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; operations, exponents, roots, and their properties; order of operations

Expressions: evaluating and simplifying expressions; translating word phrases; scientific notation; estimating

Equations: solving one- and two-step equations; simplifying; solving linear inequalities; applying equations and inequalities

Rational expressions: prime factorization; GCF and LCM; rational numbers; decimal equivalents; converting repeating decimals to fractions; ratios and proportions; the real number system

Operations with rational numbers: evaluating and simplifying expressions; solving equations involving rational numbers; operations with scientific notation

Percents: solving percent equations; applying percents; discount, markup, tips, commission, simple and compound interest; percent change; scales

Applying equations: equations with variables on both sides; identities and contradictions; writing and solving equations and inequalities to solve problems; equations with powers, radical equations

Functions: illustrating relations; defining and graphing functions; slope; writing linear equations; proportional relationships; graphing linear inequalities

Systems of linear equations: solving linear systems by graphing, substitution, and elimination; special cases of linear systems

Geometry: angles; polygons; the Pythagorean Theorem; distance and midpoint formulas; congruence and similarity; translation, reflection, rotation, and dilation transformations

Perimeter, area, and volume: perimeter and circumference; areas of quadrilaterals, triangles, circles, and composite regions; ratios of lengths and areas of similar regions; surface areas and volumes of prisms, cylinders, pyramids, cones, spheres, and composite solids

Statistics and probability: measures of central tendency and variation; representing data; distribution tables; scatterplots and trend lines; two-way tables; probabilities of simple and compound events

Algebra 1

Expressions: review of real numbers, number lines, absolute value, arithmetic operations of integers and rational numbers, exponents, using variables, algebraic expressions, and formulas, and order of operations

Solving equations: writing and solving linear equations, solving literal equations and proportions; real-world applications involving similar figures, percentages, money, motion, and mixtures

Solving inequalities: linear inequalities, including conjunctions and disjunctions; absolute-value equations and inequalities

Functions: representing relationships between data, using graphs, equations, and tables; direct and inverse variations; arithmetic sequences; 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

Linear Systems: solving systems graphically, by substitution, and by elimination; applications of systems, graphing linear inequalities and systems of inequalities

Exponents: products, quotients, and powers of exponential expressions; scientific notation; graphing exponential functions; exponential growth and decay; geometric sequences

Polynomial Operations: classification, evaluation, operations, special patterns

Factoring Polynomials: 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 and functions: 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 (Each chapter includes a feature on sequences and graphing calculator tips.)

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