A. Numbers

  1. Compare and order rational numbers
  2. Absolute value and opposites
  3. Number lines
  4. Convert between decimals and fractions
  5. Convert between repeating decimals and fractions
  6. Square roots
  7. Cube roots
  8. Sort rational and irrational numbers
  9. Classify rational and irrational numbers
  10. Properties of operations on rational and irrational numbers
  11. Classify numbers

B. Operations

  1. Add, subtract, multiply, and divide integers
  2. Evaluate numerical expressions involving integers
  3. Evaluate variable expressions involving integers
  4. Add and subtract rational numbers
  5. Multiply and divide rational numbers
  6. Simplify complex fractions
  7. Evaluate numerical expressions involving rational numbers
  8. Evaluate variable expressions involving rational numbers

C. Ratios, rates, and proportions

  1. Identify equivalent ratios
  2. Write an equivalent ratio
  3. Unit rates
  4. Unit prices
  5. Solve proportions
  6. Solve proportions: word problems
  7. Scale drawings: word problems

D. Percents

  1. Convert between percents, fractions, and decimals
  2. Solve percent equations
  3. Percent word problems
  4. Percent of change
  5. Percent of change: word problems
  6. Percent of change: find the original amount word problems
  7. Percent of a number: tax, discount, and more
  8. Find the percent: tax, discount, and more
  9. Multi-step problems with percents

E. Measurement

  1. Convert rates and measurements: customary units
  2. Convert rates and measurements: metric units
  3. Unit prices with unit conversions
  4. Multi-step problems with unit conversions
  5. Precision
  6. Greatest possible error
  7. Minimum and maximum area and volume
  8. Percent error
  9. Percent error: area and volume

F. Geometry

  1. Perimeter
  2. Area
  3. Area and perimeter: word problems
  4. Volume
  5. Surface area
  6. Similar figures: side lengths and angle measures
  7. Similar triangles and indirect measurement
  8. Dilations and scale factors
  9. Area and perimeter of similar figures
  10. Area between two shapes
  11. Similar solids
  12. Volume and surface area of similar solids
  13. Perimeter and area: changes in scale
  14. Surface area and volume: changes in scale
  15. Perimeter, area, and volume: changes in scale
  16. Pythagorean theorem
  17. Pythagorean theorem: word problems
  18. Converse of the Pythagorean theorem: is it a right triangle?
  19. Special right triangles

G. Coordinate plane

  1. Coordinate plane review
  2. Midpoint formula: find the midpoint
  3. Midpoint formula: find the endpoint
  4. Distance between two points

H. Properties

  1. Properties of addition and multiplication
  2. Distributive property
  3. Simplify variable expressions using properties
  4. Properties of equality
  5. Identify equivalent equations

I. Variable expressions and equations

  1. Write variable expressions
  2. Sort factors of variable expressions
  3. Simplify variable expressions involving like terms and the distributive property
  4. Identify equivalent linear expressions
  5. Write variable equations
  6. Does x satisfy the equation?
  7. Which x satisfies an equation?
  8. Solve equations using order of operations
  9. Does (x, y) satisfy the equation?
  10. Relate the graph of an equation to its solutions
  11. Rearrange multi-variable equations

J. Solve linear equations

  1. Model and solve linear equations using algebra tiles
  2. Write and solve linear equations that represent diagrams
  3. Solve one-step linear equations
  4. Solve two-step linear equations
  5. Solve advanced linear equations
  6. Solve linear equations with variables on both sides
  7. Solve linear equations: complete the solution
  8. Find the number of solutions to a linear equation
  9. Create linear equations with no solutions or infinitely many solutions
  10. Solve one-step and two-step linear equations: word problems
  11. Solve linear equations: mixed review

K. Single-variable linear inequalities

  1. Graph inequalities
  2. Write inequalities from graphs
  3. Identify solutions to inequalities
  4. Solve one-step linear inequalities: addition and subtraction
  5. Solve one-step linear inequalities: multiplication and division
  6. Solve one-step linear inequalities
  7. Graph solutions to one-step linear inequalities
  8. Solve two-step linear inequalities
  9. Graph solutions to two-step linear inequalities
  10. Solve advanced linear inequalities
  11. Graph solutions to advanced linear inequalities
  12. Graph compound inequalities
  13. Write compound inequalities from graphs
  14. Solve compound inequalities
  15. Graph solutions to compound inequalities
    Checkpoint skill Checkpoint: Solve linear equations and inequalities

L. Absolute value equations and inequalities

  1. Solve absolute value equations
  2. Graph solutions to absolute value equations
  3. Solve absolute value inequalities
  4. Graph solutions to absolute value inequalities

M. Matrices

  1. Matrix vocabulary
  2. Matrix operation rules
  3. Add and subtract matrices
  4. Multiply a matrix by a scalar
  5. Add and subtract scalar multiples of matrices
  6. Multiply two matrices
  7. Properties of matrices

N. Data and graphs

  1. Interpret line plots
  2. Create line plots
  3. Interpret histograms
  4. Create histograms
  5. Interpret bar graphs, line graphs, and histograms
  6. Create bar graphs, line graphs, and histograms
  7. Interpret circle graphs
  8. Interpret stem-and-leaf plots
  9. Box plots
    Checkpoint skill Checkpoint: Line plots, histograms, and box plots

O. Problem solving

  1. Word problems: mixed review
  2. Word problems with money
  3. Consecutive integer problems
  4. Rate of travel: word problems
  5. Weighted averages: word problems
    Checkpoint skill Checkpoint: Units and quantities

P. Number sequences

  1. Identify arithmetic and geometric sequences
  2. Arithmetic sequences
  3. Geometric sequences
  4. Evaluate variable expressions for number sequences
  5. Evaluate recursive formulas for sequences
  6. Identify a sequence as explicit or recursive
  7. Write variable expressions for arithmetic sequences
  8. Write variable expressions for geometric sequences
  9. Write a formula for a recursive sequence
  10. Convert a recursive formula to an explicit formula
  11. Convert an explicit formula to a recursive formula
  12. Number sequences: mixed review
    Checkpoint skill Checkpoint: Sequences

Q. Relations and functions

  1. Relations: convert between tables, graphs, mappings, and lists of points
  2. Domain and range of relations
  3. Identify independent and dependent variables
  4. Identify functions
  5. Identify functions: vertical line test
  6. Find values using function graphs
  7. Evaluate a function
  8. Evaluate a function: plug in an expression
  9. Add and subtract functions
  10. Multiply functions
  11. Find the inverse of a function
  12. Complete a function table from a graph
  13. Complete a function table from an equation
  14. Find solutions using a table
  15. Approximate solutions using a table
  16. Interpret the graph of a function: word problems
  17. Interpret functions using everyday language
    • New! Identify graphs: word problems
  18. Rate of change: tables
  19. Rate of change: graphs
    Checkpoint skill Checkpoint: Function concepts
    Checkpoint skill Checkpoint: Average rate of change
    Checkpoint skill Checkpoint: Solve equations using graphs and tables

R. Piecewise-defined functions

  1. Evaluate piecewise-defined functions
  2. Graph piecewise-defined functions

S. Direct and inverse variation

  1. Identify proportional relationships
  2. Find the constant of variation
  3. Graph a proportional relationship
  4. Write direct variation equations
  5. Write and solve direct variation equations
  6. Identify direct variation and inverse variation
  7. Write inverse variation equations
  8. Write and solve inverse variation equations

T. Linear functions

  1. Identify linear functions from graphs and equations
  2. Identify linear functions from tables
  3. Find the slope of a graph
  4. Find the slope from two points
  5. Find a missing coordinate using slope
  6. Slope-intercept form: find the slope and y-intercept
  7. Slope-intercept form: graph an equation
  8. Slope-intercept form: write an equation from a graph
  9. Slope-intercept form: write an equation
  10. Slope-intercept form: write an equation from a table
  11. Slope-intercept form: write an equation from a word problem
  12. Linear equations: solve for y
  13. Write and solve two-variable linear equations: word problems
  14. Complete a table and graph a linear function
  15. Compare linear functions: graphs and equations
  16. Compare linear functions: tables, graphs, and equations
  17. Interpret the slope and y-intercept of a linear function
  18. Write equations in standard form
  19. Standard form: find x- and y-intercepts
  20. Standard form: graph an equation
  21. Equations of horizontal and vertical lines
  22. Graph a horizontal or vertical line
  23. Point-slope form: graph an equation
  24. Point-slope form: write an equation
  25. Point-slope form: write an equation from a graph
  26. Find the slope and intercepts from an equation
  27. Slopes of parallel and perpendicular lines
  28. Write an equation for a parallel or perpendicular line
  29. Transformations of linear functions

U. Two-variable linear inequalities

  1. Does (x, y) satisfy the inequality?
  2. Linear inequalities: solve for y
  3. Graph a two-variable linear inequality
  4. Write a linear inequality from a graph
  5. Write two-variable inequalities: word problems
  6. Is (x, y) a solution to the system of linear inequalities?
  7. Solve systems of linear inequalities by graphing

V. Systems of linear equations

  1. Is (x, y) a solution to the system of equations?
  2. Solve a system of equations by graphing
  3. Solve a system of equations by graphing: word problems
  4. Find the number of solutions to a system of equations by graphing
  5. Find the number of solutions to a system of equations
  6. Classify a system of equations by graphing
  7. Classify a system of equations
  8. Solve a system of equations using substitution
  9. Solve a system of equations using substitution: word problems
  10. Solve a system of equations using elimination
  11. Solve a system of equations using elimination: word problems
  12. Solve a system of equations using augmented matrices
  13. Solve a system of equations using augmented matrices: word problems
  14. Solve a system of equations using any method
  15. Solve a system of equations using any method: word problems
    Checkpoint skill Checkpoint: Systems of equations and inequalities
    Checkpoint skill Checkpoint: Represent constraints

W. Exponents

  1. Exponents with integer bases
  2. Exponents with decimal and fractional bases
  3. Negative exponents
  4. Multiplication with exponents
  5. Division with exponents
  6. Multiplication and division with exponents
  7. Power rule
  8. Evaluate expressions using properties of exponents
  9. Identify equivalent expressions involving exponents I
  10. Identify equivalent expressions involving exponents II
  11. Evaluate integers raised to positive rational exponents
  12. Evaluate integers raised to rational exponents
  13. Multiplication with rational exponents
  14. Division with rational exponents
  15. Power rule with rational exponents
  16. Simplify expressions involving rational exponents

X. Scientific notation

  1. Convert between standard and scientific notation
  2. Compare numbers written in scientific notation
  3. Add and subtract numbers written in scientific notation
  4. Multiply numbers written in scientific notation
  5. Divide numbers written in scientific notation

Y. Exponential functions

  1. Evaluate an exponential function
  2. Graph exponential functions
  3. Match exponential functions and graphs I
  4. Match exponential functions and graphs II
  5. Domain and range of exponential functions: graphs
  6. Domain and range of exponential functions: equations
    • New! Write exponential functions: word problems
  7. Exponential growth and decay: word problems
  8. Compound interest: word problems

Z. Monomials

  1. Identify monomials
  2. Multiply monomials
  3. Divide monomials
  4. Multiply and divide monomials
  5. Powers of monomials

AA. Polynomials

  1. Polynomial vocabulary
  2. Model polynomials with algebra tiles
  3. Add and subtract polynomials using algebra tiles
  4. Add and subtract polynomials
  5. Add polynomials to find perimeter
  6. Multiply a polynomial by a monomial
  7. Multiply two binomials using algebra tiles
  8. Multiply two binomials
  9. Multiply two binomials: special cases
  10. Multiply polynomials using area models
  11. Multiply polynomials
  12. Multiply polynomials to find area
    Checkpoint skill Checkpoint: Polynomial operations

BB. Factoring

  1. GCF of monomials
  2. Factor out a monomial
  3. Factor quadratics using algebra tiles
  4. Factor quadratics with leading coefficient 1
  5. Factor quadratics with other leading coefficients
  6. Factor quadratics: special cases
  7. Factor by grouping
  8. Factor using a quadratic pattern
  9. Factor polynomials

CC. Quadratic equations

  1. Characteristics of quadratic functions: graphs
  2. Characteristics of quadratic functions: equations
  3. Complete a function table: quadratic functions
  4. Transformations of quadratic functions
  5. Graph quadratic functions in vertex form
  6. Solve a quadratic equation using square roots
  7. Solve a quadratic equation using the zero product property
  8. Solve a quadratic equation by factoring
  9. Complete the square
  10. Solve a quadratic equation by completing the square
  11. Solve a quadratic equation using the quadratic formula
    • New! Solve quadratic equations: word problems
  12. Using the discriminant
  13. Write a quadratic function in vertex form
  14. Graph quadratic functions in standard form
  15. Match quadratic functions and graphs
    • New! Domain and range of quadratic functions: graphs
  16. Domain and range of quadratic functions: equations
  17. Write a quadratic function from its vertex and another point
    • New! Interpret parts of quadratic expressions: word problems
  18. Solve a system of linear and quadratic equations by graphing
  19. Solve a system of linear and quadratic equations
    Checkpoint skill Checkpoint: Quadratic equations
    Checkpoint skill Checkpoint: Write and interpret equivalent expressions

DD. Functions: linear, quadratic, exponential

  1. Identify linear and exponential functions from graphs
  2. Identify linear, quadratic, and exponential functions from graphs
  3. Identify linear and exponential functions from tables
  4. Identify linear, quadratic, and exponential functions from tables
  5. Write linear and exponential functions: word problems
  6. Write linear and exponential functions from tables
  7. Write linear, quadratic, and exponential functions from tables
  8. Linear functions over unit intervals
  9. Exponential functions over unit intervals
  10. Describe linear and exponential growth and decay
  11. Compare linear and exponential growth
  12. Compare linear, exponential, and quadratic growth
    Checkpoint skill Checkpoint: Problem solving with equations and inequalities
    Checkpoint skill Checkpoint: Features of functions
    Checkpoint skill Checkpoint: Compare linear and exponential functions
    Checkpoint skill Checkpoint: Build functions

EE. Absolute value and function families

  1. Complete a function table: absolute value functions
  2. Graph an absolute value function
  3. Domain and range of absolute value functions: graphs
  4. Domain and range of absolute value functions: equations
  5. Transformations of absolute value functions: translations and reflections
  6. Transformations of absolute value functions: translations, reflections, and dilations
  7. Function transformation rules
  8. Translations of functions
  9. Reflections of functions
  10. Dilations of functions
  11. Transformations of functions
  12. Describe function transformations
    Checkpoint skill Checkpoint: Graph and analyze functions
    Checkpoint skill Checkpoint: Function transformations

FF. Radical expressions

  1. Simplify radical expressions
  2. Simplify radical expressions with variables
  3. Simplify radical expressions involving fractions
  4. Multiply radical expressions
  5. Add and subtract radical expressions
  6. Simplify radical expressions using the distributive property
  7. Simplify radical expressions using conjugates
  8. Simplify radical expressions: mixed review
    Checkpoint skill Checkpoint: Radicals and rational exponents

GG. Radical functions and equations

  1. Evaluate square root functions
  2. Domain and range of square root functions: graphs
  3. Domain and range of square root functions: equations
  4. Graph square root functions
  5. Solve radical equations I
  6. Solve radical equations II

HH. Rational functions and expressions

  1. Rational functions: asymptotes and excluded values
  2. Simplify rational expressions
  3. Multiply and divide rational expressions
  4. Divide polynomials by monomials
  5. Divide polynomials using long division
  6. Add and subtract rational expressions
  7. Simplify mixed rational expressions
  8. Solve rational equations
  9. Evaluate rational expressions

II. Trigonometry

  1. Trigonometric ratios: sin, cos, and tan
  2. Find trigonometric ratios using a calculator
  3. Inverses of trigonometric functions
  4. Trigonometric ratios: find a side length
  5. Trigonometric ratios: find an angle measure
  6. Solve a right triangle

JJ. Sets

  1. Sets, subsets, and complements
  2. Set-builder notation
  3. Interval notation
    • New! Unions and intersections of sets

KK. Logic

  1. Identify hypotheses and conclusions
  2. Counterexamples

LL. Probability

  1. Theoretical probability
  2. Experimental probability
  3. Find probabilities using two-way frequency tables
  4. Find conditional probabilities using two-way frequency tables
  5. Outcomes of compound events
  6. Identify independent and dependent events
  7. Probability of independent and dependent events
  8. Counting principle
  9. Permutations
  10. Permutation and combination notation
    Checkpoint skill Checkpoint: Two-way frequency tables

MM. Statistics

  1. Identify biased samples
  2. Mean, median, mode, and range
  3. Calculate quartiles and interquartile range
  4. Identify an outlier
  5. Identify an outlier and describe the effect of removing it
  6. Mean absolute deviation
  7. Variance and standard deviation
  8. Interpret a scatter plot
  9. Outliers in scatter plots
  10. Match correlation coefficients to scatter plots
  11. Calculate correlation coefficients
  12. Write equations for lines of best fit
  13. Find the equation of a regression line
  14. Interpret regression lines
  15. Analyze a regression line of a data set
  16. Correlation and causation
    Checkpoint skill Checkpoint: Compare data sets
    Checkpoint skill Checkpoint: Linear modeling