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Scope and Sequence of Secondary Math

Fundamentals of Math

Whole Numbers

Comparing and ordering; Estimating; Operations; Exponents; Roots of perfect squares

Decimals

Comparing and ordering; Rounding; Approximating square roots; Operations; Estimating square roots; Scientific notation

Number Theory

Divisibility; Factors; Prime and composite numbers GCD and LCM; Converting to and adding in other number bases

Fractions

Equivalent fractions; Mixed numbers; Comparing and ordering; Operations; Order of operations

Rational numbers

Ratio and proportion; Solving proportions; Scale drawings; Decimals as rational numbers; Finding a percent (part) of a number; Finding the percent; Finding the whole amount

Using percents

Enlargement and reduction; Sales tax; Discounts; Sale price; Simple interest; Commission; Percent change

Measurements

Customary units of length; Capacity, and weight; SI (metric) units of length, capacity, and mass; Renaming metric units; Time zones; Temperature conversions; Precision

Geometry

Measuring angles; Pairs of angles; Perpendicular and parallel lines; Transversal of parallel lines; Polygons; Circle; Perimeter and circumference; Pythagorean theorem; Congruent and similar figures

Area and Volume

Area of quadrilaterals, triangles, and circles; Areas of similar figures; Surface area of prisms, cylinders, and pyramids; Volume of prisms and cylinders

Probability and statistics

Fundamental principle of counting; Permutations; Probability; Mean, median, mode; Circle, bar, and line graphs; Histograms; Box–and–whisker plots; Stem–and–leaf diagrams

Integers

Ordering; Operations; Applying order of operations; Expansion to and properties of the real numbers

Algebra

Evaluating expressions; Solving one–and two–step equations; Solving one–and two–step inequalities

Relations and functions

Coordinate plane; Functions and function rules; Graphing linear functions; Slope; Translation of figures on a plane

Logic and set theory

Statements and negations; Compound and conditional statements and negations; Truth tables; Sets and subsets; Union and intersection of sets; Finite and infinite sets

Pre–Algebra

Integers

Absolute value; Operation ; Exponents; Order of operation; Scientific notation

Expressions

Real–number properties; Evaluating and simplifying expressions; Translating word phrases; Rounding and estimating results of operations

Equations

Solving two–step equations; Removal of parentheses; Subsets of the real numbers; Irrational numbers; Solving linear inequalities; Applying equations and inequalities

Number Theory

Prime factorization; GCD and LCM; Arithmetic and geometric sequences; Number bases other than 10, including hexadecimal; Operations in other bases

Rational Numbers

Forms of ordering fractions and decimals; Decimal equivalents of fractions; Conversion of repeating decimals to fractions; Ratios and proportions; Subsets and properties of real numbers

Operations on rational numbers

Operations; Evaluating and simplifying expressions; Solving equations involving rationals; Operations in scientific notataion

Percents

Solving percent equations; Applying percents; Scales; Discount, markup, commissions, tips, and interest (including compound); Percent change

Applications

Equations with variables on both side; Writing and solving equations and inequalities

Relations and functions

Coordinate plane; Functions; Graphing linear functions and linear inequalities; Slope; Direct variation

Statistics and probability

Population and sample; Mean, median, and mode; Scatterplot; Quartiles; Box–and–whisker; Stem–and–leaf; Histograms; Choosing the correct type of graph; Permutations; Combinations; Probability

Radicals

Square roots; Radical equations; Equations with radicals; Equations of the form ax2+b=c; Pythagorean theorem; Operations with radicals; Cube roots

Geometry

Pairs of angles; Polygons; Perimeter and circumference; Congruence and similarity; 30—60 and 45—45 right triangle ratios; Distance and midpoint formulas; Symmetry and transformation

Areas and volume

Areas of quadrilaterals, triangles, and circles; Relation of lengths and areas of similar regions; Surface areas of prisms, cylinders, pyramids, cones, and spheres

Polynomials

Definition of a polynomial; Operations with polynomials, including multiplying binomials and dividing a polynomial by a monomial

Algebra 1

Operations

Review of the real number system, number lines, absolute value, arithmetic operations of integers and rational numbers, exponents, and order of operations

Variables and equations

Using variables, algebraic expressions, and formulas; Writing and solving linear equations

Using algebra

Solving literal equations and proportions; Applying equations to applications involving similar figures, percentages, money, motion, and mixtures

Solving inequalities

Linear inequalities, including conjunctions, disjunctions; Absolute-value equations and inequalities

Relations and functions

Representing relationships between data, using graphs, equations, and tables; Direct and inverse variations; Graphing absolute value functions

Linear functions

Graphs, slopes, and intercepts of linear equations; Determining the equation of a line; Parallel and perpendicular lines; Correlation and lines of fit; Graphing linear inequalities

Systems of equations and inequalities

Solving systems graphically, by substitution, and by elimination; Applications of systems

Exponents

Products, quotients, and powers of exponential expressions; Scientific notation; Graphing exponential functions; Exponential growth and decay

Polynomials

Classification, evaluation, operations, special patterns

Factoring

Common monomials, trinomials, special patterns

Radicals

Simplification and operations with radicals; Pythagorean theorem; Distance and midpoint formulas; Solving radical equations and graphing radical functions; Applications

Quadratic Equations

Solving by factoring, taking roots, completing the square, and the quadratic formula; Graphing parabolas and finding zeros; Applications

Rational expressions and equations

Simplification and operations with rational expressions; Solving rational equations; Applications

Geometry

Foundations of Geometry

Sets; definitions; incidence postulates and theorems; segment and angle measure; circles; polygons; polyhedra

Reasoning and Proof

Inductive and deductive reasoning; truth tables; proofs using angles and segments; bisectors; constructions

Parallel and Perpendicular Lines

Characteristics; proofs; constructions; and coordinate geometry

Congruent Triangles

Angles in triangles; congruence postulates and theorems; flow-chart proofs; right triangles; midsegments

Relationships in Triangles

Circumcenter; incenter; orthocenter; centroid; indirect proof; triangle inequalities; constructions

Quadrilaterals

Classification; characteristics; proofs; analytic geometry related to trapezoids; kites; parallelograms; squares; rectangles; and rhombii

Area

Postulates; polygons; Pythagorean Theorem; special triangles; regular polygons; and circles

Circles

Chords; tangents; arc length; sectors; inscribed angles; secants; constructions; graphs

Surface Area and Volume

Nets; prisms; cylinders; pyramids; spheres; non-Euclidean geometry; perspective

Transformations and Symmetry

Reflections; translations; rotations; dilations; invariants; symmetry; applications

Similarity

Triangles; right triangles; proportions; chords and tangents of circles; golden ratio

Trigonometry

Basic ratios; solving right triangles; applications; vectors; areas; identities

Algebra 2

Operations

Real and complex numbers; Polynomial; Matrix; Function

Linear equations

Solving equations and inequalities; Absolute value equations and inequalities; Distance on number lines; Word problems; Compound inequalities

Linear relations

Graphs of linear functions; Slopes; Special functions; Linear inequalities; Distances and midpoints; Modeling with linear regressions

Systems

Solved graphically and algebraically; Systems of inequalities; Systems of three variables; Problem solving; Linear programming

Matrices

Organizing data; Operations; Determinants; Solving systems using Cramer's Rule and inverse matrices; Transformations

Quadratic equations

Solving factoring, taking roots, completing the square, and the quadratic formula; Using the discrimiant; Complex roots; Quadratic inequalities

Polynomial functions

Roots, graphing, and modeling with quadratic and polynomial functions; Problem solving; Rational root, remainder, and factor theorems; Fundamental theorem of algebra

Radicals, Exponents, and Logarithms

Rational exponents; Inverse functions; Simplifying expressions; Solving equations, graphing and modeling with radical, exponential, and logarithmic functions; Natural and common logarithms

Rational Expressions

Simplifying; Solving equations; Graphing; Variations

Trigonometry

Right triangle and coordinate plane trigonometry; Special triangles and the unit circle; Radians; Graphs of trigonometric functions; Inverse functions

Trigonometric Identities

Law of Siens; Law of Cosines; Problem solving; Proving identities; Trigonometric equations

Sequences and Series

Explicit and recursive formulas; Arithmetic and geometric sequences and series; Summation notataion

Probability and Statistics

Counting principles; Theoretical and experimental probabilities; Independent, dependent, and mutually exclusive events; Binomial distribution, descriptive statistics, representing data; Normal distributions; Making inferences

Analytic Geometry

Circles; Parabolas; Ellipses; Hyperbolas; Systems of quadratic relations

Precalculus

Trigonometry

Reference angles; Law of Sines; Law of Cosines

Polynomials

Linear; Quadratic and polynomial functions; Factoring higher–degree polynomials; Zeros; Graphing

Functions

Power; Exponential; Piece; Periodic; Trigonometric; Reciprocal; Rational

Inverse Functions

Increasing and decreasing functions; Checking and finding inverses; Radical functions; Inverse trigonometric functions; Logarithms

Equations

Polynomial; Rational; Radical; Logarithmic; Exponential functions; Identities; Trigonometric equations

Conic sections and polar graphs

Circles; Ellipses; Parabolas; Hyperbolas; Variation; Polar coordinates; Polar equations

Complex numbers

Graphs; Polar form; Powers and roots; Vectors; Dot products; Applications

Matrix Algebra

Gaussian elimination; Determinants; Cramer's Rule; Inverses

Statistics

Central tendency; Variability; Bell curve; Linear correlation; Hypothesis testing

Sequences

Recursive and explicit formula; Arithmetic and geometric sequences; Mathematical induction; Summation

Limits and Calculus

Limits of sequences; Series; Limits of functions; Continuous functions; Ssymptotes; Limit theorems

Differential calculus

Definition; Graphs, properties; Chain rule; Quotient rule; Motion applications

Consumer Math

Math Skills

Fractions, decimals, integers; Problem solving using proportions and percent; Solving linear equations; Negative exponents to prepare for finance formulas

Measurement

Customary and SI (metric) units; Conversion within and between systems using dimensional analysis; Perimeter, circumference, area, volume, and capacity

Income

Calculating hours worked from clocked times, gross pay including overtime; Payroll deductions including FICA and federal withholding; Buying and selling stocks and bonds including brokerage fees

Budgeting

A standardized budget; An annual budget; Reducing annual budget to monthly or weekly; Emergency adjustments; Revising the annual budget

Banking

Checking accounts and deposits; Overdraft penalties and protection; Service charges; Reconciling a bank statement; Simple interest; Compounding interest; Interest on savings using the minimum balance or daily interest methods; Effective interest rate; Savings programs with regular deposits

Borrowing

Simple interest loans; Add–on loans and annual percentage rate; Discount loans; Amortized loans; How credit cards work; How interest is calculated and payments are applied to the credit accounts

Transportation

Calculating the finance charge and monthly payment for a new car; Depreciation; Leasing costs including residual value, mileage penalty; Car insurance; Cost of gas, oil, and tires; Scheduled maintenance and repair costs

Food

Store specials and coupons; Unit prices; Calculating freezer payback periods; Consumer price index; Calorie counting; Finding the calories expended in activities

Clothing

Planning for seasonal buying; Calculating discounts including multiple ones; Filling out catalog orders; Internet buying tips; Savings from making clothing; Retail marketing of clothing; Returns, net profit and gross profit margin; Markup rate and breakeven point for retailer

Housing

Renting; Buying a house, including down payments, closing costs, points, and monthly payments; Owner's equity; Building a house, including converting dimensions to scale for a set of plans; Finding the area of rectangular lots in acres; Calculating the amount of shingles needed from a house plan; Allowing for pitched roofs

Maintaining a Home

Real estate tax based on mileage rates; Homeowner's insurance; Calculating utility charges for electricity, gas, water, and sewer; Residential and cell phone usage; Calculating house repairs, maintenance and home improvements

Life and health insurance

Mortality tables; Term, whole-life, and universal life insurance; Health insurance, including payout of benefits; Social security retirement benefits

Income taxes

General principles of calculating federal income taxes; 1040EZ, 1040A, and 1040, including extra schedules A and B Form 2441 for child care benefits

Vacations

Cost of food and lodging; Cost of transportation; Getting around at the site; Travel times across time zones; Economizing admissions

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