Course Content
A. Numbers and Counting
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A.01. Classify different types of numbers (e.g., natural, integer, rational, irrational).
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A.02. Represent numbers on a number line.
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A.03. Convert fluently between decimals, fractions, and percentages.
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A.04. Compare and order rational numbers, including negative fractions and decimals.
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A.05. Determine square roots of perfect squares and approximate square roots of non-perfect squares.
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A.06. Determine cube roots of perfect cubes.
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A.07. Apply number classifications to solve real-world problems.
B. Operations with Rational Numbers
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B.01. Understand and apply the rules for adding, subtracting, multiplying, and dividing integers.
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B.02. Add and subtract rational numbers (fractions and decimals), including finding common denominators.
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B.03. Multiply and divide rational numbers (fractions and decimals).
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B.04. Evaluate numerical expressions involving integers using the order of operations (PEMDAS/BODMAS).
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B.05. Evaluate variable expressions involving integers by substituting given values.
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B.06. Evaluate numerical expressions involving rational numbers using the order of operations.
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B.07. Evaluate variable expressions involving rational numbers by substituting given values.
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B.08. Solve real-world problems involving operations with rational numbers.
C. Measurement and Error
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C.01. Convert between different units of measurement using conversion factors.
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C.02. Convert rates between different units (e.g., miles per hour to feet per second).
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C.03. Understand the concept of precision in measurement.
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C.04. Calculate the greatest possible error in a measurement.
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C.05. Determine the minimum and maximum possible area and volume based on measurement precision.
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C.06. Calculate the percent error in a measurement.
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C.07. Calculate the percent error in area and volume measurements.
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C.08. Analyze the impact of measurement errors in practical situations.
D. Ratios, Rates, Proportions, and Percents
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D.01. Identify equivalent ratios and write equivalent ratios.
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D.02. Calculate unit rates and unit prices.
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D.03. Solve proportions using cross-multiplication.
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D.04. Apply proportions to solve word problems, including scale drawing problems.
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D.05. Convert between percents, fractions, and decimals.
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D.06. Solve percent equations to find the part, whole, or percent.
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D.07. Solve percent word problems, including those involving VAT (Value Added Tax) and discounts.
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D.08. Calculate the percent of change (increase or decrease).
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D.09. Apply percent of change to solve word problems.
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D.10. Calculate percentage increase and decrease in real-world scenarios (discount and mark-up).
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D.11. Solve multi-step problems involving percents, including successive discounts or markups.
E. Basic Equations and Problem Solving
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E.01. Solve one-step linear equations using inverse operations.
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E.02. Solve two-step linear equations.
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E.03. Solve advanced linear equations involving distribution and combining like terms.
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E.04. Solve linear equations with variables on both sides of the equation.
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E.05. Solve equations by completing the given solution steps.
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E.06. Determine the number of solutions (none, one, or infinite) a linear equation has.
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E.07. Create linear equations with no solutions or infinitely many solutions.
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E.08. Translate word problems into linear equations and solve them.
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E.09. Solve linear equations, including multistep equations, and check the solutions.
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E.10. Apply algebraic equation-solving techniques to practical contexts.
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E.11. Model and solve equations using algebra tiles.
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E.12. Write and solve equations that represent diagrams.
F. Basic Geometric Concepts: Lines, Angles, and Triangles
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F.01. Identify and name angle pairs formed by transversals (e.g., corresponding, alternate interior, alternate exterior).
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F.02. Determine angle measures when transversals intersect parallel lines.
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F.03. Identify complementary, supplementary, vertical, adjacent, and congruent angles.
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F.04. Calculate measures of complementary, supplementary, vertical, and adjacent angles.
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F.05. Classify triangles based on their sides and angles.
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F.06. Apply the triangle angle-sum property to find missing angle measures.
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F.07. Apply the exterior angle property of triangles to find missing angle measures.
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F.08. Understand and apply the exterior angle inequality theorem.
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F.09. Relate angle and side relationships in triangles (e.g., the longest side is opposite the largest angle).
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F.10. Apply the Triangle Inequality Theorem to determine if three given side lengths can form a triangle.
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F.11. Define and identify midsegments of triangles and their properties.
G. Properties of Polygons and Quadrilaterals
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G.01. Define and apply polygon vocabulary (e.g., vertex, side, diagonal, regular polygon).
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G.02. Calculate the sum of interior angles of polygons.
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G.03. Calculate the sum of exterior angles of polygons.
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G.04. Calculate the measure of individual interior and exterior angles in regular polygons.
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G.05. Classify different types of quadrilaterals (e.g., parallelogram, rectangle, square, rhombus, trapezoid, kite).
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G.06. Graph quadrilaterals on the coordinate plane given their vertices.
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G.07. State and apply the properties of parallelograms (e.g., opposite sides are parallel and congruent).
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G.08. Prove that a quadrilateral is a parallelogram using its properties.
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G.09. State and apply the properties of rhombuses (e.g., diagonals are perpendicular bisectors of each other).
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G.10. State and apply the properties of squares and rectangles.
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G.11. State and apply the properties of trapezoids.
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G.12. State and apply the properties of kites.
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G.13. Review and apply properties of all quadrilaterals to solve geometric problems.
H. Congruence and Similarity
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H.01. Understand congruence of angles and line segments.
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H.02. Apply Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA) theorems to prove triangle congruence.
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H.03. Determine triangle congruence in the coordinate plane by finding the measure of their sides.
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H.04. Apply congruence properties in isosceles and equilateral triangles.
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H.05. Apply the Hypotenuse-Leg (HL) Theorem to prove right triangle congruence.
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H.06. Investigate and use relationships between sides and angles of congruent and similar triangles.
I. Area and Perimeter
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I.04. Calculate the area of trapezoids.
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I.05. Calculate the area and circumference of circles.
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I.06. Calculate the area of compound figures by decomposing them into simpler shapes.
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I.07. Calculate the area between two shapes.
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I.08. Solve mixed review problems involving area and perimeter.
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I.09. Apply Heron’s formula to calculate the area of a triangle given its side lengths.
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I.10. Analyze how changes in dimensions affect the perimeter and area of geometric figures.
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I.01. Calculate the perimeter of various polygons.
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I.02. Calculate the area of rectangles and squares.
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I.03. Calculate the area of parallelograms and triangles.
J. Surface Area and Volume
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J.01. Understand the concepts of surface area and volume.
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J.02. Calculate the surface area of prisms and cylinders.
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J.03. Calculate the surface area of cones.
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J.04. Calculate the volume of prisms and cylinders.
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J.05. Calculate the volume of cones.
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J.06. Calculate the surface area and volume of spheres.
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J.07. Solve review problems involving surface area and volume of various 3D shapes.
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J.08. Investigate the relationship between surface area and volume when scaling 3D objects.
K. Circle Geometry
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K.01. Identify and define parts of a circle (e.g., center, radius, diameter, chord, secant, tangent).
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K.02. Define and measure central angles in degrees and radians.
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K.03. Calculate arc measure and arc length.
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K.04. Calculate the area of sectors of a circle.
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K.05. Solve mixed review problems involving circle measurements.
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K.06. Apply theorems related to arcs and chords.
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K.07. Apply theorems related to tangent lines.
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K.08. Calculate the perimeter of polygons with an inscribed circle.
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K.09. Apply theorems related to inscribed angles.
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K.10. Analyze angles in inscribed right triangles.
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K.11. Analyze angles in inscribed quadrilaterals.
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K.12. Apply properties of circles to real-world scenarios and problems.
L. Geometric Constructions
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L.01. Construct the midpoint or perpendicular bisector of a segment using compass and straightedge.
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L.02. Construct an angle bisector using compass and straightedge.
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L.03. Construct a congruent angle using compass and straightedge.
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L.04. Construct an equilateral triangle or regular hexagon using compass and straightedge.
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L.05. Apply geometric construction techniques to solve problems and create geometric designs.
M. Data Analysis and Probability
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M.01. Calculate the mean, median, mode, and range of a data set.
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M.02. Determine quartiles of a data set.
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M.03. Identify biased samples in statistical studies.
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M.04. Calculate the variance and standard deviation of a data set.
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M.05. Interpret bar graphs, line graphs, and histograms.
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M.06. Create bar graphs, line graphs, and histograms to represent data.
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M.07. Interpret pie charts.
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M.08. Interpret stem-and-leaf plots.
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M.09. Calculate theoretical probability of an event.
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M.10. Determine experimental probability of an event based on observed outcomes.
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M.11. Understand compound events and find the number of possible outcomes.
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M.12. Distinguish between independent and dependent events.
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M.13. Calculate the probability of independent and dependent events.
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M.14. Use factorials and the counting principle to solve combinatorial problems.
N. Logic and Reasoning
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N.01. Identify hypotheses and conclusions in conditional statements.
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N.02. Provide counterexamples to disprove mathematical statements.
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N.03. Apply logical reasoning to solve puzzles and mathematical problems.
O. Coordinate Plane
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O.01. Review the structure of the coordinate plane, including axes and quadrants.
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O.02. Identify the quadrants and axes in the coordinate plane.
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O.03. Plot points and identify their coordinates in the coordinate plane.
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O.04. Calculate the distance between two points in the coordinate plane.
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O.05. Find the midpoint of a line segment in the coordinate plane.
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O.06. Understand the relationship between geometric shapes and their representations in the coordinate plane.
P. Direct Variation
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P.01. Recognize and identify proportional relationships between two variables.
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P.02. Determine the constant of variation in a direct variation relationship.
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P.03. Graph a proportional relationship on the coordinate plane.
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P.04. Write direct variation equations to represent relationships.
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P.05. Solve direct variation equations.
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P.06. Apply direct variation to solve real-world problems.
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P.07. Analyze and compare different direct variation relationships.
Q. Linear Equations and Their Graphs
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Q.01. Recognize and identify linear equations.
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Q.02. Determine the slope of a line from its graph.
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Q.03. Calculate the slope of a line given two points on the line.
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Q.04. Find a missing coordinate of a point on a line given its slope and another point.
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Q.05. Identify the slope and y-intercept from the slope-intercept form of a linear equation (y = mx + b).
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Q.06. Graph a linear equation using the slope-intercept form.
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Q.07. Write the equation of a line in slope-intercept form from its graph.
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Q.08. Write the equation of a line in slope-intercept form given the slope and y-intercept.
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Q.09. Write the equation of a line in slope-intercept form given two points.
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Q.10. Write the equation of a line in slope-intercept form from a table of values.
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Q.11. Write the equation of a line in slope-intercept form from a word problem.
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Q.12. Solve linear equations for y to express them in slope-intercept form.
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Q.13. Translate real-world scenarios into linear equations and solve related problems.
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Q.14. Compare linear equations, graphs, and tables to analyze relationships.
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Q.15. Write linear equations in standard form (Ax + By = C).
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Q.16. Find the x- and y-intercepts from the standard form of a linear equation.
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Q.17. Graph a linear equation using its standard form and intercepts.
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Q.18. Write equations of horizontal and vertical lines.
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Q.19. Graph horizontal and vertical lines.
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Q.20. Determine the slopes of parallel and perpendicular lines.
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Q.21. Write the equation of a line that is parallel or perpendicular to a given line.
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Q.22. Apply linear equations to model and solve real-world problems.
R. Exponents and Scientific Notation
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R.01. Evaluate powers with integer bases (positive, negative, and zero exponents).
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R.02. Evaluate powers with decimal and fractional bases.
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R.03. Understand and apply negative exponents.
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R.04. Apply the product of powers property (multiplication with exponents).
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R.05. Apply the quotient of powers property (division with exponents).
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R.06. Apply the power of a power property.
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R.07. Apply multiple properties of exponents to evaluate and simplify expressions.
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R.08. Identify equivalent expressions involving exponents.
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R.09. Convert between standard and scientific notation.
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R.10. Compare numbers written in scientific notation.
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R.11. Multiply numbers written in scientific notation.
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R.12. Divide numbers written in scientific notation.
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R.13. Apply scientific notation to solve real-world problems involving very large or very small numbers.
S. Polynomials and Factoring
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S.01. Define polynomial vocabulary (e.g., term, coefficient, constant, degree, leading coefficient).
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S.02. Model polynomials with algebra tiles.
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S.03. Add and subtract polynomials using algebra tiles.
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S.04. Add and subtract polynomials algebraically.
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S.05. Add polynomials to find the perimeter of geometric figures.
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S.06. Multiply a polynomial by a monomial.
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S.07. Multiply two polynomials using algebra tiles.
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S.08. Multiply two binomials using the FOIL method.
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S.09. Multiply two binomials, including special cases (e.g., difference of squares, perfect square trinomials).
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S.10. Multiply polynomials of higher degrees.
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S.11. Write a polynomial from its roots.
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S.12. Find the roots of factorised polynomials.
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S.13. Find the greatest common factor (HCF) of monomials.
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S.14. Factor out a monomial from a polynomial.
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S.15. Factorise quadratic expressions with a leading coefficient of 1.
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S.16. Factorise quadratic expressions with other leading coefficients.
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S.17. Factorise quadratic expressions that are special cases (difference of squares, perfect square trinomials).
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S.18. Factorise quadratics using algebra tiles.
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S.19. Factorise polynomials by grouping.
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S.20. Factorise polynomials completely using various techniques.
T. Quadratic Equations and Radical Expressions
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T.07. Determine the roots of perfect integers.
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T.08. Determine the roots of perfect rational numbers.
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T.09. Find roots using a calculator.
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T.10. Simplify radical expressions with variables (excluding rational exponents).
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T.11. Simplify radical expressions with variables (including rational exponents).
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T.12. Multiply radical expressions.
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T.13. Divide radical expressions.
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T.14. Add and subtract radical expressions.
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T.15. Simplify radical expressions using the distributive property.
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T.16. Simplify radical expressions using conjugates.
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T.17. Determine nth roots of expressions, where n is an integer.
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T.18. Solve word problems involving quadratic equations and radical expressions.
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T.01. Identify the characteristics of quadratic equations (e.g., coefficients, constant term, degree).
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T.02. Complete a table of values for a given quadratic equation.
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T.03. Solve a quadratic equation using square roots.
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T.04. Solve a quadratic equation using the zero product property.
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T.05. Solve a quadratic equation by factorising.
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T.06. Solve a quadratic equation using the quadratic formula.
U. Rational Expressions
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U.01. Simplify complex fractions.
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U.02. Simplify rational expressions by cancelling common factors.
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U.03. Multiply and divide rational expressions.
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U.04. Divide polynomials using long division or synthetic division.
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U.05. Add and subtract rational expressions by finding a common denominator.
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U.06. Solve rational equations, checking for extraneous solutions.
V. Word Problems
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V.01. Solve mixed review word problems involving various mathematical concepts.
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V.02. Solve word problems involving money and financial literacy.
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V.03. Solve consecutive integer problems.
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V.04. Solve rate of travel word problems (distance, rate, and time).
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V.05. Solve weighted averages word problems.
