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	Infinite Grade 6 Math	Infinite Pre‑Algebra	Infinite Algebra 1	Infinite Geometry	Infinite Algebra 2	Infinite Precalculus	Infinite Calculus
Ratios
Introduction to ratios	✓
Equivalent ratios	✓
Part-part-whole ratios	✓
Comparing ratios	✓
Rates
Unit rates and equivalent rates	✓
Comparing rates	✓
Converting units	✓
Negative Numbers and Absolute Value
Numbers on a number line	✓
Number line word problems	✓
Opposites of numbers	✓
Comparing numbers	✓
Ordering numbers	✓
Absolute values	✓
Comparing with absolute values	✓
Ordering with absolute values	✓
Equations as Relationships between Two Variables
Equivalent ratio equations	✓
Constant rate equations	✓
Equations for other relationships	✓
Integers, Decimals, and Fractions
Naming decimal places and rounding		✓
Writing numbers with words		✓
Adding and subtracting	✓	✓	✓
Addition and subtraction with diagrams	✓
Multiplying	✓	✓	✓
Multiplication with area diagrams	✓
Dividing	✓	✓	✓
Long division	✓
Factoring	✓	✓	✓
Greatest common factor	✓	✓
Least common multiple	✓	✓
GCF and LCM word problems	✓
Simplifying fractions		✓
Converting fractions and decimals		✓
Beginning Algebra
Properties of addition and multiplication	✓
Verbal expressions	✓	✓	✓
Evaluating algebraic expressions	✓	✓	✓
Order of operations	✓	✓	✓		✓
Combining like terms	✓	✓
The Distributive Property	✓	✓	✓		✓
The Distributive property with area diagrams	✓
Sets of numbers			✓
Equations
Tape diagrams	✓
Hanger diagrams	✓
One-step equations, word problems	✓	✓
Two-step equations		✓	✓
Two-step equations word problems		✓
Multi-step equations		✓	✓	✓	✓
One-step equations	✓	✓	✓
Absolute value equations			✓		✓
Mixture word problems			✓		✓
Distance, rate, time word problems	✓		✓		✓
Work word problems			✓		✓
Literal equations			✓
Inequalities
Solutions to inequalities	✓
Inequalities word problems	✓
Hanger diagrams	✓
Graphing single-variable inequalities	✓	✓	✓
One-step inequalities	✓	✓	✓
Two-step inequalities		✓	✓
Multi-step inequalities		✓	✓		✓
Compound inequalities			✓		✓
Absolute value inequalities			✓		✓
Factors and Exponents
Divisibility		✓
Properties of exponents		✓	✓
Writing scientific notation		✓	✓
Operations and scientific notation		✓	✓
Addition and subtraction with scientific notation			✓
Graphing exponential functions			✓		✓	✓
Discrete exponential growth and decay			✓		✓
Continuous exponential growth and decay					✓
Proportions and Similarity
Checking for a proportion		✓
Solving proportions		✓	✓	✓
Proportions word problems		✓
Similar figures		✓
Similar figures word problems		✓
Similarity
Similar polygons				✓
Similar triangles				✓
Similar right triangles				✓
Proportional parts in triangles and parallel lines				✓
Percents
Fractions, decimals, and percents	✓	✓
Percents	✓	✓	✓
Percent of change		✓	✓
Solving percent problems	✓	✓
Markup, discount, and tax		✓
Simple and compound interest		✓
Relations and Introduction to Functions
Discrete relations			✓		✓
Continuous relations			✓		✓
Evaluating and graphing functions			✓		✓
Linear Equations and Inequalities
Plotting points	✓	✓
The Midpoint Formula		✓	✓	✓
Slope		✓	✓
Graphing linear equations		✓	✓	✓	✓
Writing linear equations		✓	✓	✓	✓
Graphing linear inequalities		✓	✓		✓
More on slope			✓
Graphing absolute value equations			✓		✓
Direct and inverse variation			✓		✓
Basics of Geometry
Line segments and their measures				✓
Segment Addition Postulate				✓
Angles and their measures				✓
Classifying angles				✓
Basic angle terminology				✓
Angle Addition Postulate				✓
Angle relationships		✓		✓
Geometric diagrams and notation				✓
Plane Figures
Drawing and measuring angles		✓
Angle relationships		✓
Triangles	✓	✓
Quadrilaterals	✓	✓
Area of triangles and quadrilaterals	✓	✓
Circles		✓
Transformations: Translations, rotations, and reflections		✓		✓
Parallel Lines and the Coordinate Plane
Parallel lines and transversals				✓
Points of the coordinate plane	✓			✓
Distances on the coordinate plane	✓
Shapes and perimeter on the coordinate plane	✓
Distances, word problems	✓
The Midpoint Formula		✓	✓	✓
The Distance Formula		✓	✓	✓
Slope and lines				✓
Congruent Triangles
Classifying triangles				✓
Triangle angle sum				✓
Exterior Angle Theorem				✓
Triangles and congruence				✓
Proving triangles congruent				✓
Isosceles and equilateral triangles				✓
Properties of Triangles
Midsegment				✓
Angle bisectors				✓
Medians				✓
Centroid				✓
Triangle Inequality Theorem				✓
Inequalities in one triangle				✓
Quadrilaterals and Polygons
Classifying				✓
Angles				✓
Parallelograms	✓			✓
Trapezoids	✓			✓
Rhombuses				✓
Kites	✓			✓
Area of triangles and quadrilaterals	✓	✓		✓
Polygon basics	✓			✓
Polygons on a grid or coordinate plane	✓
Polygons and shaded regions	✓
Area of regular polygons				✓
Right Triangles
Squares and square roots		✓
The Pythagorean Theorem		✓		✓
The Distance Formula		✓	✓	✓
Multi-step Pythagorean Theorem problems				✓
Special right triangles				✓
Multi-step special right triangle problems				✓
Surface Area and Volume
Solid figures: identifying, volume, and area	✓	✓		✓
Nets of solids	✓			✓
Similar solids				✓
Isometric drawings	✓
Circles
Naming arcs and central angles				✓
Measures of arcs and central angles				✓
Arcs and chords				✓
Circumference and area				✓
Arc length and sector area				✓	✓
Inscribed angles				✓
Tangents				✓
Secant and tangent angles				✓
Segment measures				✓
Using equations of circles				✓
Writing equations of circles				✓
Constructions
Line segments				✓
Perpendicular segments				✓
Angles				✓
Triangles				✓
Medians of a triangle				✓
Altitudes of a triangle				✓
Angle bisectors				✓
Circles				✓
Systems of Equations and Inequalities
Graphing systems of linear inequalities		✓	✓		✓
Solving systems by graphing			✓		✓
Solving systems by elimination			✓		✓
Solving systems by substitution		✓	✓		✓
Systems of equations word problems		✓	✓		✓
Points in three dimensions					✓
Planes					✓
Solving systems with three variables					✓
Matrices
Operations					✓	✓
Determinants					✓	✓
Inverses					✓	✓
Cramer's Rule					✓	✓
Equations					✓	✓
Geometric transformations					✓
Multivariable linear systems and row operations						✓
Partial fraction decomposition						✓
Complex Numbers
Operations					✓
Graphing					✓
Absolute value					✓
Rationalizing denominators					✓
Polynomial Functions
Naming			✓		✓
Adding and subtracting		✓	✓		✓
Multiplying		✓	✓		✓
Multiplying special cases			✓		✓
The Binomial Theorem					✓	✓
Dividing			✓		✓	✓
Factoring by grouping			✓		✓
Factoring a sum/difference of cubes					✓
Factoring quadratic form					✓
Factoring, all techniques					✓
The Remainder Theorem					✓	✓
Conjugate roots & factoring					✓
Conjugate roots & writing functions					✓	✓
Descartes' Rule of Signs					✓
Rational Zero/Root Theorem					✓
Fundamental Theorem of Algebra					✓	✓
Solving polynomial equations					✓
End behavior and general graph shape					✓	✓
Graphing					✓	✓
Polynomial inequalities						✓
Functions
Evaluating					✓
Operations					✓	✓
Inverses					✓	✓
Continuity						✓	✓
Extrema, intervals of increase and decrease						✓
Power functions						✓
Average rates of change						✓
Transformations of graphs						✓
Piecewise functions						✓
Factoring
Common factor only			✓
Quadratic expressions			✓
Special cases			✓
By grouping			✓
Quadratic Functions and Inequalities
Graphing quadratic functions			✓		✓
Graphing quadratic inequalities					✓
Factoring quadratic expressions			✓		✓
Factoring special case quadratic expressions			✓		✓
Solving equations by taking square roots			✓		✓
Solving equations by factoring			✓		✓
Completing the square			✓		✓
Solving equations by completing the square			✓		✓
Solving equations with the Quadratic Formula			✓		✓
The discriminant			✓		✓
Radical Functions and Rational Exponents
Simplifying radicals			✓	✓	✓
Adding and subtracting radical expressions			✓	✓	✓
Multiplying radical expressions			✓	✓	✓
Dividing radical expressions			✓	✓	✓
Connecting radical expressions and rational exponents					✓
Evaluating rational exponent expressions					✓
The properties of exponents		✓	✓		✓
Radical equations			✓		✓
Rational exponent equations					✓
Graphing radical equations					✓
Domain and range of radical functions					✓
Rational Expressions
Graphing					✓	✓
Simplifying			✓		✓
Multiplying and dividing			✓		✓
Adding and subtracting			✓		✓
Complex fractions					✓
Rational inequalities						✓
Equations			✓		✓	✓
Trigonometry
Right triangle trig: Finding ratios			✓	✓	✓	✓
Right triangle trig: Finding angle measures			✓	✓	✓	✓
Right triangle trig: Finding angles and sides			✓	✓	✓	✓
Multi-step trig. problems				✓
Rhombuses and kites with right triangles				✓
Trigonometry and area				✓	✓	✓
Angles and angle measure					✓	✓
Radians and degrees					✓	✓
Degrees and degrees-minutes-seconds					✓
Coterminal angles					✓
Trig functions of any angle					✓	✓
The Law of Sines					✓	✓
The Law of Cosines					✓	✓
Graphing trig functions					✓	✓
Angle sum/difference identities					✓
Double-angle/half-angle identities					✓
Equations					✓	✓
Inverse trig functions						✓
Fundamental identities						✓
Equations with factoring and fundamental identities						✓
Sum and Difference Identities						✓
Multiple-Angle Identities						✓
Product-to-Sum Identities						✓
Equations and Multiple-Angle Identities						✓
Probability and Statistics
Dot plots	✓	✓	✓
Box plots	✓	✓	✓
Histograms	✓		✓
Visualizing data	✓	✓	✓
Center and spread	✓	✓	✓
Scatter plots		✓	✓
Using statistical models		✓	✓
Sample spaces and the Fundamental Counting Principle				✓	✓	✓
Independent and dependent events, word problems				✓	✓	✓
Independent and dependent events				✓	✓	✓
Mutually exclusive events, word problems				✓	✓	✓
Mutually exclusive events				✓	✓	✓
Permutations				✓	✓	✓
Combinations				✓	✓	✓
Permutations vs combinations				✓	✓	✓
Probability with permutations and combinations				✓	✓	✓
Conic Sections
Classifying					✓
Systems of quadratic equations					✓
Parabolas, graphing & properties					✓	✓
Parabolas, writing equations					✓	✓
Circles, graphing & properties					✓	✓
Circles, writing equations					✓	✓
Ellipses, graphing & properties					✓	✓
Ellipses, writing equations					✓	✓
Hyperbolas, graphing & properties					✓	✓
Hyperbolas, writing equations					✓	✓
Rotations of conic sections						✓
Exponential and Logarithmic Expressions
Exponential equations not requiring logarithms					✓	✓
Exponents and logarithms					✓	✓
Evaluating logarithms					✓	✓
Logarithms and exponents as inverses					✓	✓
Properties of logarithms					✓	✓
Writing logs in terms of others					✓	✓
Exponential equations requiring logarithms					✓	✓
Inverses of					✓	✓
Logarithmic equations, simple					✓	✓
Logarithmic equations, hard					✓	✓
Graphing logarithmic functions					✓	✓
Discrete exponential growth and decay word problems			✓		✓
Continuous exponential growth and decay word problems					✓
Compound interest						✓
Sequences and Series
General sequences					✓	✓
Arithmetic sequences					✓	✓
Geometric sequences					✓	✓
Arithmetic and geometric mean					✓	✓
General series					✓	✓
Arithmetic series					✓	✓
Geometric series					✓	✓
Power series						✓
Parametric Equations
Parametric equations						✓
Projectile motion						✓
Polar Coordinates
Polar coordinates						✓
Graphs of polar equations						✓
Polar and rectangular forms of equations						✓
Polar forms of conic section						✓
Complex numbers in polar form						✓
Vectors
Basics						✓
Diagrams						✓
Operations						✓
Dot products						✓
Three-Dimensional Vectors
Points in three dimensions						✓
Basics						✓
Operations						✓
Cross products						✓
Discrete Mathematics
Sample spaces and The Fundamental Counting Principle						✓
Permutations						✓
Combinations						✓
Permutations vs combinations						✓
The Binomial Theorem						✓
Mathematical induction						✓
Limits
By direct evaluation						✓	✓
At jump discontinuities and kinks						✓	✓
At removable discontinuities						✓	✓
At essential discontinuities						✓	✓
At infinity						✓	✓
Differentiation
Average rates of change							✓
Definition of the derivative						✓	✓
Instantaneous rates of change						✓	✓
Power Rule						✓	✓
Higher order derivatives							✓
Product Rule							✓
Quotient Rule							✓
Chain Rule							✓
Rules, using tables							✓
Trigonometric							✓
Inverse trigonometric							✓
Natural logarithms and exponentials							✓
Other base logarithms and exponentials							✓
Logarithmic							✓
Implicit							✓
Inverse functions							✓
Applications of Differentiation
Slope, tangent, and normal lines							✓
Rolle's Theorem							✓
Mean Value Theorem							✓
Intervals of increase and decrease							✓
Intervals of concavity							✓
Relative extrema							✓
Absolute extrema							✓
Optimization							✓
Curve sketching							✓
Graphical comparison of f, f', and f''							✓
Motion along a line						✓	✓
Related rates							✓
Differentials							✓
Newton's Method							✓
Limits in form of definition of derivative							✓
L'Hopital's Rule							✓
Indefinite Integration
Power Rule						✓	✓
Logarithmic Rule and Exponentials							✓
Trigonometric							✓
Inverse trigonometric							✓
Power rule with substitution							✓
Logarithmic rule and exponentials with subs.							✓
Trigonometric with substitution							✓
Inverse trigonometric with substitution							✓
Integration by parts							✓
Definite Integration
Approximating area under a curve						✓	✓
Area under a curve by limit of sums						✓	✓
Riemann sum tables							✓
First Fundamental Theorem of Calculus							✓
Substitution with change of variables							✓
Mean Value Theorem							✓
Second Fundamental Theorem of Calculus							✓
Applications of Integration
Area under a curve							✓
Area between curves							✓
Volume by slicing, disks and washers							✓
Volume by cylinders							✓
Volume of solids with known cross sections							✓
Motion along a line revisited							✓
Differential Equations
Slope fields							✓
Introduction							✓
Separable							✓
Exponential growth and decay							✓