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Pre-AlgebraThis course covers the topics shown below.Students navigate learning paths based on their level of readiness.Inst itut ional users may customize the scope and sequence to meet curricular needs.

Curriculum (634 topics + 583 addit ional topics)

Whole Numbers and Integers (95 topics)

Place Value and Numeral Translat ion (1 topics)Whole number place value: Problem type 1

Addit ion and Subtract ion with Whole Numbers (13 topics)Adding 2-digit numbers with regrouping a hundredAdding 3 or 4 numbers with two-digits with regroupingAdding 3-digit numbers with regroupingAdding 3 numbers with two, three, and four-digitsSubtract ion involving 3-digit numbers without regroupingSubtract ion of 2-digit numbers with regroupingSubtract ion with mult iple regrouping steps involving 3-digit numbersSubtract ion with mult iple regrouping steps involving 4-digit numbersSubtract ion and regrouping with zerosWord problem with addit ion or subtract ion of whole numbersDescribing an increasing or decreasing pattern f rom a table of valuesPerimeter of a polygonPerimeter of a square or a rectangle

Mult iplicat ion and Division with Whole Numbers (21 topics)Mult iplicat ion as repeated addit ionMult iplying 2-digit and 1-digit numbers with regrouping: Problem type 2Mult iplying mult i-digit and 1-digit numbers with regroupingArea of a rectangle on a gridArea of a rectangle with one-digit side lengthsArea of a rectangle with two-digit by one-digit side lengthsIntroduct ion to mult iplicat ion of large numbersMult iplicat ion of large numbersMult iples: Problem type 1Mult iples: Problem type 2Division of whole numbers given in f ract ional formDivision involving zeroDivision with regrouping: 1-digit divisor, 2-digit dividendQuotient with remainder: 1-digit divisor, 2-digit dividendWhole number division: 2-digit by 2-digit , no remainderWord problem with mult iplicat ion or division of whole numbersWord problem with mult iplicat ion and addit ion or subtract ion of whole numbersWord problem on unit rates associated with rat ios of whole numbers: Whole number answersDivision with regrouping: 1-digit divisor, 3-digit or 4-digit dividendWhole number division: 3-digit by 2-digit , no remainderDivision with no remainder and a two-digit divisor: Problem type 2

Ordering and Est imation (5 topics)Introduct ion to inequalit iesOrdering large numbersRounding to tens or hundredsRounding to hundreds or thousandsEst imating a product

Exponents and Order of Operat ions (7 topics)Writ ing expressions using exponentsIntroduct ion to exponentsPower of 10: Posit ive exponentIntroduct ion to parenthesesIntroduct ion to order of operat ionsOrder of operat ions with whole numbersOrder of operat ions with whole numbers and exponents: Basic

Prime Numbers, Factors, and Mult iples (5 topics)Even and odd numbersFactors

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Greatest common factor of 2 numbersLeast common mult iple of 2 numbersLeast common mult iple of 3 numbers

Plott ing and Comparing Integers (7 topics)Plott ing integers on a number linePlott ing opposite integers on a number lineOrdering integersUsing a number line to compare integersWrit ing a signed number for a real-world situat ionFinding opposites of integersAbsolute value of a number

Addit ion and Subtract ion with Integers (12 topics)Integer addit ion: Problem type 1Integer addit ion: Problem type 2Identifying a sum as a point located a given distance f rom another pointIdentifying relat ive change when combining two quantit iesInteger subtract ion: Problem type 1Integer subtract ion: Problem type 2Integer subtract ion: Problem type 3Addit ion and subtract ion with 3 integersWord problem with addit ion or subtract ion of integersOperat ions with absolute value: Problem type 1Computing the distance between two integers on a number lineComputing and understanding distances between integers on a number line

Mult iplicat ion and Division with Integers (5 topics)Integer mult iplicat ion and divisionMult iplicat ion of 3 or 4 integersWord problem with mult iplicat ion or division of integersExponents and integers: Problem type 1Order of operat ions with integers

Evaluat ing and Writ ing Expressions (10 topics)Evaluat ing an algebraic expression: Whole number addit ion or subtract ionEvaluat ing an algebraic expression: Whole number mult iplicat ion or divisionEvaluat ing an algebraic expression: Whole numbers with two operat ionsEvaluat ing a formulaEvaluat ing an algebraic expression: Whole numbers with one operat ion and an exponentEvaluat ing a linear expression: Integer mult iplicat ion with addit ion or subtract ionEvaluat ing a quadrat ic expression: IntegersWrit ing a one-step expression for a real-world situat ionTranslat ing a phrase into a one-step expressionTranslat ing a phrase into a two-step expression

One-Step Equations (9 topics)Identifying solut ions to a one-step linear equation: Problem type 1Identifying solut ions to a one-step linear equation: Problem type 2Addit ive property of equality with whole numbersAddit ive property of equality with integersIntroduct ion to solving an equation with mult iplicat ion or divisionWrit ing an equation and solving a mult iplicat ive comparison word problemMult iplicat ive property of equality with whole numbersMult iplicat ive property of equality with integersTranslat ing a sentence into a one-step equation

Fract ions (51 topics)

Equivalent Fract ions (8 topics)Introduct ion to non-unit f ract ionsConversions involving division in f ract ional form and whole numbersIntroduct ion to finding equivalent f ract ions: Mult iplyingIntroduct ion to finding equivalent f ract ions: DividingEquivalent f ract ionsIntroduct ion to simplifying a f ract ionSimplifying a f ract ionIdentifying equivalent signed f ract ions

Plott ing and Ordering Fract ions (3 topics)Plott ing f ract ions using a number lineComparing f ract ions with the same denominatorComparing f ract ions by finding a common denominator

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Mixed Numbers and Improper Fract ions (2 topics)Writ ing an improper f ract ion as a mixed numberWrit ing a mixed number as an improper f ract ion

Addit ion and Subtract ion with Fract ions (10 topics)Addit ion or subtract ion of f ract ions with the same denominatorAddit ion or subtract ion of f ract ions with the same denominator and simplificat ionWord problem involving addit ion or subtract ion of f ract ions with the same denominatorFinding the LCD of two f ract ionsWrit ing unit f ract ions with a common denominator to add or subtractWrit ing f ract ions with a common denominator to add or subtractAddit ion or subtract ion of f ract ions with different denominatorsSigned f ract ion addit ion or subtract ion: BasicSigned f ract ion subtract ion involving double negationWord problem involving addit ion or subtract ion of f ract ions with different denominators

Mult iplicat ion and Division with Fract ions (15 topics)Product of a unit f ract ion and a whole numberProduct of a f ract ion and a whole number: Problem type 1Product of a f ract ion and a whole number: Problem type 2Word problem involving mult iplying a f ract ion and a whole numberIntroduct ion to f ract ion mult iplicat ionFract ion mult iplicat ionMult iplicat ion of 3 f ract ionsSigned f ract ion mult iplicat ion: BasicWord problem involving f ract ions and mult iplicat ionThe reciprocal of a numberDivision involving a whole number and a unit f ract ionDivision involving a whole number and a f ract ionFract ion divisionSigned f ract ion divisionWord problem involving f ract ions and division

Mult iplicat ion and Division with Mixed Numbers (7 topics)Mult iplying mixed numbers: Problem type 1Mult iplying mixed numbers: Problem type 2Mult iplying a mixed number and a whole number: Problem type 1Mult iplying a mixed number and a whole number: Problem type 2Division with a mixed number and a whole numberMixed number divisionWord problem involving mult iplicat ion or division with mixed numbers

Exponents and Order of Operat ions (2 topics)Exponents and f ract ionsEvaluat ing expressions with exponents of zero

Expressions and One-Step Equations (4 topics)Addit ive property of equality with signed f ract ionsMult iplicat ive property of equality with whole numbers: Fract ional answersMult iplicat ive property of equality with f ract ionsMult iplicat ive property of equality with signed f ract ions

Decimals (53 topics)

Place Value and Ordering (5 topics)Decimal place value: Tenths and hundredthsReading decimal posit ion on a number line: TenthsReading decimal posit ion on a number line: HundredthsIntroduct ion to ordering decimalsOrdering decimals

Convert ing Decimals to Fract ions (5 topics)Convert ing a decimal to a proper f ract ion without simplifying: BasicConvert ing a decimal to a proper f ract ion in simplest form: BasicConvert ing a decimal to a proper f ract ion in simplest form: AdvancedConvert ing a decimal to a mixed number and an improper f ract ion without simplifyingConvert ing a decimal to a mixed number and an improper f ract ion in simplest form: Basic

Addit ion and Subtract ion (11 topics)Addit ion of decimals: Vert ically alignedDecimal addit ion with 2 numbersDecimal addit ion with 3 numbersSubtract ion of aligned decimalsDecimal subtract ion: Basic

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Decimal subtract ion: AdvancedRounding decimalsSigned decimal addit ion and subtract ionWord problem with addit ion or subtract ion of 2 decimalsWord problem with addit ion of 3 or 4 decimals and whole numbersWord problem with subtract ion of a whole number and a decimal: Regrouping with zeros

Mult iplicat ion (9 topics)Mult iplicat ion of a decimal by a power of tenMult iplying a decimal less than 1 by a whole numberMult iplying a decimal by a whole numberMult iplying decimals less than 1: Problem type 1Decimal mult iplicat ion: Problem type 1Mult iplicat ion of a decimal by a power of 0.1Signed decimal mult iplicat ionWord problem with mult iplicat ion of a decimal and a whole numberWord problem with mult iple decimal operat ions: Problem type 1

Division (6 topics)Division of a decimal by a power of tenWhole number division with decimal answersDivision of a decimal by a whole numberDivision of a decimal by a 1-digit decimal: Problem type 1Division of a decimal by a 2-digit decimalWord problem with division of a decimal and a whole number

Convert ing Fract ions to Decimals (10 topics)Convert ing a f ract ion with a denominator of 10 or 100 to a decimalConvert ing a proper f ract ion with a denominator of 2, 4, or 5 to a decimalConvert ing a mixed number with a denominator of 2, 4, or 5 to a decimalConvert ing a f ract ion to a terminat ing decimal: BasicConvert ing a f ract ion to a terminat ing decimal: AdvancedConvert ing a f ract ion to a repeating decimal: BasicConvert ing a f ract ion to a repeating decimal: AdvancedUsing a calculator to convert a f ract ion to a rounded decimalConvert ing a mixed number to a terminat ing decimal: BasicOrdering f ract ions and decimals

Venn Diagrams and Sets of Rat ional Numbers (5 topics)Identifying numbers as integers or non-integersIdentifying rat ional decimal numbersInterpret ing a Venn diagram of 2 setsConstruct ing a Venn diagram to classify rat ional numbersConstruct ing a Venn diagram to describe relat ionships between sets of rat ional numbers

Expressions and One-Step Equations (2 topics)Addit ive property of equality with decimalsMult iplicat ive property of equality with decimals

Ratios, Proport ions, and Measurement (35 topics)

Rat ios and Unit Rates (11 topics)Simplifying a rat io of whole numbers: Problem type 1Finding a unit priceUsing tables to compare rat iosComputing unit prices to find the better buyWord problem on unit rates associated with rat ios of whole numbers: Decimal answersWord problem on unit rates associated with rat ios of f ract ionsWord problem on unit rates associated with rat ios of mixed numbersSolving a word problem on proport ions using a unit rateSolving a one-step word problem using the formula d = rtFinding missing values in a table of equivalent rat iosUsing a table of equivalent rat ios to find a missing quantity in a rat io

Proport ions (3 topics)Solving a proport ion of the form x/a=b/c: BasicSolving a proport ion of the form x/a = b/cWord problem on proport ions: Problem type 1

Similar Figures (7 topics)Identifying congruent shapes on a gridIdentifying similar or congruent shapes on a gridFinding a missing side length given two similar trianglesRelat ionships about rat ios within and between similar triangles

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Similar polygonsSimilar right trianglesIndirect measurement

Scale Factors and Scale Drawings (4 topics)Finding lengths using scale modelsFinding a scale factor: Same unitsUsing a scale drawing to find actual areaReproducing a scale drawing at a different scale

U.S. Customary Units of Measurement (4 topics)Choosing U.S. Customary measurement unitsU.S. Customary length conversion with whole number valuesU.S. Customary volume conversion with whole number valuesU.S. Customary weight conversions with whole number values

Metric Units of Measurement (3 topics)Choosing metric measurement unitsMetric distance conversion with whole number valuesMetric distance conversion with decimal values

Time and Temperature (1 topics)Time unit conversion with whole number values

Convert ing Between Systems and Dimensional Analysis (2 topics)Convert ing between metric and U.S. Customary unit systemsU.S. Customary length conversions involving dimensional analysis

Percents (33 topics)

Understanding Percents (2 topics)Convert ing a f ract ion with a denominator of 100 to a percentageConvert ing a percentage to a f ract ion with a denominator of 100

Percents, Decimals, and Fract ions (11 topics)Introduct ion to convert ing a percentage to a decimalIntroduct ion to convert ing a decimal to a percentageConvert ing between percentages and decimalsConvert ing a f ract ion to a percentage: Denominator of 4, 5, or 10Finding benchmark f ract ions and percentages for a figureConvert ing a f ract ion to a percentage: Denominator of 20, 25, or 50Using a calculator to convert a f ract ion to a rounded percentageConvert ing a f ract ion to a percentage in a real-world situat ionWrit ing a rat io as a percentageWrit ing a rat io as a percentage without a calculatorFinding the rate of a tax or commission

Percent of a Number (7 topics)Finding a percentage of a whole numberFinding a percentage of a whole number without a calculator: BasicFinding a percentage of a whole number without a calculator: AdvancedFinding a percentage of a total amount: Real-world situat ionsFinding a percentage of a total amount without a calculator: Sales tax, commission, discountEst imating a t ip without a calculatorFinding a percentage of a total amount in a circle graph

Percent Equations (2 topics)Applying the percent equation: Problem type 1Finding the total amount given the percentage of a part ial amount

Percent Increase and Decrease (7 topics)Finding the mult iplier to give a final amount af ter a percentage increase or decreaseFinding the final amount given the original amount and a percentage increase or decreaseFinding the sale price given the original price and percent discountFinding the sale price without a calculator given the original price and percent discountFinding the total cost including tax or markupFinding the percentage increase or decrease: BasicFinding the percentage increase or decrease: Advanced

Interest (3 topics)Finding simple interest without a calculatorFinding the interest and future value of a simple interest loan or investmentFinding the principal, rate, or t ime of a simple interest loan or investment

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Personal Financial Literacy (1 topics)Computing percentages for categories of a budget

Equations and Inequalit ies (59 topics)

The Distribut ive Property (8 topics)Introduct ion to the distribut ive propertyIntroduct ion to factoring with numbersFactoring a sum or difference of whole numbersMult iplying a constant and a linear monomialDistribut ive property: Whole number coefficientsDistribut ive property: Integer coefficientsDistribut ive property: Fract ional coefficientsFactoring a linear binomial

Simplifying Algebraic Expressions (7 topics)Introduct ion to propert ies of addit ionCombining like terms: Whole number coefficientsIntroduct ion to propert ies of mult iplicat ionCombining like terms: Integer coefficientsCombining like terms: Decimal coefficientsUsing distribut ion and combining like terms to simplify: UnivariateIdentifying propert ies used to simplify an algebraic expression

Mult i-Step Equations (9 topics)Identifying solut ions to a linear equation in one variable: Two-step equationsUsing two steps to solve an equation with whole numbersAddit ive property of equality with a negative coefficientSolving a two-step equation with integersIntroduct ion to solving an equation with parenthesesSolving a two-step equation with signed decimalsIdentifying propert ies used to solve a linear equationIntroduct ion to solving an equation with variables on the same sideSolving a linear equation with several occurrences of the variable: Variables on the same side

Equations with Variables on Both Sides (5 topics)Introduct ion to solving a linear equation with a variable on each sideSolving a linear equation with several occurrences of the variable: Variables on both sidesSolving a linear equation with several occurrences of the variable: Variables on the same side and distribut ionSolving a linear equation with several occurrences of the variable: Variables on both sides and distribut ionSolving equations with zero, one, or infinitely many solut ions

Solving Formulas for a Variable (2 topics)Solving for a variable in terms of other variables using addit ion or subtract ion: BasicSolving for a variable in terms of other variables using mult iplicat ion or division: Basic

Applicat ions of Equations (9 topics)Solving a f ract ion word problem using a linear equation of the form Ax = BTranslat ing a sentence into a mult i-step equationWrit ing an equation of the form Ax + B = C to solve a word problemComparing arithmetic and algebraic solut ions to a word problemSolving a decimal word problem using a linear equation of the form Ax + B = CWrit ing an equation of the form A(x + B) = C to solve a word problemSolving a word problem with two unknowns using a linear equationWrit ing an equation to represent a real-world problem: Variable on both sidesSolving a decimal word problem using a linear equation with the variable on both sides

Writ ing and Graphing Inequalit ies (5 topics)Translat ing a sentence by using an inequality symbolTranslat ing a sentence into a one-step inequalityIntroduct ion to identifying solut ions to an inequalityWrit ing an inequality for a real-world situat ionGraphing a linear inequality on the number line

One-Step Inequalit ies (5 topics)Identifying solut ions to a one-step linear inequalityAddit ive property of inequality with whole numbersAddit ive property of inequality with integersMult iplicat ive property of inequality with whole numbersMult iplicat ive property of inequality with integers

Mult i-Step Inequalit ies (4 topics)Identifying solut ions to a two-step linear inequality in one variableSolving a two-step linear inequality with whole numbers

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Solving a two-step linear inequality: Problem type 1Solving a two-step linear inequality: Problem type 2

Applicat ions of Inequalit ies (5 topics)Solving a word problem using a one-step linear inequalityTranslat ing a sentence into a mult i-step inequalitySolving a word problem using a two-step linear inequality and describing the solut ionSolving a word problem using a two-step linear inequalitySolving a decimal word problem using a two-step linear inequality

Graphs, Funct ions, and Sequences (81 topics)

Ordered Pairs (6 topics)Reading a point in quadrant 1Plott ing a point in quadrant 1Reading a point in the coordinate planePlott ing a point in the coordinate planeFinding distances between points that share a common coordinate given the graphFinding distances between points that share a common coordinate given their coordinates

Tables and Graphs of Lines (18 topics)Funct ion tables with two-step rulesTable for a linear equationWrit ing a funct ion rule given a table of ordered pairs: One-step rulesWrit ing a funct ion rule given a table of ordered pairs: Two-step rulesIdentifying solut ions to a linear equation in two variablesFinding a solut ion to a linear equation in two variablesGraphing a line in quadrant 1Graphing a linear equation of the form y = mxGraphing a line given its equation in slope-intercept form: Integer slopeGraphing a line given its equation in slope-intercept form: Fract ional slopeGraphing a line given its equation in standard formGraphing a vert ical or horizontal lineFinding x- and y-intercepts given the graph of a line on a gridFinding x- and y-intercepts of a line given the equation: BasicGraphing a line given its x- and y-interceptsGraphing a line by first finding its x- and y-interceptsIdentifying parallel and perpendicular linesInterpret ing a line graph

Proport ional Relat ionships (9 topics)Making a table and plott ing points given a unit rateWrit ing an equation to represent a proport ional relat ionshipIdentifying proport ional relat ionships in equationsIdentifying proport ional relat ionships in tables by calculat ing unit rates: Whole numbersIdentifying proport ional relat ionships in tables by calculat ing unit rates: Fract ionsIdentifying proport ional relat ionships in graphs: BasicIdentifying proport ional relat ionships in graphs: AdvancedFinding outputs and rate of increase given the graph of a line that models a real-world situat ionComparing proport ional relat ionships given in different forms

Slope (6 topics)Finding slope given the graph of a line in quadrant 1 that models a real-world situat ionFinding slope given the graph of a line on a gridFinding slope given two points on the lineFinding the slope of horizontal and vert ical linesUsing right triangles to find the slope of a lineGraphing a line given its slope and y-intercept

Direct and Inverse Variat ion (4 topics)Identifying direct variat ion f rom ordered pairs and writ ing equationsWrit ing a direct variat ion equationWord problem on direct variat ionInterpret ing direct variat ion f rom a graph

Equations of Lines (9 topics)Identifying linear equations: BasicFinding the slope and y-intercept of a line given its equation in the form y = mx + bFinding the slope and y-intercept of a line given its equation in the form Ax + By = CWrit ing an equation of a line given its slope and y-interceptWrit ing an equation in slope-intercept form given the slope and a pointFinding the slope and a point on a line given its equation in point-slope formWrit ing an equation in point-slope form given the slope and a pointWrit ing an equation of a line given the y-intercept and another point

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Writ ing the equation of the line through two given points

Applicat ions (10 topics)Finding outputs of a one-step funct ion that models a real-world situat ion: Two variable equationFinding outputs of a two-step funct ion with decimals that models a real-world situat ion: Two variable equationWrit ing and evaluat ing a funct ion that models a real-world situat ion: BasicWrit ing and evaluat ing a funct ion that models a real-world situat ion: AdvancedWrit ing an equation and drawing its graph to model a real-world situat ion: BasicWrit ing an equation and drawing its graph to model a real-world situat ion: AdvancedFinding the intercepts and rate of change given a graph of a linear funct ionFinding the init ial amount and rate of change given a table for a linear funct ionComparing propert ies of linear funct ions given in different formsInterpret ing the parameters of a linear funct ion that models a real-world situat ion

Introduct ion to Funct ions (4 topics)Identifying funct ions f rom relat ionsVert ical line testDomain and range f rom ordered pairsTable for a linear funct ion

Graphs of Funct ions (3 topics)Finding where a funct ion is increasing, decreasing, or constant given the graphChoosing a graph to fit a narrat ive: BasicChoosing a graph to fit a narrat ive: Advanced

Systems of Equations (12 topics)Identifying solut ions to a system of linear equationsIdentifying the solut ion of systems of linear equations f rom graphsGraphically solving a system of linear equations both of the form y=mx+bGraphically solving a system of linear equationsIntroduct ion to using subst itut ion to solve a linear equationSolving a system of linear equations of the form y = mx + bSolving a system of linear equations using subst itut ionSolving a system of linear equations using eliminat ion with addit ionSolving systems of linear equations with 0, 1, or infinitely many solut ionsInterpret ing the graphs of two funct ionsSolving a word problem involving a sum and another basic relat ionship using a system of linear equationsSolving a word problem using a system of linear equations of the form y = mx + b

Exponents, Polynomials, and Radicals (59 topics)

Product, Power, and Quotient Rules (10 topics)Introduct ion to the product rule with posit ive exponents: Whole number baseUnderstanding the product rule of exponentsIntroduct ion to the product rule of exponentsProduct rule with posit ive exponents: UnivariateIntroduct ion to the power of a power rule with posit ive exponents: Whole number baseUnderstanding the power rules of exponentsIntroduct ion to the power of a power rule of exponentsIntroduct ion to the power of a product rule of exponentsIntroduct ion to the quotient rule with posit ive exponents: Whole number baseIntroduct ion to the quotient rule of exponents

Negative Exponents (9 topics)Power of 10: Negative exponentEvaluat ing an expression with a negative exponent: Whole number baseEvaluat ing an expression with a negative exponent: Posit ive f ract ion baseEvaluat ing an expression with a negative exponent: Negative integer baseIntroduct ion to the product rule with negative exponents: Whole number baseIntroduct ion to the product rule with negative exponentsIntroduct ion to the quotient rule with negative exponents: Whole number baseQuotient rule with negative exponents: Problem type 1Introduct ion to the power of a power rule with negative exponents: Whole number base

Scient ific Notat ion (16 topics)Introduct ion to scient ific notat ion with posit ive exponentsScient ific notat ion with posit ive exponentIntroduct ion to scient ific notat ion with negative exponentsScient ific notat ion with negative exponentConvert ing between scient ific notat ion and standard form in a real-world situat ionEst imating numbers using scient ific notat ionChoosing metric units and convert ing to the base unit in scient ific notat ionExpressing calculator notat ion as scient ific notat ionMult iplying numbers writ ten in scient ific notat ion: Basic

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Mult iplying numbers writ ten in scient ific notat ion: AdvancedMult iplying numbers writ ten in decimal form or scient ific notat ion in a real-world situat ionDividing numbers writ ten in scient ific notat ion: BasicDividing numbers writ ten in scient ific notat ion: AdvancedFinding the scale factor between numbers given in scient ific notat ion in a real-world situat ionAdding or subtract ing numbers writ ten in scient ific notat ion: Same exponents, basicAdding or subtract ing numbers writ ten in scient ific notat ion: Different exponents

Square Roots and Irrat ional Numbers (14 topics)Square root of a perfect squareSquare root of a rat ional perfect squareSquare roots of perfect squares with signsUsing a calculator to approximate a square rootEst imating a square rootUsing numerical methods to approximate a square root to the nearest tenthUsing numerical methods to approximate a square root to the nearest hundredthApproximating the locat ion of irrat ional numbers on a number lineOrdering real numbersConvert ing a repeating decimal to a f ract ionIdentifying true statements about rat ional and irrat ional numbersIdentifying numbers as rat ional or irrat ionalConstruct ing a Venn diagram to classify real numbersConstruct ing a Venn diagram to describe relat ionships between sets of real numbers

Higher Roots and Nonlinear Equations (4 topics)Solving an equation of the form x2 = a using the square root propertyFinding side lengths of squares given an area and a perimeterCube root of an integerSolving an equation of the form x3 = a using integers

Applying the Pythagorean Theorem (6 topics)Introduct ion to the Pythagorean TheoremPythagorean TheoremWord problem involving the Pythagorean TheoremUsing the Pythagorean Theorem repeatedlyUsing the Pythagorean Theorem to find distance on a gridDistance between two points in the plane: Decimal answers

Lines, Angles, and Polygons (27 topics)

Classifying and Measuring Angles (3 topics)Acute, obtuse, and right anglesMeasuring an angle with the protractorDrawing an angle with the protractor

Angle Relat ionships (6 topics)Introduct ion to angle addit ionFinding an angle measure in a figure with a right or straight angleWrit ing and solving an equation involving complementary or supplementary anglesIdentifying supplementary and vert ical anglesFinding angle measures given two intersect ing linesSolving equations involving vert ical angles

Parallel Lines (4 topics)Identifying corresponding and alternate anglesFinding angle measures given two parallel lines cut by a transversalSolving equations involving angles and a pair of parallel linesEstablishing facts about the angles created when parallel lines are cut by a transversal

Classifying Triangles (1 topics)Acute, obtuse, and right triangles

Angles of Triangles (7 topics)Finding an angle measure of a triangle given two anglesFinding an angle measure for a triangle with an extended sideFinding an angle measure given extended trianglesFinding an angle measure given a triangle and parallel linesWrit ing an equation to find angle measures of a triangle given angles with variablesEstablishing facts about the interior angles of a triangleEstablishing facts about the interior and exterior angles of a triangle

Triangle Construct ions and Triangle Inequalit ies (6 topics)Creat ing triangles f rom given side lengths: Problem type 1Creat ing triangles f rom given side lengths: Problem type 2

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Using triangle inequality to determine if side lengths form a triangleDetermining if a triangle is possible based on given angle measuresDetermining if given measurements define a unique triangle, more than one triangle, or no triangleDrawing triangles with given condit ions: Angle measures

Transformations (35 topics)

Congruence and Similarity (3 topics)Identifying transformationsIdentifying and naming congruent parts of congruent trianglesFinding angle measures of a triangle given two angles of a similar triangle

Translat ions (6 topics)Translat ing a point and giving its coordinates: One stepTranslat ing a point and giving its coordinates: Two stepsPropert ies of translated figuresDetermining if figures are related by a translat ionTranslat ing a polygonWrit ing a rule to describe a translat ion

Reflections (11 topics)Reflect ing a point across an axisReflect ing a point across both coordinate axesReflecting a point across an axis and giving its coordinatesFinding the coordinates of a point reflected across an axisFinding the coordinates of a point reflected across both axesReflecting a polygon across the x-axis or y-axisPropert ies of reflected figuresDetermining if figures are related by a reflect ionFinding the coordinates of a point reflected across an axis and translatedWrit ing a rule to describe a reflect ionDrawing lines of symmetry

Rotat ions (9 topics)Finding an angle of rotat ionIdentifying rotat ional symmetry and angles of rotat ionRotat ing a point and giving its coordinatesPropert ies of rotated figuresDetermining if figures are related by a rotat ionRotat ing a figure about the originWrit ing a rule to describe a rotat ionDetermining if figures are congruent and related by a transformationDetermining if figures are congruent and related by a sequence of transformations

Dilat ions (6 topics)Dilat ing a segment and giving the coordinates of its endpointsThe effect of dilat ion on side lengthDetermining if figures are related by a dilat ionDilat ing a figureWrit ing a rule to describe a dilat ionDetermining if figures are similar and related by a sequence of transformations

Perimeter, Area, and Volume (50 topics)

Perimeter (1 topics)Finding the missing length in a figure

Area of Rectangles (3 topics)Dist inguishing between the area and perimeter of a rectangleWord problem involving the area of a rectangle: Problem type 2Finding side lengths of rectangles given one dimension and an area or a perimeter

Area of Parallelograms, Triangles, and Trapezoids (5 topics)Area of a parallelogramFinding the area of a right triangle on a gridArea of a triangleFinding the area of a trapezoid on a grid by using triangles and rectanglesArea of a trapezoid

Area of Composite Figures (6 topics)Finding the area of a composite figure on a gridIntroduct ion to area of a piecewise rectangular figureArea of a piecewise rectangular figureWord problem on finding the area of a piecewise rectangular figure

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Area between two rectanglesArea involving rectangles and triangles

The Converse and a Proof of the Pythagorean Theorem (3 topics)Identifying side lengths that give right trianglesDemonstrat ing the converse of the Pythagorean TheoremInformal proof of the Pythagorean Theorem

Circumference and Area of Circles (7 topics)Circumference of a circleFinding the radius or the diameter of a circle given its circumferenceArea of a circleCircumference and area of a circleDist inguishing between the area and circumference of a circleArea involving rectangles and circlesArea between two concentric circles

Three-Dimensional Figures (3 topics)Classifying solidsNets of solidsIdentifying horizontal and vert ical cross sect ions of solids

Volume of Prisms and Cylinders (10 topics)Volume of a rectangular prism made of unit cubesVolume of a rectangular prismWrit ing equivalent expressions for the volume of a rectangular prismFinding the side length of a cube given its volumeWord problem involving the volume of a rectangular prismVolume of a piecewise rectangular prismWord problem involving the volume of a piecewise rectangular prismVolume of a triangular prismVolume of a cylinderWord problem involving the volume of a cylinder

Volume of Pyramids, Cones, and Spheres (5 topics)Volume of a pyramidVolume of a coneWord problem involving the volume of a coneVolume of a sphereWord problem involving the volume of a sphere

Surface Area (7 topics)Surface area of a cube or a rectangular prismDist inguishing between surface area and volumeUsing a net to find the surface area of a rectangular prismWord problem involving the surface area of a rectangular prismSurface area of a triangular prismUsing a net to find the surface area of a triangular prismSurface area of a cylinder

Data Analysis and Probability (56 topics)

Collect ing Data (3 topics)Choosing an appropriate method for gathering data: Problem type 1Choosing an appropriate method for gathering data: Problem type 2Introduct ion to expectat ion

Frequency Tables (6 topics)Interpret ing a tally tableConstruct ing a f requency distribut ion for grouped dataConstruct ing a two-way f requency table: BasicConstruct ing a two-way f requency table: AdvancedComputing a percentage f rom a table of valuesMaking an inference using a two-way f requency table

Graphs of Data (6 topics)Construct ing a line plotConstruct ing a bar graph for non-numerical dataInterpret ing a bar graphInterpret ing a double bar graphConstruct ing a f requency distribut ion and a histogramConstruct ing a percent bar graph

Scatter Plots and Lines of Best Fit (6 topics)

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Construct ing a scatter plotSketching the line of best fitScatter plots and correlat ionPredict ions f rom the line of best fitClassifying linear and nonlinear relat ionships f rom scatter plotsIdentifying out liers and clustering in scatter plots

Mean, Median, and Mode (6 topics)Mean of a data setFinding the mean of a symmetric distribut ionFinding sample size and comparing samples for est imating the meanMean and median of a data setMode of a data setChoosing the best measure to describe data

Measures of Variat ion (8 topics)Range of a data setFinding the mode and range f rom a line plotFive-number summary and interquart ile rangeConstruct ing a box-and-whisker plotUsing box-and-whisker plots to compare data setsComparing sample meansComputing mean absolute deviat ion f rom a list of numerical valuesAssessing the degree of overlap of two distribut ions

Counting (2 topics)Interpret ing a tree diagramIntroduct ion to the counting principle

Probability of Simple Events (7 topics)Classifying likelihoodDetermining a sample space and outcomes for a simple eventIntroduct ion to the probability of an eventProbability involving one die or choosing f rom n dist inct objectsProbability involving choosing f rom objects that are not dist inctUnderstanding likelihoodExperimental and theoret ical probability

Probability of Compound Events (6 topics)Determining a sample space and outcomes for a compound eventOutcomes and event probabilityProbabilit ies involving two rolls of a dieIdentifying independent events given descript ions of experimentsProbability of independent eventsProbability of dependent events

Simulat ions (6 topics)Identifying outcomes in a random number table used to simulate a simple eventUsing a random number table to simulate a simple eventGenerat ing a random number table with technology to simulate a simple eventIdentifying outcomes in a random number table used to simulate a compound eventUsing a random number table to simulate a compound eventGenerat ing a random number table with technology to simulate a compound event

Other Topics Available(*) (583 addit ional topics)

Whole Numbers and Integers (50 topics)Whole number place value: Problem type 2Comparing place values of digits in a whole number: Problem type 1Numeral t ranslat ion: Problem type 1Numeral t ranslat ion: Problem type 2Expanded form: 2 and 3-digit numbersExpanded form: 4 and 5-digit numbersExpanded form with zerosPerimeter of a rectangle on a gridUnderstanding mult iplicat ion of a one-digit number with a larger numberIntroduct ion to mult iplicat ion using an area modelMult iplying a mult i-digit and a 1-digit number using an area modelWrit ing a division sentence for equal groupsWrit ing a division sentence for equal groups and a remainderQuotient with remainder: 1-digit divisor, 3-digit or 4-digit dividendDivision involving quotients with intermediate zeros: Problem type 1Division involving quotients with intermediate zeros: Problem type 2

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Division with remainder involving quotients with intermediate zeros: Problem type 1Division with remainder involving quotients with intermediate zeros: Problem type 2Division with remainder and a two-digit divisor: Problem type 1Division with remainder and a two-digit divisor: Problem type 2Word problem with division of whole numbers and rounding: Problem type 1Word problem with division of whole numbers and rounding: Problem type 2Comparing a numerical expression with a numberRounding to thousands, ten thousands, or hundred thousandsEst imating a sum of whole numbers: Problem type 1Est imating a sum of whole numbers: Problem type 2Est imating a difference of whole numbers: Problem type 1Est imating a difference of whole numbers: Problem type 2Est imating a quotientComparing numerical expressions with parenthesesOrder of operat ions with whole numbers and grouping symbolsOrder of operat ions with whole numbers and exponents: AdvancedDivisibility rules for 2, 5, and 10Divisibility rules for 3 and 9Prime numbersPrime factorizat ionGreatest common factor of 3 numbersWord problem involving the least common mult iple of 2 numbersWord problem with common mult iplesInterpret ing a table of signed numbers that relate to a real-world situat ion: Problem type 1Interpret ing a table of signed numbers that relate to a real-world situat ion: Problem type 2Comparing signed numbers relat ing to a real-world situat ionFinding all numbers with a given absolute valueAddit ion and subtract ion with 4 or 5 integersOperat ions with absolute value: Problem type 2Exponents and integers: Problem type 2Order of operat ions with integers and exponentsEvaluat ing an algebraic expression: Whole number operat ions and exponentsPlott ing the solut ion for a one-step equation on a number lineDist inguishing between expressions and equations

Fract ions (38 topics)Understanding equivalent f ract ions: Problem type 1Understanding equivalent f ract ions: Problem type 2Modeling and writ ing equivalent f ract ionsPosit ion of f ract ions on a number lineComparing f ract ions with the same numeratorWrit ing a mixed number and an improper f ract ion for a shaded regionPosit ion of mixed numbers on a number linePlott ing mixed numbers on a number linePlott ing rat ional numbers on a number lineDecomposing a f ract ion into a sum of f ract ions with the same denominatorIntroduct ion to adding f ract ions with variables and common denominatorsAddit ion and subtract ion of 3 f ract ions with different denominatorsSigned f ract ion addit ion or subtract ion: AdvancedAddit ion and subtract ion of 3 f ract ions involving signsFract ional part of a circleAddit ion or subtract ion of mixed numbers with the same denominatorAddit ion of mixed numbers with the same denominator and renaming: Problem type 1Addit ion of mixed numbers with the same denominator and renaming: Problem type 2Subtract ion of mixed numbers with the same denominator and renaming: Problem type 1Subtract ion of mixed numbers with the same denominator and renaming: Problem type 2Addit ion or subtract ion of mixed numbers with different denominators without renamingAddit ion of mixed numbers with different denominators and renamingSubtract ion of mixed numbers with different denominators and renamingAddit ion and subtract ion of 3 mixed numbers with different denominatorsWord problem involving addit ion or subtract ion of mixed numbers with different denominatorsModeling mult iplicat ion of proper f ract ionsSigned f ract ion mult iplicat ion: AdvancedMult i-step word problem involving f ract ions and mult iplicat ionDetermining if a quantity is increased or decreased when mult iplied by a f ract ionFact families for mult iplicat ion and division of f ract ionsModeling division of a whole number by a f ract ionExponents and signed f ract ionsOrder of operat ions with f ract ions: Problem type 1Order of operat ions with f ract ions: Problem type 2Order of operat ions with f ract ions: Problem type 3Complex f ract ion without variables: Problem type 1Evaluat ing a linear expression: Signed f ract ion mult iplicat ion with addit ion or subtract ionAddit ive property of equality with f ract ions and mixed numbers

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Decimals (37 topics)Writ ing a decimal and a f ract ion for a shaded regionDecimal place value: Hundreds to ten thousandthsWrit ing a decimal number less than 1 given its nameWrit ing a decimal number greater than 1 given its nameWrit ing a decimal number given its name: AdvancedUnderstanding decimal posit ion on a number line using zoom: HundredthsUnderstanding decimal posit ion on a number line using zoom: ThousandthsConvert ing a decimal to a proper f ract ion without simplifying: AdvancedConvert ing a decimal to a mixed number and an improper f ract ion in simplest form: AdvancedDecimal addit ion and subtract ion with 3 or more numbersEst imating a decimal sum or differenceSigned decimal addit ion and subtract ion with 3 numbersFinding a point on a number line given the length of a segment and another pointComputing distances between decimals on a number lineDecimal mult iplicat ion: Problem type 2Mult iplying decimals less than 1: Problem type 2Est imating a product of decimalsWord problem with mult iplicat ion of two decimalsDivision of a decimal by a power of 0.1Decimal division with roundingAverage of two numbersSigned decimal divisionWord problem with mult iple decimal operat ions: Problem type 2Word problem with division of two decimalsConvert ing a f ract ion with a denominator of 100 or 1000 to a decimalConvert ing a mixed number to a terminat ing decimal: AdvancedConvert ing a f ract ion or mixed number to a rounded decimalInterpret ing a Venn diagram of 3 setsSquaring decimal bases: Products greater than 0.1Exponents and decimals: Products less than 0.1Order of operat ions with decimals: Problem type 1Order of operat ions with decimals: Problem type 2Order of operat ions with decimals: Problem type 3Addit ion or subtract ion with a decimal and a mixed numberMult iplicat ion with a decimal and a f ract ionEvaluat ing a linear expression: Signed decimal addit ion and subtract ionEvaluat ing a linear expression: Signed decimal mult iplicat ion with addit ion or subtract ion

Ratios, Proport ions, and Measurement (44 topics)Writ ing rat ios using different notat ionsWrit ing rat ios for real-world situat ionsIdentifying statements that describe a rat ioSimplifying a rat io of decimalsWord problem on proport ions: Problem type 2Word problem with powers of tenInvest igat ing the effects on the area for non-proport ional and proport ional figuresChoosing a measuring toolMeasuring length to the nearest inchMeasuring length to the nearest quarter or half inchConversions involving measurements in feet and inchesAdding measurements in feet and inchesU.S. Customary length conversions involving rounding decimalsWord problem involving a U.S. Customary length conversionU.S. Customary unit conversion with whole number values: Two-step conversionU.S. Customary unit conversion with mixed number values: One-step conversionU.S. Customary unit conversion with mixed number values: Two-step conversionU.S. Customary area unit conversion with whole number valuesWord problem on area involving conversions of U.S. Customary units: Problem type 1Unit conversions involving acres and hectaresMeasuring length to the nearest cent imeterMeasuring length to the nearest millimeterFinding a rate given a pictorial representat ion of a real-world situat ionMetric mass or volume conversion with whole numbersMetric conversion with decimal values: Two-step problemMetric area unit conversion with decimal valuesWord problem involving adding or subtract ing t ime within the hourIntroduct ion to adding t imeAdding t imeWord problem on elapsed t ime within the hourWord problem on elapsed t ime less than one hourWord problem on elapsed t ime more than one hourWord problem on elapsed t imes crossing AM and PMReading a posit ive temperature f rom a thermometer

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Reading the temperature f rom a thermometerConvert ing between temperatures in Fahrenheit and CelsiusSimplifying a rat io of whole numbers: Problem type 2Solving a word problem involving rates and t ime conversionConvert ing between compound units: BasicWord problem involving U.S. Customary length conversions using dimensional analysisWord problem involving a conversion between U.S. Customary units of weight and metric units of massConvert ing between compound units: AdvancedConversions with currencyWord problem involving conversion between compound units using dimensional analysis

Percents (41 topics)Finding the percentage of a grid that is shadedRepresenting benchmark percentages on a gridConvert ing a mixed number percentage to a decimalConvert ing between percentages and decimals in a real-world situat ionConvert ing a percentage to a f ract ion in simplest formConvert ing a decimal percentage to a f ract ionMaking a reasonable inference based on proport ion stat ist icsMaking part-to-part and equivalence comparisons given a circle graphApplying the percent equation: Problem type 2Interpret ing a circle graph or pie chartComputat ions f rom a circle graphCombined effect of more than one markup or discountFinding the original amount given the result of a percentage increase or decreaseFinding the original price given the sale price and percent discountFinding the absolute error and percent error of a measurementComputing the interest and repayment amount for a simple interest loan whose term is given in months or daysFinding the principal, rate, or t ime for a simple interest loan whose term is given in months or daysIntroduct ion to compound interestCalculat ing income taxComparing discountsExamining a savings plan for collegeCalculat ions involving paying for collegeComparing total costs for attending different collegesDist inguishing between fixed and variable expensesComputat ions involving cost of living and hourly wageUsing a family budget est imator to determine the minimum monthly budget and average hourly wage needed for afamilyComparing annual salaries of different occupationsHourly gross pay with overt imeGross pay with commission and salaryCalculat ions involving purchases with debit and credit cardsComparing costs of checking accountsBalancing a check registerReading a credit reportUnderstanding the impact of a credit scoreComputing a person's net worthWord problem on financial responsibilityCalculat ing and comparing monthly payments using the ALEKS loan calculatorCalculat ing monthly payment, total payment, and interest using the ALEKS loan calculatorCalculat ing and comparing total loan payments using the ALEKS loan calculatorUsing the ALEKS periodic deposit calculator to compute savings which include periodic depositsCalculat ing and comparing simple interest and compound interest

Equations and Inequalit ies (57 topics)Understanding the distribut ive propertyIdentifying like termsPropert ies of addit ionPropert ies of real numbersCombining like terms: Fract ional coefficientsUsing algebra t iles to determine if two expressions are equivalentIdentifying parts in an algebraic expressionIdentifying equivalent algebraic expressionsUsing distribut ion with double negation and combining like terms to simplify: Mult ivariateCombining like terms in a quadrat ic expressionAdding rat ional expressions with different denominators and a single occurrence of a variablePlott ing the solut ion for a two-step equation on a number lineSolving an equation to find the value of an expressionSolving a mult i-step equation given in f ract ional formClearing f ract ions in an equationSolving a two-step equation with signed f ract ionsSolving a proport ion of the form (x+a)/b = c/dIntroduct ion to solving a rat ional equation

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Solving a rat ional equation that simplifies to linear: Denominator xIntroduct ion to solving an absolute value equationSolving an absolute value equation: Problem type 1Solving a linear equation with several occurrences of the variable: Variables on both sides and two distribut ionsSolving a linear equation with several occurrences of the variable: Fract ional forms with monomial numeratorsSolving a linear equation with several occurrences of the variable: Variables on both sides and f ract ional coefficientsSolving a proport ion of the form a/(x+b) = c/xSolving for a variable in terms of other variables using addit ion or subtract ion: AdvancedSolving for a variable in terms of other variables using mult iplicat ion or division: AdvancedSolving for a variable in terms of other variables using addit ion or subtract ion with divisionSolving for a variable inside parentheses in terms of other variablesSolving for a variable in terms of other variables in a linear equation with f ract ionsChoosing stories that can be represented by given one-step equationsChoosing stories that can be represented by given two-step equationsWrit ing and solving a real-world problem given an equation with the variable on both sidesSolving a f ract ion word problem using a linear equation with the variable on both sidesSolving a word problem with three unknowns using a linear equationSolving a word problem involving consecutive integersSolving a value mixture problem using a linear equationSolving a percent mixture problem using a linear equationSolving a distance, rate, t ime problem using a linear equationWrit ing an inequality given a graph on the number lineTranslat ing a sentence into a compound inequalityGraphing a compound inequality on the number lineWrit ing a compound inequality given a graph on the number lineAddit ive property of inequality with signed f ract ionsAddit ive property of inequality with signed decimalsMult iplicat ive property of inequality with signed f ract ionsSolving a two-step linear inequality with a f ract ional coefficientSolving a linear inequality with mult iple occurrences of the variable: Problem type 1Solving a linear inequality with mult iple occurrences of the variable: Problem type 2Solving a linear inequality with mult iple occurrences of the variable: Problem type 3Solving a decimal word problem using a linear inequality with the variable on both sidesConstruct ing a Venn diagram with 2 setsInterpret ing Venn diagram cardinalit ies with 2 sets for a real-world situat ionConstruct ing a Venn diagram with 2 sets to solve a word problemConstruct ing a Venn diagram with 3 setsInterpret ing Venn diagram cardinalit ies with 3 sets for a real-world situat ionConstruct ing a Venn diagram with 3 sets to solve a word problem

Graphs, Funct ions, and Sequences (87 topics)Plott ing a point in quadrant 1: Mixed number coordinatesPlott ing a point in the coordinate plane: Mixed number coordinatesNaming the quadrant or axis of a point given its graphNaming the quadrant or axis of a point given its coordinatesNaming the quadrant or axis of a point given the signs of its coordinatesMidpoint of a line segment in the planeComparing two rules with forms of y=ax and y=x+aFinding x- and y-intercepts of a line given the equation: AdvancedClassifying slopes given graphs of linesFinding the coordinate that yields a given slopeGraphing a line through a given point with a given slopeIdentifying direct variat ion equationsWrit ing an inverse variat ion equationIdentifying direct and inverse variat ion equationsIdentifying direct and inverse variat ion f rom ordered pairs and writ ing equationsWord problem on inverse variat ionWord problem on inverse proport ionsIdentifying linear funct ions given ordered pairsRewrit ing a linear equation in the form Ax + By = CGraphing a line by first finding its slope and y-interceptWrit ing an equation and graphing a line given its slope and y-interceptFinding the slope, y-intercept, and equation for a linear funct ion given a table of valuesGraphing a line given its equation in point-slope formWrit ing an equation in standard form given the slope and a pointWrit ing the equations of vert ical and horizontal lines through a given pointFinding slopes of lines parallel and perpendicular to a line given in slope-intercept formFinding slopes of lines parallel and perpendicular to a line given in the form Ax + By = CIdentifying parallel and perpendicular lines f rom equationsWrit ing equations of lines parallel and perpendicular to a given line through a pointIdentifying parallel and perpendicular lines f rom coordinatesFinding inputs and outputs of a two-step funct ion that models a real-world situat ion: Two variable equationGraphing ordered pairs and writ ing an equation f rom a table of values in contextApplicat ion problem with a linear funct ion: Finding a coordinate given the slope and a point

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Applicat ion problem with a linear funct ion: Finding a coordinate given two pointsIdentifying independent and dependent quantit ies f rom tables and graphsIdentifying independent and dependent variables f rom equations or real-world situat ionsEvaluat ing funct ions: Linear and quadrat ic or cubicFinding outputs of a one-step funct ion that models a real-world situat ion: Funct ion notat ionFinding outputs of a two-step funct ion with decimals that models a real-world situat ion: Funct ion notat ionFinding inputs and outputs of a two-step funct ion that models a real-world situat ion: Funct ion notat ionDomain and range of a linear funct ion that models a real-world situat ionFinding an output of a funct ion f rom its graphFinding inputs and outputs of a funct ion f rom its graphDomain and range f rom the graph of a discrete relat ionFinding domain and range f rom a linear graph in contextGraphing an integer funct ion and finding its range for a given domainGraphing a funct ion of the form f (x) = ax + b: Integer slopeGraphing a funct ion of the form f (x) = ax + b: Fract ional slopeGraphing an absolute value equation of the form y = A|x|Graphing an absolute value equation in the plane: BasicGraphing an absolute value equation in the plane: AdvancedGraphing a parabola of the form y = ax2Graphing a parabola of the form y = ax2 + cGraphing a funct ion of the form f (x) = ax2Graphing a funct ion of the form f (x) = ax2 + cGraphing a cubic funct ion of the form y = ax3Finding the first terms of an arithmetic sequence using an explicit ruleFinding the next terms of an arithmetic sequence with whole numbersFinding the next terms of an arithmetic sequence with integersIdentifying arithmetic sequences and finding the common differenceFinding a specified term of an arithmetic sequence given the first termsFinding a specified term of an arithmetic sequence given the common difference and first termWrit ing an explicit rule for an arithmetic sequenceFinding the first terms of a geometric sequence using an explicit ruleFinding the next terms of a geometric sequence with whole numbersFinding the next terms of a geometric sequence with signed numbersIdentifying arithmetic and geometric sequencesIdentifying geometric sequences and finding the common rat ioFinding a specified term of a geometric sequence given the first termsFinding a specified term of a geometric sequence given the common rat io and first termArithmetic and geometric sequences: Identifying and writ ing an explicit ruleFinding patterns in shapesWrit ing a system of linear equations given its graphSolving a system of linear equations using eliminat ion with mult iplicat ion and addit ionSolving a word problem using a system of linear equations of the form Ax + By = CWrit ing and solving a system of two linear equations given a table of valuesSolving a value mixture problem using a system of linear equationsAddit ion or subtract ion of matricesIdentifying solut ions to a linear inequality in two variablesGraphing a linear inequality in the plane: Vert ical or horizontal lineGraphing a linear inequality in the plane: Slope-intercept formGraphing a linear inequality in the plane: Standard formWrit ing an inequality given its graph in the plane: Horizontal or vert ical boundary lineWrit ing an inequality given its graph in the plane: Slanted boundary lineGraphing a system of two linear inequalit ies: BasicGraphing a system of two linear inequalit ies: AdvancedWrit ing a linear inequality in two variables given a table of values

Exponents, Polynomials, and Radicals (62 topics)Product rule with posit ive exponents: Mult ivariateOrdering numbers with posit ive exponentsPower rules with posit ive exponents: Mult ivariate productsPower rules with posit ive exponents: Mult ivariate quotientsSimplifying a rat io of mult ivariate monomials: BasicSimplifying a rat io of univariate monomialsQuotient of expressions involving exponentsSimplifying a rat io of mult ivariate monomials: AdvancedOrdering numbers with negative exponentsRewrit ing an algebraic expression without a negative exponentPower of a power rule with negative exponentsAdding or subtract ing numbers writ ten in scient ific notat ion: Same exponents, advancedEst imating the sum or difference of two numbers writ ten in scient ific notat ionDegree and leading coefficient of a univariate polynomialDegree of a mult ivariate polynomialSimplifying a sum or difference of two univariate polynomialsSimplifying a sum or difference of three univariate polynomials

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Mult iplying a univariate polynomial by a monomial with a posit ive coefficientMult iplying a univariate polynomial by a monomial with a negative coefficientMult iplying a mult ivariate polynomial by a monomialMult iplying binomials with leading coefficients of 1Mult iplying binomials with leading coefficients greater than 1Mult iplying binomials in two variablesMult iplying conjugate binomials: UnivariateSquaring a binomial: UnivariateMult iplicat ion involving binomials and trinomials in one variableMult iplicat ion involving binomials and trinomials in two variablesIntroduct ion to the LCM of two monomialsLeast common mult iple of two monomialsIntroduct ion to the GCF of two monomialsGreatest common factor of three univariate monomialsGreatest common factor of two mult ivariate monomialsFactoring out a monomial f rom a polynomial: UnivariateFactoring a quadrat ic with leading coefficient 1Factoring a perfect square trinomial with leading coefficient 1Factoring a difference of squares in one variable: BasicFactoring a difference of squares in one variable: AdvancedDividing a polynomial by a monomial: UnivariateDividing a polynomial by a monomial: Mult ivariateFinding the roots of a quadrat ic equation with leading coefficient 1Finding all square roots of a numberIntroduct ion to simplifying a radical expression with an even exponentSquare root of a perfect square monomialSimplifying the square root of a whole number less than 100Simplifying the square root of a whole number greater than 100Simplifying a radical expression with an even exponentIntroduct ion to simplifying a radical expression with an odd exponentSimplifying a radical expression with an odd exponentIntroduct ion to square root addit ion or subtract ionSquare root addit ion or subtract ionIntroduct ion to square root mult iplicat ionSquare root mult iplicat ion: BasicSquare root mult iplicat ion: AdvancedSimplifying a quotient of square rootsRationalizing a denominator: Quotient involving square rootsIntroduct ion to solving a radical equationSolving a radical equation that simplifies to a linear equation: One radical, basicWord problem involving radical equations: BasicSolving an equation using the odd-root property: Problem type 1Rat ional exponents: Unit f ract ion exponents and whole number basesRational exponents: Non-unit f ract ion exponent with a whole number baseDistance between two points in the plane: Exact answers

Lines, Angles, and Polygons (46 topics)Naming segments, rays, and linesNaming angles, sides of angles, and vert icesFinding supplementary and complementary anglesSolving an equation involving complementary or supplementary anglesConstruct ing congruent line segmentsConstruct ing an angle bisectorConstruct ing congruent anglesConstruct ing the perpendicular bisector of a line segmentConstruct ing a pair of perpendicular linesConstruct ing a pair of parallel linesClassifying scalene, isosceles, and equilateral t riangles by side lengthsClassifying scalene, isosceles, and equilateral t riangles by side lengths or anglesIdentifying congruent segments in the planeIdentifying scalene, isosceles, and equilateral t riangles given coordinates of their vert icesFinding angle measures of a triangle given angles with variablesFinding side lengths and angle measures of isosceles and equilateral t rianglesFinding angle measures of an isosceles triangle given angles with variablesFinding an angle measure for a triangle sharing a side with another triangleDrawing triangles with given condit ions: Side lengths and angle measuresDrawing a circle with a given radius or diameterDrawing triangles with given side lengths using a compassRelat ionship between angle measures and side lengths in a triangleRelat ionship between angle measures and side lengths in two trianglesSine, cosine, and tangent rat ios: Numbers for side lengthsSine, cosine, and tangent rat ios: Variables for side lengthsUsing a calculator to approximate sine, cosine, and tangent valuesUsing the Pythagorean Theorem to find a trigonometric rat io

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Understanding trigonometric rat ios through similar right trianglesRelat ionship between the sines and cosines of complementary anglesUsing a trigonometric rat io to find a side length in a right triangleSolving a right triangleUsing trigonometry to find a length in a word problem with one right triangleUsing a trigonometric rat io to find an angle measure in a right triangleUsing trigonometry to find angles of elevat ion or depression in a word problemSpecial right triangles: Decimal answersNaming polygonsDrawing and identifying a polygon in the coordinate planeShared attributes among categories of quadrilateralsIdentifying parallelograms, rectangles, and squaresPropert ies of quadrilateralsClassifying parallelogramsFinding the coordinates of a point to make a parallelogramSum of the angle measures of a quadrilateralFinding the sum of the interior angle measures of a convex polygon given the number of sidesFinding the number of sides of a convex polygon given the sum of the measures of the interior anglesFinding a missing interior angle measure in a convex polygon

Transformations (7 topics)Identifying and naming congruent trianglesExploring the triangle congruence theoremsFinding angle measures and side rat ios to determine if two triangles are similarUsing a translated point to find coordinates of other translated pointsReflect ing a polygon over a vert ical or horizontal lineFinding the coordinates of three points reflected over an axisThe effect of dilat ion on area

Perimeter, Area, and Volume (68 topics)Perimeter of a piecewise rectangular figureWrit ing algebraic expressions for the perimeter of a figureFinding a side length given the perimeter and side lengths with variablesSides of polygons having the same perimeterPerimeter of a polygon involving mixed numbers and f ract ionsArea of a rectangle with f ract ional side lengthsArea of a rectangle involving mixed number and f ract ional side lengthsAreas of rectangles with the same perimeterWord problem on area involving conversions of U.S. Customary units: Problem type 2Word problem on area involving conversions between systemsEst imates and exact answersWrit ing algebraic expressions for the area of a figureWord problem on optimizing an area or perimeterFinding the dimensions of a rectangle given its perimeter and a relat ionship between sidesFinding the perimeter or area of a rectangle given one of these valuesFinding the perimeter or area of a rectangle in the coordinate planeFinding the area of a right triangle or its corresponding rectangleSolving a word problem involving area using a one-step linear inequality: Area and lengthsFinding the area of a right triangle using the Pythagorean TheoremFinding the area of a triangle or parallelogram in the coordinate planeWord problem involving the area between two rectanglesFinding an area in terms of variablesFinding the area of a trapezoid, rhombus, or kite in the coordinate planeIntroduct ion to a circle: Diameter, radius, and chordIdentifying chords, secants, and tangents of a circleNaming and finding measures of central angles, inscribed angles, and arcs of a circleInformal argument for the formula of the circumference of a circleCircumference rat iosPerimeter involving rectangles and circlesCircumference and area of a circle: Exact answers in terms of piInformal argument for the formula of the area of a circleWord problem involving the area between two concentric circlesArea involving inscribed figuresArea involving mult iple inscribed figuresArea of a sector of a circle: Exact answer in terms of piVert ices, edges, and faces of a solidIdentifying geometric shapes that model real-world objectsCounting the cubes in a solid made of cubesSide views of a solid made of cubesVolume of a solid made of cubes with unit f ract ion edge lengthsVolume of a rectangular prism with f ract ional edge lengthsWord problem involving the rate of filling or emptying a rectangular prismWord problem on volume involving conversions of U.S. Customary unitsWord problem involving the volume of a triangular prism

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Word problem involving the rate of filling or emptying a cylinderRatio of volumesConvert ing between U.S. Customary units of volume: Problem type 1Convert ing between metric units of volume and capacityRelat ing the volumes of a rectangular prism and a rectangular pyramidRelat ing the volumes of a triangular prism and a triangular pyramidVolume of a cone: Exact answers in terms of piRelat ing the volumes of a cylinder and a coneSurface area of a rectangular prism made of unit cubesUsing a net to find the lateral surface area and total surface area of a rectangular prismWord problem involving U.S. Customary conversions, surface area, and costSurface area of a piecewise rectangular prism made of unit cubesUsing a net to find the lateral surface area and total surface area of a triangular prismSurface area of a cylinder: Exact answers in terms of piWord problem involving the surface area of a cylinderWord problem involving the surface area of rectangular prisms and cylindersUsing a net to find the lateral surface area and total surface area of a pyramidWord problem involving the surface area of rectangular prisms and pyramidsSurface area of a sphereSide lengths, perimeters, and areas of similar polygonsIdentifying similar solidsComputing rat ios of side lengths, surface areas, and volumes for similar solidsComputing side length, surface area, and volume for similar solidsWord problem involving volumes of similar solids

Data Analysis and Probability (46 topics)Identifying stat ist ical quest ionsClassifying samplesMaking predict ions using experimental data for compound eventsConstruct ing a f requency distribut ion for non-grouped dataConstruct ing a relat ive f requency distribut ion for grouped dataCalculat ing relat ive f requencies in a contingency tableFinding if a quest ion can be answered by the dataConstruct ing a line plot with f ract ional values: FourthsMaking part-to-whole, part-to-part , and equivalence comparisons given a line plotMaking part-to-whole, part-to-part , and equivalence comparisons given a bar graphInterpret ing a histogramIntroduct ion to interpret ing a pictographInterpret ing a pictograph tableInterpret ing a stem-and-leaf plotAngle measure in a circle graphApproximating the equation of a line of best fit and making predict ionsLinear relat ionship and the correlat ion coefficientUsing a model to find the meanUnderstanding the mean graphically: Two barsUnderstanding the mean graphically: Four or more barsComputat ions involving the mean, sample size, and sum of a data setFinding the value for a new score that will yield a given meanReject ing unreasonable claims based on average stat ist icsWeighted meanHow changing a value affects the mean and medianIdentifying peaks, symmetry, gaps, and clusters in a line plotIdentifying the center, spread, and shape of a data setComparing measures of center and variat ionUsing back-to-back stem-and-leaf plots to compare data setsComputing mean absolute deviat ion f rom a bar graphFinding out liers in a data setCounting principleCounting principle with repetit ion allowedFactorial expressionsComputing permutat ions and combinat ionsWord problem involving permutat ionsWord problem involving combinat ionsIntroduct ion to permutat ions and combinat ionsProbabilit ies of an event and its complementFinding the odds in favor and againstConvert ing between probability and oddsArea as probabilityExperimental and theoret ical probability for compound eventsProbabilit ies of a permutat ion and a combinat ionGenerat ing random samples f rom a populat ion with known characterist icsUsing a random number table to make a fair decision

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*Other Topics Available By default , these topics are NOT included in the course, but can be added using the content editor inthe Teacher Module.