Course Content
A. Numbers and Operations
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A.01. Understand and apply the properties of integers in addition, subtraction, multiplication, and division.
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A.02. Evaluate and simplify numerical expressions involving integers using order of operations.
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A.03. Convert between decimals, fractions, and percentages with precision.
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A.04. Perform operations with rational numbers, including addition, subtraction, multiplication, and division.
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A.05. Simplify complex numerical expressions involving rational numbers.
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A.06. Estimate and approximate values of irrational numbers in decimal form.
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A.07. Explore the historical significance and real-world applications of rational and irrational numbers.
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A.08. Compare and order rational and irrational numbers.
B. Exponents and Scientific Notation
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B.01. Understand the concept of exponents and evaluate powers with positive integer bases.
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B.02. Multiply and divide powers with integer bases.
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B.03. Understand and apply the power of a power rule for integer bases.
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B.04. Evaluate expressions using properties of exponents with integer bases.
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B.05. Understand negative and zero exponents and evaluate powers with these exponents.
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B.06. Evaluate powers with decimal and fractional bases.
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B.07. Convert between standard and scientific notation.
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B.08. Perform arithmetic operations (addition, subtraction, multiplication, division) with numbers in scientific notation.
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B.09. Compare numbers written in scientific notation.
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B.10. Apply scientific notation to solve real-world problems.
C. Square Roots and Cube Roots
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C.01. Find square roots of perfect squares.
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C.02. Estimate positive square roots.
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C.03. Understand positive and negative square roots and estimate their values.
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C.04. Understand the relationship between squares and square roots.
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C.05. Solve equations using square roots.
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C.06. Find cube roots of perfect cubes.
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C.07. Solve equations using cube roots.
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C.08. Estimate cube roots.
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C.09. Identify rational and irrational square roots.
D. Proportions and Percents
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D.01. Convert between percents, fractions, and decimals.
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D.02. Compare percents to fractions and decimals.
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D.03. Find what percent one number is of another.
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D.04. Solve proportions.
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D.05. Solve percent equations.
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D.06. Calculate percent of change.
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D.07. Apply proportions and percents to solve real-world problems, including those involving sales tax, discounts, and simple interest.
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D.08. Estimate percents of numbers.
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D.09. Solve multi-step problems involving percents.
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D.10. Estimate population size using proportions.
E. Consumer Math and Measurement
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E.01. Calculate unit prices.
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E.02. Calculate unit prices with unit conversions.
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E.03. Convert rates and measurements within the customary and metric systems.
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E.04. Convert between customary and metric systems.
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E.05. Convert between Celsius and Fahrenheit.
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E.06. Solve multi-step problems involving unit prices and percents.
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E.07. Calculate simple and compound interest.
F. Algebraic Expressions and Equations
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F.08. Solve multi-step equations, including those with variables on both sides and those requiring the distributive property.
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F.09. Solve equations with fractional coefficients.
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F.10. Determine the number of solutions for an equation.
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F.11. Create equations with no solutions or infinitely many solutions.
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F.01. Write variable expressions with one or more operations.
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F.02. Evaluate one-variable and multi-variable expressions.
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F.03. Identify terms and coefficients in algebraic expressions.
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F.04. Simplify algebraic expressions using the distributive property and combining like terms.
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F.05. Write equivalent expressions using properties of addition and multiplication.
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F.06. Solve one-step equations.
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F.07. Solve two-step equations.
G. Inequalities and Coordinate Plane
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G.01. Understand solutions to inequalities.
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G.02. Graph inequalities on number lines.
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G.03. Write inequalities from number lines.
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G.04. Solve one-step inequalities.
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G.05. Solve two-step inequalities.
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G.06. Solve multi-step inequalities.
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G.07. Graph solutions to one-step, two-step, and multi-step inequalities.
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G.08. Review coordinate plane concepts (quadrants, axes).
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G.09. Find the distance between two points on the coordinate plane.
H. Lines, Angles, and Geometric Figures
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H.01. Identify and classify polygons, including triangles and quadrilaterals.
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H.02. Identify complementary, supplementary, vertical, and adjacent angles.
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H.03. Find measures of angles using angle relationships.
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H.04. Identify alternate interior and alternate exterior angles formed by transversals intersecting parallel lines.
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H.05. Use the Triangle Angle-Sum Theorem and Exterior Angle Theorem to find missing angles in triangles.
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H.06. Find missing angles in quadrilaterals.
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H.07. Understand the properties of parallel lines and transversals.
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H.08. Find lengths and measures of bisected line segments and angles.
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H.09. Calculate the interior angles of polygons.
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H.10. Understand parts of a circle (radius, diameter, circumference, area).
I. Transformations and Congruence
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I.01. Identify reflections, rotations, and translations.
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I.02. Graph the image of a figure after a transformation.
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I.03. Find the coordinates of a figure’s image after a transformation.
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I.04. Describe a sequence of transformations.
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I.05. Identify congruent figures and corresponding parts.
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I.06. Determine if two figures are congruent and justify the answer.
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I.07. Understand side lengths and angle measures of congruent figures.
J. Transformations and Similarity
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J.01. Identify similar and congruent figures.
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J.02. Understand dilations and find the scale factor.
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J.03. Graph the image of a figure after a dilation.
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J.04. Identify similar triangles.
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J.05. Apply the Angle-Angle criterion for similar triangles.
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J.06. Understand side lengths and angle measures of similar figures.
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J.07. Use similar triangles for indirect measurement.
K. Pythagorean Theorem and Three-Dimensional Figures
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K.01. Use the Pythagorean Theorem to find the length of the hypotenuse or a leg of a right triangle.
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K.02. Use the Pythagorean Theorem to find perimeter.
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K.03. Apply the Pythagorean Theorem to solve word problems.
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K.04. Understand and apply the converse of the Pythagorean Theorem.
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K.05. Understand parts of three-dimensional figures (faces, edges, vertices).
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K.06. Identify nets of three-dimensional figures.
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K.07. Determine front, side, and top views of three-dimensional figures.
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K.08. Understand similar solids.
L. Perimeter, Area, Surface Area, and Volume
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L.01. Calculate perimeter and area of two-dimensional figures.
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L.02. Calculate area and circumference of circles.
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L.03. Calculate area and perimeter of semicircles and quarter circles.
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L.04. Calculate the area between two shapes.
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L.05. Calculate the volume and surface area of cubes, prisms, pyramids, cylinders, cones, and spheres.
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L.06. Understand how changes in scale affect perimeter, area, and volume.
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L.07. Calculate volume and surface area of similar solids.
M. Proportional Relationships and Direct Variation
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M.01. Identify proportional relationships from tables, graphs, and equations.
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M.02. Find the constant of proportionality from a table or graph.
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M.03. Write equations for proportional relationships.
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M.04. Graph proportional relationships and find the slope.
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M.05. Interpret graphs of proportional relationships.
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M.06. Identify direct variation and write direct variation equations.
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M.07. Solve problems involving proportional relationships and direct variation.
N. Slope and Linear Equations
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N.01. Find the slope from a graph, two points, or a table.
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N.02. Find a missing coordinate using slope.
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N.03. Graph a line using slope and a point.
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N.04. Write a linear equation in slope-intercept, point-slope, and standard forms.
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N.05. Convert between different forms of linear equations.
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N.06. Graph linear equations.
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N.07. Understand the slopes of parallel and perpendicular lines.
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N.08. Determine if a point is a solution to a linear equation.
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N.09. Relate the graph of an equation to its solutions.
O. Functions and Linear Functions
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O.01. Identify functions from tables and graphs.
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O.02. Identify independent and dependent variables.
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O.03. Find values using function graphs.
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O.04. Understand domain and range of functions.
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O.05. Evaluate linear functions.
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O.06. Complete a table for a linear function.
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O.07. Graph linear functions.
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O.08. Interpret points on the graph of a linear function.
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O.09. Understand rate of change in linear functions from tables and graphs.
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O.10. Interpret the slope and y-intercept of a linear function.
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O.11. Write linear functions from tables and graphs.
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O.12. Compare linear functions represented in different ways.
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O.13. Write and evaluate linear functions in word problems.
P. Nonlinear Functions and Interpreting Functions
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P.01. Identify linear and nonlinear functions from graphs, tables, and equations.
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P.02. Evaluate nonlinear functions.
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P.03. Determine if a point is a solution to a nonlinear equation.
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P.04. Understand rate of change from tables and graphs (linear and nonlinear).
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P.05. Identify graphs that match real-world situations.
Q. Sequences and Systems of Equations
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Q.01. Identify arithmetic and geometric sequences.
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Q.02. Write variable expressions for arithmetic sequences.
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Q.03. Solve problems involving sequences.
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Q.04. Determine if a point is a solution to a system of equations.
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Q.05. Solve systems of equations by graphing, substitution, and elimination.
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Q.06. Classify systems of equations.
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Q.07. Solve systems of equations in word problems.
R. Statistics and Probability
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R.01. Calculate mean, median, mode, and range.
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R.02. Interpret charts and graphs to find mean, median, mode, and range.
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R.03. Calculate mean absolute deviation, quartiles, and interquartile range.
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R.04. Create and interpret box plots.
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R.05. Identify outliers and describe their effects.
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R.06. Interpret and create line graphs and scatter plots.
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R.07. Identify trends and make predictions with scatter plots.
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R.08. Identify lines of best fit.
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R.09. Write equations for lines of best fit.
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R.10. Understand representative, random, and biased samples.
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R.11. Calculate probabilities of simple events.
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R.12. Calculate probabilities of opposite, mutually exclusive, and overlapping events.
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R.13. Calculate experimental probability.
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R.14. Use two-way frequency tables to find probabilities.
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R.15. Make predictions using probability.
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R.16. Understand compound events and the counting principle.
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R.17. Identify independent and dependent events and calculate their probabilities.
