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    Algebra I Course Content
    Algebra I Course Content
     
    Unit 1: Equations & Inequalities
     
    Students will be able to:
    • Solve one-variable equations using the distributive property with and without technology
    • Solve equations with variables on both sides of the equation with and without technology
    • solve one-variable inequalities using the distributive property with and without technology
    • solve inequalities with variables on both sides of the equation with and without technolgy
    • evaluate reasonableness of solutions
    • solve mathematical and scientific formulas for a specific variable
    • solve literal equations for a specific variable
     
     
    Unit 2A: Representations of Functions
     
    Students will be able to:
    • Determine the domain and range of functions in mathematical problems
    • Represent domain and range using inequalities
    • Determine reasonable domain and range values for real-world situations (including both discrete and continuous)
    • Graph functions on the coordinate plane in mathematical and real-word problems
    • Decide whether relations define a function represented verbally, tabularly, graphically, and symbolically
    • Evaluate functions expressed in function notation given some domain values
    • Comprehend graphs and equations of transformations in function form
    Unit 2B: Slope, Direct Variation & Arithmetic Sequences
     
    Students will be able to:
    • Write equations involving direct variation
    • Solve equations involving direct variation
    • Represent y = kx in tables, graphs, and equations (proportional)
    • Represent y = mx + b in tables, graphs, and equations (linear non-proportional)
    • Distinguish between proportional and linear non-proportional situations using tables, graphs, and equations in mathematical and real-world situations
    • Use similar right triangles to develop an understanding of slope, where the slope is the same for any two points in a line (8th grade)
    • Describe a slope as either positive, negative, zero, or undefined
    • Determine the slope: given a table; given a graph; given two points
    • Calculate the rate of change in mathematical and real-world problems: given a table; given a graph
    • Identify terms of arithmetic sequence (given the recursive rule, find the terms of the sequence)
    • Given an arithmetic sequence, write the rule or formula for the nth term

    Unit 2C: Forms of Linear Functions, Inequalities & Regressions

    Students will be able to:
    • Write linear equations in various forms, including slope intercept, standard, and point-slope form: given 1 point and slope; given 2 point; given a table; given a graph; given a verbal description
    • Determine the slope: given a table; given a graph; given two points; given an equation (written in all 3 forms)
    • Graph linear functions on a coordinate plane
    • Identify key features of linear functions from mathematical and real-world problems, including: x-intercept; y-intercept; zeros; slope
    • Write the equation of a line that contains a given point and is parallel to a given line
    • Write the equation of a line that contains a given point and is perpendicular to a given line
    • Determine the slope of a line when the line is given in various forms to determine parallel or perpendicular
    • Write linear inequalities in two variables: given a table of values (and an equation); given a graph; given a verbal description
    • Graph the solution set of linear inequalities in two variables on the coordinate plane
    • Compare and contrast association and causation in real-world problems
    • Write linear functions with technology that provide a reasonable fit to date (line of best fit/regression)
    • Write linear functions without technology that provide a reasonable fit to data (line of best fit)
    • Estimate solutions and make predictions in real world problems using the line of best fit
    • Use the calculator to find the correlation coefficient between two variables
    • Interpret the correlation coefficient to determine strength of the relationaship
    • Determine the mean absolute deviation of a set of no more than 10 data points

     Unit 3: Systems of Equations & Inequalities

    Students will be able to:
    • Write systems of two linear equations: given a table of values; given a graph; given a verbal description
    • Graph systems of two linear equations and determine the solutions if they exist
    • Use the graph to estimate the solutions to systems of two linear equations in real-world problems
    • Graph the solution set of systems of two linear inequalities on the coordinate plane
    • Solve systems of two linear equations for mathematical and real-world problems (using the most efficient method): substitution; graphing; tables; elimination
    • Evaluate solutions to systems of linear equations and inequalities for reasonableness
    • Interpret the meaning of the solution(s) to a system of linear equation or inequalities in real-world problems

    Unit 4A & 4B: Exponents, Radicals & Exponential Functions

    Students will be able to:

    • Represent and use real numbers in a variety of forms
    • Represent sets and subsets visually (Venn Diagrams) of real numbers
    • Describe relationships between sets of real numbers
    • Locate irrational numbers (their rational approximation) on a number line
    • Convert between standard decimal notation and scientific notation
    • Order real numbers arising from mathematical contexts
    • Order real numbers arising from real-world contexts
    • Solve real-world problems comparing how interest rate and loan length affect the cost of credit
    • Compare loans with different interest rates
    • Compare loans with different loan lengths
    • Calculate the total cost of loans with different interest rates using an online calculator
    • Calculate the total cost of loans with different loan lengths using an online calculator
    • Explain how continuously investing can grow over time (exponentially)
    • Calculate simple interest
    • Calculate compound interest
    • Compare simple and compound interest
    • Identify the advantages and disadvantages of different payment methods (stored value cards, debit cards, and online payment systems)
    • Analyze situations to determine if they represent financially responsible decisions
    • Identify the benefits of financial responsibility
    • Identify the costs of financial irresponsibility
    • Outline a financial plan to pay for a two-year or four-year college education
    • Determine the domain and range of exponential functions 
    • Represent the domain and range of exponential functions using inequalities
    • Interpret the meaning of the values of a and b in exponential functions
    • Write exponential functions to describe problems arising from mathematical and real-world situations, including growth and decay
    • Graph exponential functions that model growth and decay
    • Identify key features of the graphs of exponential functions in mathematical and real-world problems, including: y-intercept; asymptote
    • Write exponential functions using technology that provide a reasonable fit to date (best fit/regression)
    • Make predictions for real-worls problems using the function of best fit for exponential relationships
    • Simplify numerical radical expressions involving square roots
    • Simplify numeric and algebraic expressions using the laws of exponents, including integral (integers) and rational (fractions) exponents: product of a power; power of a power; power of a product; quotient of powers; power of quotients
    • Identify terms of geometric sequences (given the recursive rule, find the terms of the sequence)
    • Given a geometric sequence, write the rule or formula for the nth term

    Unit 4C: Polynomial Operations & Factoring

     Students will be able to:

    • add and subtract polynomials of degree one and degree two
    • multiply polynomials of degree one and degree two
    • determine the quotient of a polynomial using long division
    • rewrite polynomial expressions of degree one and degree two in equivalent formd using the distributive property
    • Factor quadratic polynomials (including difference of two squares
    • Identify if a binomial is the difference of two squares  

    Unit 5A: Graphing Quadratic Functions

    Students will be able to:
    • Determine the domain and range of quadratic functions
    • Represent the domain and range of quadratic functions using inequalities
    • Write the equation of a quadratic function: given the vertex and another point; in vertex form; from vertex form to standard form; when given real solutions; when given a graph
    • Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property
    • Graph quadratic functions on the coordinate plane
    • Identify key attributes of the graph of quadratics, including: x-intercept; y-intercept; zeros; maximum value; minimum value; vertex; the equation of the axis of symmetry
    • Determine the effects on the graph of the parent function
    • Write quadratic functions using technology that provide a reasonable fit to data (best fit/regression)
    • Make predictions for real-world problems using the function of best fit for quadratic relationships

    Unit 5B: Solving Quadratic Functions

    Students will be able to:
    • Describe the relationship between the linear factors of quadratic expressions and the zeros
    • Identify if a binomial is the difference of two squares
    • Factor quadratic polynomials including difference of two squares
    • Solve quadratic equations having real solutions by: graphing; factoring (if possible); taking square roots; completing the square; applying the quadratic formula
    • Evaluate the solutions to quadratic equations for reasonableness

    Unit 6: Graphs & Statistics

    Students will be able to:
    • Construct representations of real world data
    • Compare distributions of data, commenting on similarities and differences
    • Use box plots to summarize data
    • Use the mean and standard deviation to fit normal distributions
    • Use technology to estimate the percentages under the normal curve
    • Interpret the slope of the line of best fit in the context of the data
    • Distinguish between scatterplots that show a linear relationship and those where the relationship is not linear
    • Summarize bivariate categorical data in a two-way frequency table
    • Interpret frequencies and relative frequencies in two-way tables
    • Recognize and describe patterns of association in two-way tables

    Unit: Math 8 

    Students will be able to:
    • Compare and contrast the attributes of a shape and its dilation on a coordinate plane
    • Use an algebraic representation to explain the effects of a scale factor applied to a two-dimensional figure on a coordinate palne
    • Identify angle pairs and relationships when parallel lines are cut by a transversal
    • Solve problems and determine the measures of angles formed by parallel lines and transversals using equations with one variable
    • Solve problems involving interior and exterio angles of triangles using equations with one variable
    • Solve problems involving sums of angles using equations with one variable
    • Recognize translations, rotations, reflections, and dilations in models
    • Determine the effect of transformations on two-dimensional figures on a coordinate plane
    • Differentiate transformations that preserve congruence and those that do not
    • Explain the effects of translations to two-dimensional shapes on a coordinate plane using algebraic representations
    • Explain the effects of rotations to two-dimensional shapes on a coordinate plane using algebraic representations
    • Model the effect on linear (perimeter/circumference) and area measurements of dilated two-dimensional shapes
    • Make connections to geometric formulas
    • Describe the volume formula, V = Bh, of a cylinder in terms of its base area and height
    • Model the relationship between the volume of a cylinder and a cone having the same base area and height
    • Solve problems involving the volume of cylinders, cones, and spheres
    • Solve surface area problems (lateral and total) involving rectangular prisms, triangular prisms, and cylinders
    • Use previous knowledge of surface area to make connections to the formulas for lateral and total surface areas of rectangular prisms, triangular prisms, and cylinders
    • Use models and diagrams to explain the Pythagorean Theorem
    • Use the Pythagorean Theorem to solve problems
    • Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle
    • Determine the distance between two points on a coordinate plane using the Pythagorean Theorem
     
     

     

     

     

     

     

Last Modified on August 12, 2018