# 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