testGEAR for Math

Scope and Sequence

Module Name

Section Name



Fractions and Mixed Numbers

fractions, mixed numbers, equivalent fractions, multiply fractions, divide fractions, add fractiona, subtract fractions, numerator, denominator, improper fraction, complex fraction, cross product, equivalent fraction

Equivalent Fractions

Multiply and Divide Fractions

Add and Subtract Fractions

Fractions Comparison

Compare Fractions with the Same Denominator or Numerator

compare fractions, same denominator or numerator, different denominator or numerator, convert fractions

Compare Fractions with Different Numerators and Denominators

Convert to Equivalent Fractions

Ratios and Proportions


ratios, ratio variations, proportions, conversion, units

Ratio Variations


Conversion of Units


Multiply and Divide by Powers of 10

multiply, divide, powers of 10, conversion, decimals, fractions, arithmetic, scientific notation, decimal points, divisor, dividend, quotient

Convert Between Decimals and Fractions

Perform Arithmetic with Decimals

Scientific Notation


What's a Percent?

percent, conversion, decimals, fractions, equivalents, calculate interest, calculate discount, find percent

Change from Decimals to Percents or Fractions

Identify Equivalents

Use Percent to Calculate Interest

Use Percent to Calculate Discount

Find Percent of a Given Quantity

Algebra and Signed Numbers


transitivity, add same number, subtract same number, multiply by same number, divide by same number, commutativity, signed numbers, algebraic sums, multiply signed numbers, divide signed numbers, associative properties, distributive properties, order of o

Add or Subtract the Same Number in Equations

Multiply or Divide by the Same Number in Equations


Signed Numbers

Algebraic Sums of Signed Numbers

Multiply or Divide Signed Numbers

Associative and Distributive Properties

Order of Operations

Algebraic Expressions

Add and Subtract Algebraic Expressions

add algebraic expressions, subtract algebraic expressions, multiply algebraic expressions, divide algebraic expressions, substitution, coefficients, variables, fraction, numerator, denominator

Add Expressions That Are Fractions

Multiply Algebraic Expressions

Divide Algebraic Expressions

Use Substitution to Solve Algebraic Expressions


Find Common Factors

common factors, factor differences, two squares, factor trinomials, binomials, factor expressions, perfect square, FOIL, firsts, outers, inners, lasts

Factor Differences of Two Squares

Factor Trinomials into Binomials

Factor an Expression Completely


Solve Equations by Substitution

solve equations, substitution, linear equations, one unknown, quadratic equations, multiple unknowns, solutions to solve equations, use a formula, determinant

Solve Linear Equations With One Unknown

Solve Quadratic Equations

Solve Equations With More Than One Unknown

Use a Solution of One Equation to Solve Another

General Quadratic Equations Using a Formula

Rate, Work, and Mixture Problems

Distance Problems

distance problems, work problems, alternative methods, mixture problems, rate, distance, time, volume

Work Problems

Work Problems--An Alternative Method

Mixture Problems


Add or Subtract Quantities to Inequalities

add quantities to inequalities, subtract quantities from inequalities, multiply an inequality, divide an inequality, find products in inequalities, linear inequalities, one unknown, higher order inequalities, compare fractions, greater than, less than, eq

Multiply or Divide an Inequality

Find the Product of Two Numbers or Expressions in Inequalities

Solve Linear Inequalities in One Unknown

Solve Higher Order Inequalities in One Unknown

Use Inequalities to Compare Fractions

Exponents and Roots


exponents, roots, evaluate expressions, power zero, base number, square root, cube, cube root


Evaluate Expressions Involving Exponents

Coordinate Geometry

Number Lines

number lines, definitions, distances, points, midpoint, line segment, plot graphs, y-intercept, x-intercept, slope, coordinate plane, x-axis, y-axis, ordered pair


Distance Between Two Points

Determine the Midpoint of a Line Segment

Plot the Graph of a Line

The Y-Intercept

The X-Intercept

Find the Slope

Plane Geometry

Plane Geometry—Basic Concepts

plane geometry, angles, complimentary angles, supplementary angles, vertical angles, parallel lines, point, line, line segment, plane


Complimentary and Supplementary Angles

Vertical Angles

Parallel Lines


Triangle Basics

triangles, perpendicular bisectors, equilateral triangles, altitude, area of triangles, perimeter of triangles, area of right triangles, perimeter of right triangles, area of equilateral triangles, perimeter of equilateral triangles, right triangles

Perpendicular Bisectors

Equilateral Triangles


Area and Perimeter of Triangles

Area and Perimeter of Right Triangles

Area and Perimeter of Equilateral Triangles

Figures with Four Sides or More


parallelograms, rectangles, rhombus, squares, trapezoids, regular polygons, irregular polygons, other shapes, quadrilateral, right angle, vertex angle,





Regular and Irregular Polygons and Other Shapes

3-D Figures

Rectangular Solids

rectangular solids, cubes, cylinders, rectangular prism




Tangents to a Circle

tangents, circles, central angles, inscribed angles, tangents, area of a circle, circumference of a circle, radius, diameter, cord, line, ray, line segment, intercepted arc, vertex

Central Angles

Inscribed Angles

Two Tangents to a Circle

Area and Circumference of a Circle



averages, medians, modes, histograms, percentiles, quartiles, range, standard deviation, variance




Percentiles, Quartiles, and Range

Standard Deviation and Variance

Numbers and Integers


numbers, sum of two integers, product of two integers, divisibility, absolute values

Sum and Product of Two Integers


Absolute Values


Round Off

rounding, approximate sums, approximate products, approximate square roots

Approximate Sums

Approximate Products

Approximate Square Roots

Permutations, Combinations, and Probability

Permutations and Combinations

permutations, combinations, probability



Tables and Charts

tables, charts, graphs, bar graphs, circle graphs, line graphs, scale


Bar Graphs

Circle Graphs

Line Graphs


Statements, Negations, and Compound Sentences

statements, negations, compound sentences, language of logic, truth values, venn diagrams, conjunction, disjunction, conditional statement, biconditional statement, converse, inverse, contrapositive

The Language of Logic

Truth Values

Venn Diagrams


Measurement Instruments and Techniques

measurement instruments, measurement techniques, measurement problems, metric systems, formulas, area, volume

Measurement Problems


Angles and Trigonometric Functions

angles, trigonometric functions, trigonometric identities, trigonometric formulas, periodicity of trigonometric functions, sides,vertex, initial side, terminal side, acute, obtuse, reflex, right, straight, round, sine, cosine, tangent, cotangent, secant,

Trigonometric Identities and Formulas

Periodicity of Trigonometric Functions

Data Presentation


graphs, diagrams, tables



Find a Reasonable Solution

Determine the Reasonableness of a Solution

reasonableness of solutions, evaluate predictions, evaluate conclusions, numerical information, graphical information

Evaluate Predictions or Conclusions Based on Numerical or Graphical Information

Visualize Equations

Graph Equations

graph equations


Loci Basics

loci, intersections of loci, locus problems, coordinate geometry

Find Intersections of Loci

Solve Locus Problems in Coordinate Geometry

Special Graphs

Box-and-Whisker and Stem-and-Leaf Plots

box-and-whisker plots, stem-and-leaf plots, median, upper quartile, lower quartile, extreme values

Transformation Geometry

Translation and Reflection

translation, reflection, dilation, rotation

Dilation and Rotation

More 3-D Figures


prisms, pyramids, cones, spheres, bases, sides, lateral faces, edge, vertex, surface area, net, radius, diameter




Chances Are: More Probability

A Closer Look at Probablity

probability, replacement, compound events, charts, tree diagrams

Effect of Replacement

Compound Events

Number Patterns

Recognize Famous Patterns

famous patterns, pattern problems, Fibonacci, Mersenne, matrix

Solve Pattern Problems

Getting Into Shape

The Language of Geometry

language of geometry, congruence, similarity, reflection, rotation, translation, dialation

Congruence and Similarity

Systems of Linear Equations

Solve Systems of Linear Equations Algebraically

linear equations, algebraic solutions, graphic solutions, slope-intercept

Solve Systems of Linear Equations Graphically

Systems of Nonlinear Equations

Solve a Line-Parabola System Algebraically

line-parabola systems, line-circle systems, algebraic solutions, graphic solutions

Solve a Line-Parabola System Graphically

Solve a Line-Circle System Algebraically

Solve a Line-Circle System Graphically

Systems of Inequalities

Solve Systems of Inequalities Algebraically

inequalities, algebraic solutions, graphic solutions

Solve Systems of Inequalities Graphically

Solve Word Problems Using Equations

Set Up the Equation

set up equations, use linear equations, use quadratic equations, variable, factoring, binomial

Use Linear Equations

Use Quadratic Equations

Find Hidden Conditions

Extract the Formula

formula, givens, simultaneous

Find the Given

Fractions in Equations

Solve Equations Containing Fractional Coefficients

fractional coefficients, fractional equations

Solve Fractional Equations

Solve Graph Problems

Study the Graph's Shape

shapes of graphs, slope, x-intercept, y-intercept, real solutions, max, min

Look at the Slope

Examine the X- and Y- Intercepts

Search for the Real Solutions

Determine Max or Min


Bases and Powers

bases, powers, base number, exponent


Addition and Subtraction

addition, subtraction, scalar multiplication, matrix

Scalar Multiplication

Discrete Mathematics

Concepts in Discrete Mathematics

discrete mathematics, sets, induction, iteration, recurrence, mathematical models


Induction, Iteration, and Recurrence

Make Mathematical Models


Time for a Change

change, form, function, rate of change, continuous, limit, distribution, deviation, linear

A Matter of Proportion

Change a Dimension

change dimensions, change variables, two dimensional, three dimensional

Change a Variable


Understand Scatterplot Data

scatterplot data, ordered pairs, positive correlation, negative correlation, line of best fit

Use and Misuse of Statistics

Numbers Can Lie

decisions based on data

Make Decisions Based on Data

Get Rid of Pesky Numbers

Cancel Out Numbers or Expressions

cancel numbers, factor, add, subtract, multiply divide, common denominator, common numerator, reduce terms

Math Speak

Translate Words into Math

translate word problems, mathematical notation

Use the Known to Find the Unknown

Use What You Know

geometry, area, distance, angles, unknowns, knowns

Pick a Number, Any Number

Plug in a Number

substitute whole numbers, variables, integers, average formula

Keep Your Units Straight

Set Up or Verify with Units

work with same units, manipulate units to match, verify units, variables

Simply Simplify

Simplify to Avoid Tedious Calculations

simplify expressions, avoid long calculations, easier ways, multiply, add, divide, subtract

Become an Artist

Add Labels and Draw on Diagrams

draw lines in diagrams, label unknown quantities

And Then There Was One

Eliminate Choices

eliminate answers

Use the Best, Leave the Rest

Recognize Relevant Information

use known information, use relevant information

Test-Taking Tips and Tricks

Don't Panic

don't panic, focus, time, take notes, process of elimination, deep breathing, visualization, counting, affirmation, box, circle, underline

Use Your Time Wisely

Own Your Exam

Use the Process of Elimination

Know Yourself

Are You a Tortoise or a Hare?

pace, speed, use strengths, sort questions, classify questions, easy questions first, focus, relax, accuracy,

Use Your Strengths

Know Your Test History

Master Math Questions

Round Off and Guesstimate

round, guesstimate, simplify numbers, simplify calculations, only necessary calculator use, make notes, show work, graphs, diagrams, check answers

Use Your Calculator Sparingly

Show Your Work

Check Backwards

What’s Up, Doc?

Define Your Variables

define variables, rewrite questions, translate word problems

Morph When Necessary

Change to Equivalent Forms

appropriate expressions, simplify expressions, equivalent forms

It’s The Words that Count

Check Your Answers, Not Your Equations

check answers, use equations, translate word problems

Be Fair

Distribute All The Way Through

distributive property, multiplication, addition, rewrite expressions, simplify expressions

Get the Point

Plot Clear Points

graph, visual picture, draw neatly, draw clearly, small points, end points, line segments, range, solution, upper bounds, lower bounds,

Check End Points

Look At It Another Way

Interpret Different Views of an Object

visualize problem, top view, side view, front view, perspective, 2-dimensional, 3-dimensional, length, height, keywords, sketch, missing blocks

Break It Up

Divide Weird Shapes into Familiar Shapes

simple figure, complex figure, 3-dimensional, composite figure, area, volume