Scope and Sequence of Middle & High Math
Math 6
Number Sense
Recognize and write 0–100,000,000,000 as numerals and words; Roman numerals I–C; Place value: ten thousandths to hundred billions; comparing; expanded form; even/odd, positive/negative, prime/composite numbers; number line; expressions and equations; Part-whole relationships; inverse operations
Addition & Subtraction
Basic facts (fact families and other strategies); nine-digit column addition; Mental compensation; Properties: commutative, associative, identity; zero principle
Multiplication
Basic facts (fact families and other strategies); multiples; repeated addition; vertical form; one to three digits times two to four digits; renaming; factor trees; prime/composite numbers; GCF; LCM; Properties: commutative, associative, identity, zero, distributive
Division
Basic facts (fact families and other strategies); equal sets; measurement/partition; fraction form; equations; mental division by 10; two to four digits by one or two digits; remainders; mixed number and decimal quotients; decimal equivalent for a fraction
Equations
Inverse operations; compensation; simplify expressions; evaluate expressions; if-then statements; solve for an unknown
Pre-Algebra
Missing addend/subtrahend/minuend/factor; add, subtract, multiply, and divide integers; positive/negative numbers; Variables in expressions and equations; solve for a variable in an equation
Fractions
Part of a whole; part of a set; equivalent fractions; comparing; ordering; lowest terms; renaming improper fractions and mixed numbers; Add, subtract, multiply, and divide like and unlike fractions; cross-products; cancellation; pictorial representations or journal entries to express understanding of operations
Decimals
Read and write tenths, hundredths, thousandths; write as fractions and mixed numbers; comparing; ordering; renaming to thousandths; word forms; Add and subtract; Multiply a decimal by a whole number, by a decimal, and by a power of 10; Divide a decimal by a one-digit whole number; divide a whole number by a whole number with a decimal quotient; divide to rename a fraction as a decimal; divide a decimal by a power of 10
Geometry
Points; lines: parallel, intersecting, perpendicular; line segments; rays; symmetry; similar/congruent; constructions; angles: right, acute, obtuse; measure angles; sum of angles in a triangle = 180°; Plane figures: regular/irregular; polygons; triangles: scalene, isosceles, equilateral; quadrilaterals; parallelograms; transformations: translation, reflection, rotation; perimeter; area; Solid figures: sphere, cone, cylinder, polyhedron, cube, prism, pyramid; face, edge, vertex, curved surface; nets; surface area; volume; Circle: center point, radius, diameter, chord, central angles, circumference
Estimating
Round whole numbers and decimals to a given place; round fractions to the nearest half or whole; front-end estimation; Round to estimate a sum, difference, product, and quotient
Measurement
Length; capacity; weight; mass; Temperature: Fahrenheit; Celsius; Time: elapsed time; time zones; timeline; 24-hour clock; wages; Rename within the metric and customary systems to add, subtract, multiply, and divide
Problem Solving
Graphs; tables; charts; schedule; map skills; probability; money; Venn diagram; Using a problem-solving plan; multistep problems; problems with too little or too much information; group planning; Strategies: patterns; logic; guess and check; diagram/model; simpler problem; formulas; working backwards; writing an equation
Statistics & Graphs
Pictograph; bar/double bar graph; line/double line graph; histogram; circle graph; coordinate graph; Tables; charts; tallies; frequency table; line plot; stem-and-leaf plot; box-and-whisker plot; Mean, median, mode; range; frequency; scale; interval
Ratios, Proportions, Percents
Equivalent ratios; unit rate; scale drawings; map scale; Percents as fractions and decimals; writing fractions and decimals as percents; comparing percents to decimals and fractions; finding the percent of a number; determining the sales price given a discount as a percent; Proportionate geometric figures
Additional content
Introduction of speed, distance, and time; unit multipliers; comparing types of graphs, independent and dependent events; patterns; squares and square roots; Roman numerals through M (1,000); additional multistep problems
Fundamentals of Math
Whole numbers and decimals: ordering, rounding and comparing; operations and estimating; exponents; roots of perfect squares; approximating square roots; order of operations
Integers: numbers sets and subsets; opposite numbers and absolute value; ordering and rounding; operations; order of operations involving integers
Numerical and Algebraic Expressions: variables and expressions; properties of addition and multiplication; factoring common factors; combining like terms; adding linear expressions; properties of exponents; scientific notation
Fraction theory: divisibility; factors; prime and composite numbers; GCF and LCM; renaming fractions; rational numbers; comparing and ordering rational numbers
Fractions: operations; order of operations involving rational numbers; evaluating algebraic expressions involving rational numbers
Algebra: Writing equations; solving one- and two-step equations; solving equations with grouping symbols; solving one- and twostep inequalities
Ratios and proportion: ratios and rates; simplifying complex ratios; solving proportions; scale models; proportional relationships
Percents: proportions and percent; percent equations; enlargements and reductions; percent change; sales tax; discounts; sale price; simple interest
Measures: customary units of length, capacity, and weight; SI (metric) units of length, capacity, and mass; relating metric and customary units; converting rates
Introduction to Geometry: basic terms; measuring angles; pairs of angles; perpendicular and parallel lines; characteristics and area of triangles and quadrilaterals; exploring triangle theorems
Exploring area and volume: circles; areas of similar polygons; surface area of prisms, cylinders, and pyramids; volume of prisms and cylinders
Probability: simple events; theoretical and experimental probabilities; compound events: simulations
Statistics: populations and samples; descriptive measures (mean, median and mode); mean absolute deviation; comparing populations using line graphs, histograms, box-and-whisker plots, stem-and-leaf plot; visualizing data
Relations and functions: coordinate plane; functions and function rules; graphing linear functions; slope; sequences
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; polyhedrons
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 by 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
Analyzing functions
Relations; linear, quadratic, power, and piecewise functions; continuity, transformations, and operations of functions, parametric representations and modeling with functions
Radical, polynomial, and rational functions
Describing zeros, asymptotes, and end behavior of radical, polynomial, and rational functions and solving related equations and inequalities
Exponential and logarithmic functions
Graphing, applying properties, solving equations, and modeling
Trigonometric functions
Angle and arc measures; trigonometric functions in a right triangle, for other angles, and of real numbers; graphs of trig functions; inverse trig functions
Trigonometric identities and equations
Derive and verify identities; use identities to solve equations; derive and apply the law of sines and law of cosines
Vectors, polar graphs, and complex numbers
Describe and perform operations on 2-D and 3-D vectors; graph polar coordinates and equations; represent and perform operations on complex numbers in polar form
Systems and matrices
Using Gaussian elimination; determinants, and inverse matrices to solve systems of equations and inequalities; decomposing into partial fractions
Analytic geometry
Analyzing parabolas, ellipses, circles, and hyperbolas; rotated conics; parametric and polar representations
Sequences and series
Recursive and explicit formulas; arithmetic and geometric sequences; summations; the binomial theorem; mathematical induction
Descriptive statistics
Counting principles and basic probability; graphic representations; measures of central tendency and variability; normal distributions
Inferential statistics
Probability distributions; the central limit theorem; confidence intervals; hypothesis testing; research studies
Limits, derivatives, and integrals
Limit theorems; tangents to the curve; derivative theorems including product, quotient, and chain rules; area under a curve and integration; the fundamental theorem of calculus
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 clock 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 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; online shopping; 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 millage rates; homeowner’s insurance; calculating utility charges for electricity, gas, water, and sewer; communications; 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 and Form 2441 for childcare benefits
Vacations
Costs of food and lodging; cost of transportation; getting around at the site; travel times across time zones; economizing admissions