bx) where b ≠ 0.

Chapter 10 Radical Functions

   Lessons:

     10-2 Simplifying Radical Expressions

     10-3 Operations with Radical Expressions

     10-4 Radical Equations

SPI 3102.2.1Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions.

3102.2.3Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, quadratic, and square root function. Use technology where appropriate.

3102.2.4Operate efficiently with both rational and irrational numbers.

3102.1.18Translate syntax of technology to appropriate mathematical notation.

3102.3.7Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.

 

FOURTH NINE WEEK

 

Chapter 10 Geometry part

    Lessons:

     10-5 The Pythagorean Theorem

     10.6 Distance Formula & Midpoint Formula

SPI 3102.4.2 Solve contextual problems using the Pythagorean Theorem.

3102.4.2 Use the Pythagorean Theorem to find the missing measure in a right triangle including those from contextual situations.

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

3102.4.3 Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates; develop the distance formula for a coordinate plane using the Pythagorean Theorem.

3102.4.4Develop the midpoint formula for segments on a number line or in the coordinate plane.

Chapter 12 Statistics and Probability

    Lessons:

12-7 Probability Simulations

SPI 3102.5.5 Determine theoretical and/or experimental probability of an event and/or its complement including using relative frequency.

3102.5.13 Determine the complement of an event and the probability of that complement.

3102.5.14 Determine if two events are independent or dependent.

3102.5.15 Explore joint and conditional probability.

3102.5.17Perform simulations to estimate probabilities.

3102.5.16 Identify situations for which the Law of Large Numbers applies.

3102.5.18 Make informed decisions about practical situations using probability concepts.

EOC PREP 4+ weeks 

Chapter 6 Continued Systems of Equations

    Lessons:

6-2 Substitution

6-3 Elimination Using Addition and Subtraction

6-4 Elimination Using Multiplication 

 

SPI 3102.3.9 Solve systems of linear equation/inequalities in two variables.

3102.3.28 Solve systems of linear equations graphically, algebraically, and with technology.