6th Grade Skills

Whole Numbers

Addition of Whole Numbers

Basic Addition of Whole Numbers
 Add three & fourdigit whole numbers
 Condensed: Add fourdigit & three or fourdigit whole numbers
 Add fourdigit whole numbers

Application of Addition of Whole Numbers
 Add three & fourdigit whole numbers, realworld context
 Add fourdigit whole numbers, realworld context
 Condensed: Add whole numbers, up to five digits, including realworld context
 Condensed: Add whole numbers, up to five digits, realworld context
 Add fivedigit whole numbers, realworld context
 Add five or sixdigit whole numbers, realworld context


Subtraction of Whole Numbers

Basic Subtraction of Whole Numbers
 Subtract whole numbers, fourdigit & threedigit
 Condensed: Subtract whole numbers, fourdigit & three or fourdigit
 Subtract whole numbers, fivedigit & four or fivedigit
 Condensed: Subtract whole numbers, four to sixdigit & two to fivedigit
 Subtract whole numbers, six or sevendigit & up to six digits
 Subtract whole numbers, sevendigit & six or sevendigit

Application of Subtraction of Whole Numbers
 Subtract whole numbers, fourdigit & three or fourdigit, realworld context
 Subtract whole numbers, fivedigit & four or fivedigit, realworld context
 Subtract whole numbers, sixdigit & five or sixdigit, realworld context
 Subtract whole numbers, sevendigit & six or sevendigit, realworld context
 Condensed: Subtract whole numbers, four to sevendigit & three to sixdigit, including realworld context
 Condensed: Subtract whole numbers, four to sevendigit & three to sixdigit, including realworld context
 Condensed: Subtract whole numbers, four to sevendigit & three to sixdigit, realworld context


Multiplication of Whole Numbers

Application & Modeling of Multiplication of Whole Numbers
 Condensed: Multiply whole numbers, onedigit & up to fourdigit, realworld context
 Condensed: Multiply whole numbers, one or twodigit & up to fourdigit, realworld context
 Condensed: Multiply whole numbers using area models or decomposition, up to fourdigit & onedigit
 Condensed: Multiply whole numbers using area models or decomposition, twodigit & twodigit
 Multiply whole numbers, threedigit & twodigit, including addition or subtraction step, realworld context

Basic Multiplication of Whole Numbers
 Condensed: Multiply whole numbers, three or fourdigit & onedigit
 Multiply whole numbers, twodigit & twodigit
 Multiply whole numbers by decomposing factors, twodigit & twodigit
 Multiply whole numbers, twodigit & two or threedigit
 Multiply whole numbers, threedigit & twodigit
 Condensed: Multiply whole numbers, three or fourdigit & twodigit
 Multiply whole numbers, fourdigit & twodigit
 Multiply whole numbers, both up to three digits
 Condensed: Multiply whole numbers, up to fourdigit & up to threedigit, no more than six total digits

Multiplicative Comparisons of Whole Numbers
 Solve problems involving multiplicative comparisons
 Solve problems involving multiplicative & additive comparisons of whole numbers
 Solve problems involving multiplicative & additive comparisons
 Condensed: Solve problems involving division of positive integers & multiplicative & additive comparisons, realworld context


Division of Whole Numbers

Basic Division of Whole Numbers
 Apply divisibility rules to twodigit dividends, divisor 2, 3, 4, 5, 6, 9, 10
 Condensed: Determine quotient & remainder, twodigit dividend, up to twodigit divisor
 Condensed: Determine quotient & remainder, threedigit dividend, up to twodigit divisor
 Condensed: Determine quotient & remainder, fourdigit dividend, up to twodigit divisor
 Condensed: Determine quotient & remainder as fraction, twodigit dividend, up two twodigit divisor
 Condensed: Determine quotient & remainder as fraction, threedigit dividend, up two twodigit divisor
 Condensed: Determine quotient & remainder as fraction, fourdigit dividend, up two twodigit divisor
 Divide whole numbers with decimal quotient, up to threedigit dividend, up to threedigit divisor

Application of Division of Whole Numbers
 Determine division equations, realworld context
 Determine equivalence between area models & division equations
 Determine equivalence between arrays & division equations
 Condensed: Determine equivalence between models & division equations
 Divide positive integers, up to fourdigit dividend, onedigit divisor, realworld context
 Divide positive integers, up to fourdigit dividend, up to twodigit divisor, realworld context
 Determine quotient, up to fourdigit dividend, up to twodigit divisor, realworld context
 Determine quotient or remainder, up to fourdigit dividend, onedigit divisor, realworld context
 Divide positive integers for decimal result, realworld context


Mixed Operations of Whole Numbers

Diagrams of Mixed Operations of Whole Numbers
 Solve multistep problems involving models & whole number operations, initially add, realworld context
 Solve multistep problems involving models & whole number operations, initially subtract, realworld context
 Solve multistep problems involving models & whole number operations, initially multiply, realworld context
 Solve multistep problems involving models & whole number operations, initially divide, realworld context
 Condensed: Solve multistep problems involving models & whole number operations, realworld context

Equations of Mixed Operations of Whole Numbers
 Solve twostep equation with isolated variable, realworld context
 Identify multistep equations, realworld context
 Solve multistep problems involving equations & whole number operations, initially add, realworld context
 Solve multistep problems involving equations & whole number operations, initially subtract, realworld context
 Solve multistep problems involving equations & whole number operations, initially multiply, realworld context
 Solve multistep problems involving equations & whole number operations, initially divide, realworld context
 Condensed: Solve multistep problems involving equations & whole number operations, realworld context
 Determine & solve twostep equations with isolated variable, realworld context

Diagrams & Equations of Mixed Operations of Whole Numbers
 Condensed: Solve multistep problems involving equations, models, & whole number operations, realworld context

Application of Mixed Operations of Whole Numbers
 Determine & evaluate addition or subtraction expressions, realworld context
 Solve multistep problems involving whole number operations, initially add, realworld context
 Solve multistep problems involving whole number operations, initially subtract, realworld context
 Solve multistep problems involving whole number operations, initially multiply, realworld context
 Solve multistep problems involving whole number operations, initially divide, realworld context
 Solve multistep problems involving division of positive integers, realworld context
 Solve multistep problems involving operations with whole numbers
 Condensed: Solve multistep problems involving whole number operations, realworld context


Rounding & Estimating Whole Numbers

Basic Rounding & Estimating Whole Numbers
 Round whole numbers to nearest ten
 Round whole numbers to nearest hundred
 Round whole numbers to nearest thousand
 Condensed: Round whole numbers to nearest ten, hundred, & thousand
 Round whole numbers using frontend rounding
 Round whole numbers to specified place value, up to hundredthousand

Application of Rounding Whole Numbers
 Round whole numbers to nearest ten, realworld context
 Round whole numbers to nearest hundred, realworld context
 Round whole numbers to nearest thousand, realworld context
 Condensed: Round whole numbers to nearest ten, hundred, & thousand, including realworld context
 Condensed: Round whole numbers to nearest ten, hundred, & thousand, realworld context

Application of Estimating Whole Numbers
 Estimate sums of whole numbers, up to six digits, including realworld context
 Estimate differences of whole numbers, up to six digits, including realworld context
 Estimate sums & differences of whole numbers by rounding to specified place values
 Estimate products of whole numbers, twodigit factor times onedigit factor
 Estimate quotients of whole numbers, up to sixdigit dividend, up to threedigit divisor
 Condensed: Estimate sums, differences, & products of whole numbers
 Estimate sum of rational numbers, round both to nearest whole, realworld context
 Determine division expression to estimate quotient using compatible numbers
 Identify division expression to estimate quotient using compatible numbers, realworld context


Comparing & Ordering Whole Numbers
 Compare two positive integers
 Compare threedigit whole numbers
 Compare fourdigit whole numbers
 Compare fivedigit whole numbers
 Compare sixdigit whole numbers
 Order whole numbers up to 1,000,000,000, including realworld context
 Condensed: Order whole numbers, up to 1,000,000,000, including realworld context
 Order whole numbers up to 1,000,000,000, realworld context


Fractions

Representing Fractions
 Identify fractions or mixed numbers on decimal grid
 Identify fractions on strip diagrams
 Identify common fractions or mixed numbers on number line

Equivalent Fractions
 Determine how many fraction parts are in whole
 Determine equivalent fractions, strip diagrams
 Determine equivalent fractions, number lines
 Determine equivalent fractions, area models
 Determine equivalent fraction equations, area models
 Determine equivalent fraction components
 Identify or determine equivalent fraction components or fractions

Simplifying Fractions
 Reduce fractions, denominators less than 20
 Reduce fractions, answer denominators less than 10
 Reduce fractions, answer denominators less than 30
 Reduce fraction part of mixed numbers
 Simplify & reduce mixed numbers, improper fraction part

Converting Fractions

Converting Fractions to Decimals
 Given model, determine fraction & decimal equivalents, unreduced
 Identify decimal equivalent of fractions, realworld context
 Convert fractions to decimals, denominator power of 10
 Convert fractions to decimals, denominator factor of power of 10
 Convert fractions to decimals, denominator factor of 100
 Convert fractions to decimals, realworld context
 Convert fractions to decimals, up to two decimal places, realworld context
 Convert fractions to rounded decimals
 Convert fractions to decimals, including improper fractions, including repeating decimals
 Convert mixed numbers to decimals, including repeating decimals

Converting Improper Fractions & Mixed Numbers
 Convert mixed numbers to improper fractions, denominators less than 10
 Convert mixed numbers to improper fractions, includes denominators more than 10
 Convert whole numbers to improper fractions
 Convert improper fractions to mixed numbers, whole part up to 3
 Convert improper fractions to mixed numbers, whole part up to 12
 Condensed: Convert between improper fractions & mixed numbers

Converting Fractions to Percents
 Convert fractions to percents, denominator factor of 100
 Convert fractions to percents, denominator factor of 100, rounding directions
 Convert fractions to rounded percents
 Convert improper fractions to rounded percents
 Convert fractions to mixed number percents
 Convert fractions to mixed number percents over 100


Comparing & Ordering Fractions

Modeling Comparing Fractions
 Determine equivalent fractions, strip diagrams
 Compare two fractions, different denominators, number lines
 Compare two fractions, different denominators, strip diagrams
 Compare two fractions, different denominators, area models
 Compare fractions, different denominators, visual model
 Compare fractions, denominators less than 10

Basic Comparing & Ordering Fractions
 Compare fractions, denominators less than 10
 Compare fractions, denominators less than 30
 Compare fractions between onehalf & one
 Compare fractions, same numerators, denominators differ by one, denominators less than 10,000
 Compare fractions, different denominators
 Order positive fractions
 Determine equivalent fractions, strip diagrams
 Compare two fractions, different denominators, area models
 Compare two fractions, different denominators, number lines
 Compare two fractions, different denominators, strip diagrams
 Compare fractions, denominators less than 10
 Compare fractions, denominators less than 30
 Compare fractions between onehalf & one
 Compare fractions, same numerators, denominators differ by one, denominators less than 10,000
 Compare fractions, different denominators
 Compare fractions, different denominators, visual model
 Order positive fractions


Addition of Fractions
 Condensed: Add fractions, common denominators, including realworld context
 Add fractions, common denominators, realworld context
 Add fractions, denominators of 10 & 100
 Add fractions, one denominator multiple of other, including improper sums
 Add fractions, one denominator multiple of other, including mixed number sums
 Add fractions, different denominators, including improper sums
 Add fractions, different denominators, including mixed number sums
 Add mixed numbers, different denominators
 Add mixed numbers, different denominators, fractional sum greater than one

Subtraction of Fractions
 Subtract fractions, one denominator multiple of other, proper fraction difference
 Subtract fractions, one denominator multiple of other, including improper differences
 Subtract fractions, different denominators, positive proper differences
 Subtract fractions, different denominators, including mixed number differences
 Subtract mixed numbers, different denominators
 Subtract mixed numbers, different denominators, borrowing required

Mixed Addition & Subtraction of Fractions

Modeling & Application of Mixed Addition & Subtraction of Fractions
 Identify expressions that represent addition or subtraction of unreduced fractions modeled by area models
 Identify expressions that represent addition or subtraction of unreduced fractions modeled on number lines
 Condensed: Given model, determine or interpret addition & subtraction of fractions
 Add & subtract fractions, fraction strips
 Add & subtract fractions, area models
 Add & subtract fractions, number lines
 Add & subtract fractions, various models

Basic Mixed Addition & Subtraction of Fractions
 Condensed: Add or subtract fractions, common denominators, unreduced
 Condensed: Add or subtract fractions, common denominators, realworld context
 Condensed: Add or subtract fractions, different denominators
 Add or subtract fractions, including estimation, realworld context
 Add & subtract fractions, realworld context
 Given subtraction expression of two fractions, identify expression using fourths that best estimates difference


Multiplication of Fractions

Modeling Multiplication of Fractions
 Identify model representation of multiplication of fraction & whole number
 Condensed: Identify models or multiply whole numbers & fractions using area models
 Multiply whole numbers & fractions, area models
 Multiply whole numbers & fractions, including visual models
 Multiply mixed numbers & proper fractions, visual models, realworld context

Basic Multiplication of Fractions
 Multiply whole numbers & unit fractions, whole number first
 Multiply whole numbers & unit fractions
 Multiply whole numbers & fractions, positive
 Multiply fractions, positive, mixed number directions
 Multiply proper & improper fractions, positive
 Multiply fractions, positive
 Multiply mixed numbers, positive
 Condensed: Multiply fraction & mixed numbers, including mixed signs, mixed number directions

Application of Multiplication of Fractions
 Multiply whole numbers & fractions, realworld context
 Multiply fractions, positive, realworld context
 Multiply mixed numbers & proper fractions, realworld context
 Determine part of whole using fraction multiplication, including visual models, including realworld context
 Estimate products of rational numbers, no decimals, round both factors to nearest whole number, realworld context

Scaling Fractions
 Determine whether quantities are increased or decreased when multiplied by fractions
 Determine products & identify whether quantities are increased or decreased when multiplied by fraction
 Compare products of fractions, mixed numbers, & whole numbers, including realworld context
 Interpret fractional parts & fraction multiplication, realworld context


Division of Fractions

Reciprocals
 Determine reciprocals of whole numbers or fractions
 Determine equivalent division & multiplication expressions using reciprocals

Modeling Division of Fractions
 Divide whole numbers & unit fractions, area models
 Divide whole numbers by unit fractions, number lines
 Divide whole numbers & unit fractions, fraction strips
 Divide whole numbers by unit fractions, models
 Condensed: Divide whole numbers & fractions, various models
 Identify division models & divide unit fractions by unit fractions
 Determine visual representation & fraction quotient of division problems

Basic Division of Fractions
 Determine representation of fraction as division expression
 Divide whole numbers by unit fractions
 Divide whole numbers & unit fractions
 Divide fractions, positive, mixed number directions
 Divide mixed numbers, positive

Application of Division of Fractions
 Determine fraction & mixed number equivalence of division problems, realworld context
 Determine or estimate quotients of whole numbers, fraction quotients
 Estimate & determine quotients as fraction representation of division problem
 Divide whole numbers & unit fractions, including unit fraction multiplication, realworld context
 Divide fractions & mixed numbers, positive, realworld context
 Divide fractions, mixed numbers, & whole numbers, multistep, realworld context



Decimals

Representing Decimals
 Given tenths model, identify decimal
 Given hundredths model, identify decimal
 Given hundredths model, identify decimal as monetary amount
 Determine value of decimal model, including money

Comparing & Ordering Decimals

Basic Comparing & Ordering Decimals
 Compare whole numbers up to 1,000,000,000
 Given decimals, identify locations on number line
 Compare decimals on number line
 Compare decimals up to two decimal places, including realworld context
 Compare decimals up to two decimal places & justify relationship, including realworld context
 Compare decimals written in word form, up to three decimal places
 Compare numbers, up to fourdigit whole numbers or threedigit decimals
 Identify & compare rational numbers on number lines, positive
 Compare decimals written in word form, up to four decimal places
 Order positive decimals
 Order decimals up to 1,000,000,000

Application of Comparing & Ordering Decimals
 Compare decimals up to two decimal places, including realworld context
 Compare decimals up to three decimal places
 Compare decimals up to three decimal places, realworld context
 Order decimals up to two decimal places, including realworld context
 Order decimals from table of place values, realworld context
 Order decimals up to three decimal places, including realworld context
 Condensed: Compare or order numbers up to 1,000,000,000
 Compare & order decimals up to 1,000,000,000, realworld context
 Compare or order positive & negative decimals, up to three decimal places


Converting Decimals
 Convert decimals to percents
 Convert decimals to percents over 100
 Given model, determine fraction & decimal equivalents, unreduced
 Convert decimals to fractions
 Convert decimals to fractions, realworld context
 Convert decimals to mixed numbers
 Convert decimals to fractions or mixed numbers
 Convert decimals to fractions or mixed numbers, including repeating decimals of thirds
 Convert decimals to fractions or mixed numbers, including repeating decimals
 Condensed: Convert decimals to fractions & percents

Addition of Decimals

Basic Addition of Decimals
 Add decimals, positive, up to two decimal places
 Add positive decimals, up to three decimal places
 Add decimals, positive, up to four decimal places

Application of Addition of Decimals
 Condensed: Add decimals, positive, up to two decimal places, including realworld context
 Add decimals, positive, up to two decimal places, realworld context


Subtraction of Decimals

Basic Subtraction of Decimals
 Subtract decimals, up to two decimal places
 Subtract decimals, two decimal places
 Subtract decimals, up to three decimal places, positive difference

Application of Subtraction of Decimals
 Condensed: Subtract decimals, up to two decimal places, including realworld context
 Subtract decimals, up to two decimal places, realworld context
 Make change


Addition & Subtraction of Decimals

Basic Addition & Subtraction of Decimals
 Condensed: Add & subtract decimals, up to two decimal places

Application of Addition & Subtraction of Decimals
 Condensed: Add & subtract decimals, up to two decimal places, including realworld context
 Add & subtract decimals, up to two decimal places, realworld context
 Condensed: Add & subtract decimals, up to two decimal places, realworld context
 Add & subtract decimals, up to three decimal places, realworld context
 Add or subtract whole numbers or decimals, realworld context
 Condensed: Add & subtract rational numbers, realworld context


Multiplication of Decimals

Application & Modeling of Multiplication of Decimals
 Determine equivalence between area models & multiplication equations
 Determine equivalence between base10 models & multiplication equations
 Determine equivalence between number line models & multiplication equations
 Condensed: Determine equivalence between models & multiplication equations
 Multiply decimals, products limited to two decimal places, realworld context

Basic Multiplication of Decimals
 Multiply decimals times onedigit whole numbers
 Multiply decimals, products limited to two decimal places
 Multiply positive decimals, each factor up to two decimal places, factors up to 10 after decimal shift
 Multiply positive decimals, each factor up to two decimal places, factors up to 20
 Multiply positive decimals, each factor up to two decimal places
 Multiply positive decimals, each factor up to three decimal places
 Condensed: Multiply decimals
 Multiply three positive decimals, products limited to three decimal places


Division of Decimals

Application & Modeling of Division of Decimals
 Identify expressions & equations representing multiplication & division of rational numbers
 Identify base10 model that represents quotient of decimal division
 Determine equivalence of base10 model & components of decimal division
 Determine equivalence of base10 model & components of decimal division, quotient limited to tenths
 Given area model representing decimal division, interpret model & determine quotient, including realworld context
 Given number line model representing decimal division, interpret model & determine quotient, including realworld context
 Given model representing decimal division, interpret model & determine quotient, including money
 Condensed: Given model representing decimal division, interpret model & determine quotient, including realworld context
 Divide decimals, up to three decimal places, realworld context
 Divide fourdigit dividends by twodigit whole number divisors, including realworld context

Basic Division of Decimals
 Divide whole numbers by decimals, up to two decimal places, integer quotients
 Divide decimals by whole numbers, up to two decimal places
 Divide decimals, up to two decimal places in quotients
 Divide decimals, up to three decimal places in dividend & divisor
 Divide decimals, up to three decimal places
 Divide fourdigit dividends by twodigit whole number divisors
 Condensed: Divide decimals or whole numbers


Mixed Operations with Decimals
 Condensed: Solve problems with decimal & whole numbers, realworld context
 Condensed: Add, subtract, multiply, & divide decimals, up to two decimal places
 Solve multistep problems with rational numbers, including percents, realworld context

Rounding & Estimating Decimals

Basic Rounding & Estimating Decimals
 Round decimal numbers to nearest whole, tenth, & hundredth
 Round decimal numbers to nearest whole, tenth, hundredth, & thousandth

Application of Rounding & Estimating Decimals
 Round numbers to nearest whole, ten, hundred, & thousand, realworld context
 Round decimal numbers to nearest tenth & hundredth, including realworld context
 Round decimal numbers to nearest tenth & hundredth, realworld context
 Round decimal numbers to nearest tenth, hundredth, & thousandth, realworld context
 Round decimal numbers to nearest whole, tenth, hundredth, & thousandth, including realworld context
 Round decimal & whole numbers to specified place value

Rounding & Operations with Decimals
 Round decimal numbers to nearest whole, tenth, & hundredth, realworld context
 Condensed: Round decimal numbers to nearest whole, tenth, & hundredth, including realworld context
 Estimate sum by rounding addends to nearest whole number, up to two decimal places
 Estimate differences of decimals by rounding to nearest whole number
 Condensed: Estimate sum or difference by rounding addends, minuend, & subtrahend, up to two decimal places
 Estimate quotients of decimals & whole numbers using compatible numbers
 Estimate solutions involving all operations, realworld context
 Determine sums & differences of decimals then round solution, realworld context



Integers

Classifying Numbers
 Classify rational numbers by definitions
 Classify rational numbers using graphic organizers
 Classify rational numbers, including graphic organizers

Absolute Value & Opposites
 Determine opposites of numbers
 Identify opposite integers on number line
 Add opposite integers, up to two digits
 Identify situations represented by positive & negative numbers, realworld context
 Determine representations of quantities using positive & negative numbers, realworld context
 Determine change, opposite integers, realworld context
 Determine absolute value of integers
 Determine absolute value of integers, including realworld context
 Determine absolute value of rational numbers
 Determine absolute value of numeric expression

Comparing Integers
 Compare two positive integers
 Compare two integers, one positive & one negative
 Compare two negative integers
 Interpret inequalities as statements about position

Addition of Integers

Modeling Addition of Integers
 Determine number represented by counters
 Add integers using counters
 Classify sum of integers on number line
 Given number line model, determine or interpret integer sum expression, same signs
 Given number line model, determine or interpret integer sum expression, mixed signs

Basic Addition of Integers
 Add opposite integers
 Add opposite integers, up to two digits
 Add integers with same sign, start one digit & advance to two digits
 Add integers, one digit
 Add integers, positive sum
 Add integers, negative sum
 Add integers, start one digit & advance to two digits
 Add negative integers
 Add integers, up to two digits, positive sum
 Add integers, up to two digits, negative sum
 Add negative integers, up to two digits
 Condensed: Add positive & negative integers

Application of Addition of Integers
 Add integers with same sign, up to three digits, realworld context
 Add integers, up to three digits, realworld context
 Given model or table, add integers, realworld context
 Condensed: Add integers, realworld context


Subtraction of Integers

Modeling Subtraction of Integers
 Subtract integers using counters
 Given variables on number line, classify difference
 Subtract integers on number line, same signs
 Subtract integers on number line, mixed signs

Basic Subtraction of Integers, Positive Difference
 Subtract integers, positive difference
 Subtract negative integers, positive difference
 Subtract negative integers, up to two digits, positive difference
 Subtract integers, opposite signs, up to two digits, positive difference

Basic Subtraction of Integers, Negative Difference
 Subtract integers, negative difference
 Subtract positive integers, negative difference
 Subtract negative integers, negative difference
 Subtract positive integers, up to two digits, negative difference
 Subtract negative integers, up to two digits, negative difference
 Subtract integers, opposite signs, up to two digits, negative difference

Basic Subtraction of Integers, Mixed Differences
 Rewrite subtraction as addition & evaluate expression
 Subtract positive integers, onedigit & onedigit
 Subtract integers, various signs
 Condensed: Subtract integers, various signs, up to two digits

Application of Subtraction of Integers
 Determine differences between integers, same signs, realworld context
 Determine differences between integers, mixed signs, realworld context
 Determine differences between integers, various signs, realworld context


Multiplication of Integers

Modeling Multiplication of Integers
 Multiply integers using counters
 Multiply positive integers using number line models, includes negatives shown on number line
 Multiply positive integers times negative integers using number line models

Basic Multiplication of Integers
 Multiply negative integers
 Multiply integers, opposite signs
 Multiply integers, start one digit & advance to two digits
 Multiply negative integers, twodigit times twodigit
 Multiply integers, opposite signs, twodigit times twodigit
 Multiply negative integers, twodigit times two or threedigit
 Multiply integers, opposite signs, twodigit times two or threedigit
 Multiply three integers

Application of Multiplication of Integers
 Multiply positive integers, realworld context
 Multiply integers, mixed signs, realworld context


Division of Integers

Modeling Division of Integers
 Divide integers using counters
 Divide integers, both positive, up to twodigit dividend, number line model
 Divide integers, opposite signs, up to twodigit dividend, number line model

Basic Division of Integers
 Divide integers, one or both negative, start onedigit, advance up to threedigits
 Divide integers, one or both negative, start onedigit, advance up to threedigits, includes undefined
 Divide integers, both negative, up to threedigit dividend, up to twodigit divisor
 Divide integers, opposite signs, up to threedigit dividend, up to twodigit divisor
 Divide integers, both negative, up to fivedigit dividend, up to twodigit divisor
 Divide integers, opposite signs, up to fivedigit dividend, up to twodigit divisor

Application of Division of Integers
 Divide integers, same signs, realworld context
 Divide integers, opposite signs, realworld context


Mixed Operations of Integers
 Determine number of zero pairs or evaluate expressions using counters
 Estimate sums & differences of integers using frontend rounding
 Condensed: Add or subtract integers using counters
 Condensed: Multiply & divide integers
 Condensed: Add, subtract, multiply, & divide integers


Percents

Representing Percents
 Identify percents, decimal grids
 Identify percents, strip diagrams, realworld context
 Identify percents, area models
 Determine percents & specified quantities, double number lines, realworld context
 Condensed: Determine ratios & percents, decimal grids
 Condensed: Determine ratios & percents, strip diagrams, realworld context
 Condensed: Determine ratios & percents, various models
 Condensed: Determine ratios & percents, double number lines, including realworld context

Converting Percents
 Convert percents to decimals
 Convert decimal percents to decimals
 Convert decimal percents less than one to decimals
 Convert percents to fractions
 Convert percents to fractions, realworld context
 Convert percents to mixed numbers
 Condensed: Convert percents to decimals & fractions

Finding Tip, Tax, Markup, Markdown, & Commission
 Given percent, identify table that shows percent
 Determine tips
 Determine tax
 Determine markups
 Determine increases involving tips, tax, & markups
 Determine commissions
 Determine income tax for earned wages
 Determine discount, tax, or total cost
 Determine decreases involving sales, discounts, & markdowns
 Condensed: Determine tip, tax, discount, or markup
 Determine & compare savings from sales, rebates, & coupons

Finding Total, Part, or Percent of a Number
 Given model, determine & identify fractions, decimals, & percents
 Given percent & whole, determine part, whole number answers
 Given percent & whole, determine part, exact answers
 Given percent & whole, determine rounded part
 Given percent & whole, determine part, realworld context
 Given part & percent, determine whole, exact answers
 Given part & percent, determine whole
 Given part & percent, determine whole, realworld context
 Given part & whole, determine percent
 Given part & whole, determine percent, realworld context
 Determine specified values in tables involving percents

Finding Percent of Change
 Determine percent of change, whole numbers, including realworld context
 Determine percent of change, including realworld context

Calculating Simple Interest
 Determine simple interest
 Determine simple interest & total amount
 Given simple interest earned, determine principal, rate, or time


Fractions, Decimals, & Percents Combined

Comparing & Ordering Fractions & Decimals Combined
 Condensed: Order positive decimals & fractions
 Order positive rational numbers, no radicals, no exponents
 Given set or list, order rational numbers, realworld context
 Given table, order rational numbers, realworld context

Fraction, Decimal, & Percent Conversions
 Identify part of whole, realworld context
 Given model, determine & identify fractions, decimals, & percents
 Condensed: Convert proper & improper fractions to rounded percents
 Condensed: Convert fractions to decimals & percents

Basic Fractions & Decimals Combined
 Multiply decimals times fractions, both positive
 Multiply fractions times decimals, both positive

Application of Fractions & Decimals Combined
 Multiply decimals & fractions, realworld context
 Add or subtract whole numbers, fractions, or decimals, realworld context
 Condensed: Add & subtract rational numbers, realworld context
 Solve multistep problems with rational numbers, including percents, realworld context


Ratios, Rates, & Proportions

Ratios

Basic Representing Ratios
 Determine part to part ratio, decimal grids
 Determine part to whole ratio, decimal grids
 Condensed: Determine ratios & percents, decimal grids
 Determine part to part ratio, various models
 Determine part to whole ratio, various models
 Condensed: Determine ratios & percents, various models

Representing Ratios RealWorld
 Given part & percent, identify model & determine whole, realworld context
 Given double number line model, determine percent or specified quantity, realworld context
 Determine part to part ratio, strip diagrams, realworld context
 Determine part to whole ratio, strip diagrams, realworld context
 Condensed: Determine ratios & percents, strip diagrams, realworld context
 Determine part to part ratio, including double number lines, including realworld context
 Determine part to whole ratio, double number lines, realworld context
 Condensed: Determine ratios & percents, double number lines, including realworld context

Basic Ratios
 Rewrite ratios
 Given ratio, determine reduced form
 Identify equivalent ratios or determine missing component of proportion
 Given table, determine ratios, integers
 Determine ratios, various forms, realworld context
 Determine ratios, realworld context

Application of Ratios
 Given ratio, determine relationship between ratio terms, realworld context
 Interpret & apply ratios
 Given proportional relationship as ratio, determine specified quantity, realworld context
 Determine specified quantity in proportional relationship, including mixed numbers, realworld context
 Condensed: Determine ratios, relationship between ratio terms, & specified quantities, realworld context
 Given ratios a : b & b : c, determine a : c, realworld context
 Given ratios a : b & b : c, determine specified quantity, realworld context
 Condensed: Given extended ratio, determine ratio or specified quantity, realworld context
 Given proportional relationship & extended ratio, determine specified quantity, realworld context


Rates

Basic Unit Rates
 Identify unit rates
 Determine unit rates, ratio tables, realworld context
 Determine unit rates, strip diagrams, realworld context
 Given double number line, determine unit rate, realworld context
 Identify measurement conversion unit rates

Application of Rates
 Determine unit rates, whole numbers, realworld context
 Determine unit rates, fractions, realworld context
 Determine unit rates, mixed numbers, realworld context
 Condensed: Determine or apply unit rates, realworld context
 Determine & compare unit rates, realworld context
 Given proportional relationship, determine specified quantity, realworld context
 Given rate, convert time unit to determine quantity over time interval, realworld context
 Given rate of travel, determine distance or time
 Given unit conversion rate, convert measurement units
 Identify measurement conversion rates


Proportions
 Solve proportions, whole numbers
 Solve proportions
 Solve proportions, mixed number components
 Solve proportions to convert measurement units
 Solve proportions, exact answers, realworld context
 Solve proportions, rounded answers, realworld context
 Compare rates or determine specified values in proportional relationships, realworld context


Number Lines

Number Lines, Only Positives
 Given range & increment, identify blank number line
 Identify decimals on number lines, positive
 Identify decimals on number lines, vertical number lines, positive
 Identify or plot decimals on number lines, increment 0.5
 Identify or plot decimals on number lines, increment 0.2
 Condensed: Identify or plot decimals on number lines
 Plot or locate percents on number line
 Identify or plot fractions or determine lengths on number line
 Determine location of rational numbers on number line
 Determine location of rational numbers on number line, including negatives
 Condensed: Identify or plot decimals or fractions on number lines

Number Lines, Including Negatives
 Identify integers on number lines, negative
 Identify rational numbers on number lines, negative
 Identify rational numbers on number lines, vertical number lines
 Identify rational numbers on number lines, negative, vertical number lines
 Condensed: Identify rational numbers on number lines, vertical
 Condensed: Identify rational numbers on number lines, including vertical number lines
 Identify or determine rational values on number line, vertical number lines
 Plot rational numbers on number lines, negative
 Identify or plot rational numbers on number lines & interpret, realworld context
 Condensed: Identify or plot rational numbers on number lines
 Identify & compare rational numbers on number lines


Number Theory

Prime & Composite Numbers
 Identify prime & composite numbers
 Identify prime & composite numbers, realworld context

Factors & Multiples
 Identify factors or nonfactors of whole numbers
 Identify multiples or nonmultiples of whole numbers
 Identify factors or multiples of whole numbers
 Condensed: Identify factors, nonfactors, multiples, & nonmultiples of whole numbers

Prime Factorization
 Determine prime factorization of numbers up to 50
 Determine prime factorization of numbers up to 100
 Identify or complete prime factorization of numbers up to 144
 Identify equivalent expressions involving prime factorization

Greatest Common Factors
 Determine GCF of two numbers up to 100
 Determine GCF of two numbers up to 100 or multiples of 10
 Determine GCFs, realworld context
 Apply GCFs to determine number of items in groups, realworld context

Least Common Multiples
 Determine LCM of two numbers up to 100
 Determine LCM of two numbers up to 100 or multiples of 10
 Determine LCMs, realworld context
 Apply LCMs to determine number of items in groups, realworld context

Greatest Common Factors & Least Common Multiples
 Condensed: Determine GCF or LCM of two numbers up to 100 or multiples of 10
 Condensed: Determine GCFs & LCMs, realworld context
 Condensed: Apply GCFs & LCMs to determine number of items in groups, realworld context


Expressions

Expression Vocabulary
 Determine definitions of coefficient, fill in the blank
 Determine definitions of constant, fill in the blank
 Determine definitions of variable, fill in the blank
 Determine definitions of term, fill in the blank
 Determine definitions of expression, fill in the blank
 Determine definitions of evaluate, fill in the blank
 Determine definitions of operation, fill in the blank
 Determine definitions of arithmetic vocabulary, fill in the blank
 Determine definitions of relationship vocabulary, fill in the blank
 Identify parts of expressions
 Identify multiple parts of expressions

Whole Number Exponents
 Convert expanded numerical expressions to exponential form
 Convert exponential numerical expressions to expanded form
 Convert descriptions of numerical exponential expressions to exponential form
 Determine components & properties of wholenumber exponents
 Square positive integers up to 10
 Simplify or evaluate numerical exponential expressions

Translating Expressions
 Identify words or phrases that indicate specified operation or comparison
 Determine algebraic expressions that represent realworld situations
 Given phrase, determine onestep algebraic expression
 Interpret numerical expressions
 Identify equivalent multistep algebraic expressions & phrases
 Given phrase, determine multistep algebraic expression
 Given phrase, determine & evaluate multistep algebraic expression
 Determine algebraic expressions that represent realworld situations, including twovariable expressions

Equivalent Expressions
 Identify equivalent numerical expressions using counters
 Identify equivalent algebraic expressions using algebra tiles
 Identify equivalent expressions or determine simplified expressions
 Identify equivalent algebraic expressions, including realworld context
 Evaluate & identify equivalent numerical expressions, including realworld context

Evaluating Expressions

Basic Evaluating Expressions, Addition & Subtraction
 Evaluate addition expressions for specified value, one variable, whole numbers
 Evaluate subtraction expressions for specified value, one variable, whole numbers
 Evaluate addition expressions for specified value, one variable, at least one fraction
 Evaluate addition expressions for specified value, one variable, at least one decimal
 Evaluate subtraction expressions for specified value, one variable, at least one fraction
 Evaluate subtraction expressions for specified value, one variable, at least one decimal
 Evaluate expressions for specified value, one variable, only sums, at least one decimal
 Evaluate subtraction expressions for specified value, one variable, at least one decimal

Basic Evaluating Expressions, Multiplication & Division
 Evaluate multiplication expressions for specified value, one variable
 Evaluate division expressions for specified value, one variable
 Evaluate multiplication expressions for specified value, one variable, at least one fraction
 Evaluate multiplication expressions for specified value, one variable, at least one decimal
 Evaluate division expressions for specified value, one variable, at least one fraction
 Evaluate division expressions for specified value, one variable, at least one decimal

Application of Evaluating Expressions
 Condensed: Evaluate expressions for specified value, one variable
 Evaluate expressions for specified values, two variables, multiple operations, including powers & realworld context
 Condensed: Evaluate expressions, including powers, fractions, whole numbers, & decimals, including realworld context
 Evaluate or identify expressions that represent situations from descriptions, realworld context
 Evaluate expressions for specified value, one variable, including multiple operations, at least one decimal


Distributing or Factoring Expressions
 Identify equivalent expressions involving distribution
 Identify equivalent expressions involving distribution, two or more terms
 Identify algebraic expressions, involving distribution, realworld context
 Apply distributive property to numerical expressions, realworld context
 Factor GCF from linear binomial expressions, both terms positive
 Distribute or factor, linear binomial expressions

Simplifying Variable Expressions
 Simplify algebraic expressions, combine two terms, positives
 Simplify algebraic expressions, one variable, product of two factors, positives
 Simplify algebraic expressions, one variable, product of three factors, positives
 Simplify algebraic expressions, one variable, positive integer coefficients
 Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
 Simplify algebraic expressions, two variables, positive integer coefficients


Equations & Inequalities

Equations

Equivalent Equations
 Identify missing operations in numerical sentences

Solving Equations, Only Positives
 Solve x + a = b, a > 0, b > 0, x > 0
 Solve x – a = b, a > 0, b > 0, x > 0
 Solve ax = b, a > 0, b > 0
 Solve x/a = b, a > 0, b > 0
 Solve onestep linear equations, rationals

Properties of Equations
 Identify properties used in numerical expressions
 Identify properties used in numerical & algebraic expressions
 Identify properties used to solve linear equations

Solving Addition & Subtraction Equations, Including Negatives
 Solve x + a = b, a > 0, b > 0, x < 0
 Solve x + a = b, a > 0, b < 0, x < 0
 Solve x + a = b, a < 0, b > 0, x > 0
 Solve x + a = b, a < 0, b < 0, x > 0
 Solve x + a = b, a < 0, b < 0, x < 0
 Solve a + x = b
 Solve x – a = b, a < 0, b > 0, x > 0
 Solve x – a = b, a < 0, b > 0, x < 0
 Solve x – a = b, a < 0, b < 0, x < 0
 Solve x – a = b, a > 0, b < 0, x > 0
 Solve x – a = b, a > 0, b > 0, x < 0
 Condensed: Solve onestep linear equations, addition or subtraction

Solving Multiplication & Division Equations, Including Negatives
 Solve ax = b, a > 0, b < 0
 Solve ax = b, a < 0, b < 0
 Solve ax = b, a < 0, b > 0
 Solve x = b
 Solve x/a = b, a > 0, b < 0
 Solve x/a = b, a < 0, b > 0
 Solve x/a = b, a < 0, b < 0
 Condensed: Solve onestep linear equations, multiplication or division

Checking Solutions
 Identify values that solve equations, variable & constant on left side
 Identify values that solve equations, constant times variable
 Identify values that solve equations, variable divided by constant
 Identify values that solve equations, variable & constant on right side
 Identify values that solve equations
 Identify equations with given solution

Writing & Solving Equations, Addition
 Determine addition equations, realworld context
 Determine & solve addition equations, including realworld context
 Determine, solve, & apply addition equations, realworld context
 Solve addition equations, realworld context
 Determine & solve or apply addition equations, realworld context

Writing & Solving Equations, Multiplication
 Determine multiplication equations, realworld context
 Determine & solve multiplication equations, realworld context
 Determine & solve multiplication equations, including realworld context
 Determine & solve multiplication equations, including required rounding, realworld context
 Determine, solve, & apply multiplication equations, realworld context
 Determine, solve, & apply multiplication equations, including required rounding, realworld context

Writing & Solving Equations, Mixed
 Determine onestep equations, including decimals, realworld context
 Given onestep linear equation, identify realworld situation represented by equation
 Given rate & time, determine distance
 Given distance & rate or time, determine missing quantity
 Determine solutions to problems using common formulas, including simple interest, area & perimeter, & d = rt, realworld context


Inequalities

Checking Solutions
 Identify values that solve inequalities, variable & constant on left side
 Identify values that solve inequalities, variable & constant on right side
 Identify values that solve inequalities, constant minus variable on left side
 Identify values that solve inequalities, constant minus variable on right side
 Identify values that solve inequalities

Solving Inequalities, Only Positives
 Solve onestep inequalities, x + #
 Solve onestep inequalities, x – #
 Condensed: Solve onestep inequalities, x ± #
 Solve onestep inequalities, a * x, a > 0
 Solve & graph onestep inequalities, x + #
 Solve & graph onestep inequalities, x – #
 Condensed: Solve & graph onestep inequalities, x ± #
 Solve & graph onestep inequalities, a * x, a > 0

Solving Inequalities, Including Negatives
 Solve onestep inequalities, a * x, a < 0
 Solve onestep inequalities, x/a, a > 0
 Solve onestep inequalities, x/a, a < 0
 Condensed: Solve onestep inequalities, x/a

Solving & Graphing Inequalities, Including Negatives
 Condensed: Solve & graph onestep inequalities, x ± #
 Solve & graph onestep inequalities, a * x, a < 0
 Condensed: Solve & graph onestep inequalities, a * x
 Solve & graph onestep inequalities, x/a, a > 0
 Solve & graph onestep inequalities, x/a, a < 0
 Condensed: Solve & graph onestep inequalities, x/a
 Solve & graph onestep inequalities, whole number coefficients
 Solve & graph onestep inequalities, integer coefficients
 Solve & graph onestep inequalities, including fractional coefficients
 Solve & graph onestep inequalities, including negative & fractional coefficients

Basic Writing & Graphing Inequalities
 Determine graph from inequality or inequality from graph
 Graph inequalities on number line
 Given graph, determine inequality

Application of Writing Inequalities
 Represent realworld problems as inequalities
 Determine onestep inequalities, including realworld context
 Determine onestep inequalities, rational numbers, including realworld context
 Given description, determine inequality, graph, & possible solutions
 Given inequality, identify phrase or realworld problem that represents inequality
 Given onestep inequality, identify realworld problem modeled by inequality
 Given onestep inequality, identify realworld problem modeled by inequality, rational numbers
 Identify onestep inequalities that model realworld problems or interpret inequality components
 Determine, solve, & graph onestep inequalities, including realworld context



Linear Relationships

Linear Relationships, Only Proportional

Identifying Independent & Dependent Variables
 Given description, identify dependent or independent variable
 Given equation, identify dependent or independent variable
 Given table, identify dependent or independent variable
 Given table or graph, identify dependent or independent variable

Interpreting Points
 Determine or interpret points on graphs showing proportional relationships
 Given constant of proportionality, determine or interpret point, realworld context

Writing Equations, Completing Tables & Graphs
 Given unit rate, determine graph of proportional relationship, realworld context
 Determine graph of proportional relationship, realworld context
 Given two points, determine linear graph & constant of proportionality
 Given constant of proportionality, determine table, graph, or equation
 Given table, determine constant of proportionality, graph, or equation
 Given equation, determine constant of proportionality, graph, or table
 Given graph, determine constant of proportionality, table, or equation
 Condensed: Determine equivalent representations of proportional relationships
 Determine or identify equivalent representations of proportional relationships
 Determine equations, tables, & graphs for proportional relationships, realworld context
 Given visual representation of proportional relationship, determine equation, table, & graph, realworld context
 Identify representation of proportional relationship, various representations, realworld context


Linear Relationships, Proportional & NonProportional

Additive & Multiplicative Relationships
 Identify graphs of additive & multiplicative relationships
 Given table, determine additive or multiplicative equation
 Identify components of additive & multiplicative equations
 Identify equivalent representations of additive & multiplicative relationships
 Identify equivalent representations of additive & multiplicative relationships, including decimals & fractions
 Identify situations modeled by additive & multiplicative relationships
 Identify situations modeled by tables or equations, y = mx or y = x + b
 Identify proportional & nonproportional relationships, realworld context
 Identify tables that represent realworld situations, y = mx or y = x + b
 Determine equations that represent realworld situations, y = mx or y = x + b

Finding Constant of Proportionality
 Given equation, determine constant of proportionality
 Given equation, determine constant of proportionality, realworld context
 Given table, determine constant of proportionality
 Given graph, determine constant of proportionality, including realworld context
 Determine constants of proportionality, realworld context
 Condensed: Determine constants of proportionality
 Given table, determine graph & constant of proportionality

Identifying Proportional vs. NonProportional
 Identify tables showing proportional relationship
 Identify graphs showing proportional relationship
 Identify equations showing proportional relationship
 Identify tables, graphs, or equations showing proportional relationship

Writing Equations, Completing Tables & Graphs
 Given linear equation & table, identify graph
 Given linear equation & table, determine graph
 Given linear graph, determine yvalues in table
 Given linear graph, determine yvalues in table & equation
 Given linear equation, determine yvalues in table & graph, first quadrant
 Determine equations that represent realworld situations, including twostep equations
 Determine additive & multiplicative equations that represent realworld situations
 Given graph of proportional relationship, determine table & equation, realworld context



Geometry

2D Figures
 Classify angles from figure
 Classify triangles by sides
 Classify triangles by angles
 Classify triangle based on given angle measures
 Classify triangles based on angles & sides
 Classify quadrilaterals shapes based on attributes
 Classify polygons based on number of sides or relationship to other shapes
 Classify polygons based on angles & parallel or perpendicular lines
 Classify polygons using graphic organizers
 Classify polygons using graphic organizers, including types of triangles

3D Figures
 Identify 3D figures & their bases
 Identify equivalent representations of 3D figures & nets
 Determine 2D orthographic representation of 3D blocks

Triangle AngleSide Relationships
 Given two angle measures in triangle, determine angle measure
 Determine smallest & largest sides or angles in triangle
 Order angles in triangles
 Given congruent sides, identify congruent angles of isosceles triangle
 Given congruent angles, identify congruent sides of isosceles triangle
 Apply triangle inequality theorem to determine range of values for unknown side
 Apply triangle inequality theorem to determine side lengths
 Apply triangle angle sum theorem to determine appropriate equation & angles, algebraic expressions

Perimeter

Modeling Perimeter
 Given model, identify formula & determine perimeter of rectangles
 Given model, identify formula & determine perimeter of rectangles, including decimal dimensions
 Condensed: Identify formula & determine perimeter of rectangles & squares

Basic Perimeter
 Determine perimeter of rectangles
 Given sides of rectangle, determine perimeter
 Determine perimeter of rectangles, including decimal dimensions
 Determine side length or perimeter of squares
 Given perimeter & one dimension of rectangle, determine missing dimension
 Given perimeter of rectangle & one side, determine dimension
 Given perimeter of rectangle & one side, determine dimension, including decimals

Application of Perimeter
 Given sides of rectangle, determine perimeter
 Condensed: Determine perimeter of rectangles, including realworld context
 Determine perimeter of rectangles, realworld context
 Determine perimeter of rectangles, including decimal dimensions, realworld context
 Given perimeter & relationship between sides, determine specific dimension
 Determine perimeter of polygons, including realworld context
 Determine circumference of circle, exact answers, multiple choice, including realworld context
 Given radius or diameter, determine circumference
 Estimate diameter or circumference & identify equations using π


Area

Trapezoid Area

Basic Trapezoid Area
 Determine area of trapezoids
 Given area & base lengths of trapezoid, determine height

Application & Modeling of Trapezoid Area
 Determine area of triangles using models that decompose & rearrange parts
 Given height & bases of trapezoid, determine area
 Determine equations that represent area of trapezoids, realworld context
 Given area & bases of trapezoid, determine height


Composite & Mixed Figure Area
 Determine algebraic expressions that represent area of rectangles & triangles
 Determine areas of triangles & trapezoids
 Given area, determine dimensions of triangles
 Condensed: Determine areas & dimensions of triangles & trapezoids
 Condensed: Determine equations that represent area of triangles & quadrilaterals, realworld context
 Determine perimeter of composite figures containing rectangles & squares, including realworld context
 Determine area of composite figures on coordinate plane, no circular shapes
 Determine area of polygons in coordinate plane
 Determine area of polygons in coordinate plane, realworld context
 Determine area of composite figures, rectangle with various figures attached, no circular parts
 Determine area of composite figures, no circular shapes
 Condensed: Determine area using models that decompose & rearrange parts

Triangle Area

Basic Triangle Area
 Determine area of triangles, internal height
 Determine area of triangles, external height
 Determine area of triangles
 Determine area of triangles, internal height, mixed numbers
 Determine area of triangles, external height, mixed numbers
 Determine area of triangles, mixed numbers
 Given area & one dimension of triangle, determine missing dimension
 Given area & one dimension of triangle, determine missing dimension, mixed numbers

Application & Modeling of Triangle Area
 Given base & height of triangle, determine area
 Determine area of triangles using models that decompose & rearrange parts
 Determine equations that represent area of triangles, realworld context
 Given area & one dimension of triangle, determine missing dimension


Circle Area
 Determine area of circle, exact answers, including realworld context
 Given radius or diameter, determine area
 Given radius or diameter, determine area or circumference
 Condensed: Determine area or circumference of circle
 Identify approximate formulas for circumference & area of circles

Rectangle & Parallelogram Area

Modeling Area of Rectangles & Parallelograms
 Given sides of rectangle, determine area, model provided
 Given model, identify formula & determine area of square
 Given model, identify formula & determine area of rectangle
 Condensed: Given model, identify formula & determine area of square or rectangle
 Determine area of rectangles with fractional dimensions using tiling method
 Determine area of parallelograms, model provided
 Determine area of parallelograms using models that decompose & rearrange parts

Basic Area of Rectangles & Parallelograms
 Given length & width of rectangle, determine area
 Given sides of rectangle, determine area
 Determine area of rectangles with fractional dimensions
 Determine area of parallelograms
 Determine areas of rectangles & parallelograms
 Given area & one dimension of rectangle, determine missing dimension
 Given area of rectangle & one dimension, determine other dimension
 Given area & one dimension of parallelogram, determine missing dimension
 Given area, determine dimensions of rectangles & parallelograms
 Condensed: Determine areas & dimensions of rectangles & parallelograms

Application of Area of Rectangles & Parallelograms
 Determine equations that represent area of rectangles, realworld context
 Condensed: Determine area of rectangles, including realworld context
 Given sides of rectangle & cost per square unit, determine area & total cost, realworld context
 Determine area of shaded region between nested rectangles
 Given perimeter or side length, determine area of square, including realworld context
 Determine equations that represent area of parallelograms, realworld context
 Given base & height of rectangle or parallelogram, determine area
 Determine area of missing dimension of rectangles, realworld context
 Given area & one dimension of rectangle or parallelogram, determine missing dimension



Area & Perimeter
 Condensed: Identify formula & determine perimeter of rectangles & squares
 Determine area or perimeter of parallelograms
 Condensed: Determine equations that represent area of triangles & quadrilaterals, realworld context
 Determine dimension of rectangles, including realworld context

Surface Area

Calculating Surface Area with Nets
 Identify equivalent representations of 3D figures & nets
 Given net, determine surface area of rectangular prism
 Given net, determine surface area of prisms
 Given net, determine lateral surface area of prisms

Surface Area of Rectangular & Triangular Prisms
 Determine surface area of rectangular prisms
 Determine surface area of triangular prisms
 Determine surface areas of 3D figures, no circles


Volume

Unit Cube Volume
 Determine relationship between area, volume, & dimensions
 Determine relationship between area, volume, square units, & cubic units
 Determine volume of rectangular 3D figures using unit cubes
 Determine volume of rectangular prisms using unit cubes
 Determine volume of rectangular prisms using unit cubes
 Determine volume of rectangular prisms, various representations

Basic Volume, Cubes
 Determine volume of cubes, whole numbers or decimals
 Determine volume of cubes, whole numbers, decimals, or fractions, no visual provided
 Determine volume of cubes, whole numbers, decimals, or fractions

Basic Volume, Rectangular Prisms
 Determine volume of rectangular prisms, whole numbers, volume less than 10,000
 Determine volume of rectangular prisms, whole numbers or decimals
 Determine volume of rectangular prisms, whole numbers, decimals, or fractions
 Given base area & edge or all edges, determine volume of rectangular prism
 Determine volumes of rectangular & triangular prisms, fractional dimensions
 Given volume, determine edges of rectangular prisms
 Determine volume or edge of rectangular prisms, whole numbers, volume less than 10,000
 Determine volume or edge of rectangular prisms, whole numbers
 Condensed: Determine volume or dimension of rectangular prisms, fractional dimensions
 Determine volume of rectangular prisms, whole numbers or decimals
 Determine volumes of rectangular prisms, fractional dimensions
 Given volume, determine edge of rectangular prisms, up to fourdigit dividend, up to twodigit divisor

Application of Volume, Cubes
 Determine volume of cubes, whole numbers or decimals, realworld context
 Determine volume of cubes, whole numbers, decimals, or fractions, realworld context
 Condensed: Determine volume or side length of cubes, whole numbers, decimals, or fractions, including realworld context

Application of Volume, Rectangular Prisms
 Determine volume of rectangular prisms using repeated layers of base area, realworld context
 Determine volume of rectangular prisms using various representations of cubic units, realworld context
 Determine volume of rectangular prisms, whole numbers, including realworld context
 Determine volumes of rectangular prisms, rational dimensions, realworld context
 Determine volumes of cubes & rectangular prisms
 Determine volume of triangular prisms
 Given volume & two dimensions of rectangular prism, determine missing dimension
 Determine volume or edge of rectangular prisms, whole numbers, decimals, or fractions, realworld context
 Determine volume or edge of rectangular prisms, whole numbers or decimals, realworld context
 Determine volume of composite rectangular prisms
 Determine volume of rectangular prisms & apply associative property to volume expressions
 Condensed: Determine volumes or edges of rectangular prisms, whole numbers, decimals, or fractions, including realworld context


Coordinate Plane

Basic Coordinate Plane, Only First Quadarant
 Determine coordinates of first quadrant points
 Determine coordinates of first quadrant point, various scales
 Determine coordinates of first quadrant rational points
 Plot first quadrant points
 Plot first quadrant points, various scales
 Plot first quadrant rational points
 Plot or determine coordinates of first quadrant points
 Condensed: Plot or determine coordinates of first quadrant points
 Condensed: Plot or determine coordinates of first quadrant rational points, various scales

Application of Coordinate Plane, Only First Quadrant
 Identify description of process to plot first quadrant points
 Identify locations or parts of coordinate plane using first quadrant points
 Identify first quadrant points or parts of coordinate plane
 Determine or identify first quadrant points, realworld context
 Determine or identify first quadrant points, including cardinal directions, realworld context
 Condensed: Plot or determine coordinates of first quadrant rational points

Basic Coordinate Plane, All Quadrants
 Given integer point on graph, determine coordinates, point on axis
 Given integer point on graph, determine coordinates
 Given lattice point, determine coordinates
 Given rational point, determine location on coordinate plane
 Plot integer points on coordinate plane, point on axis
 Plot integer points
 Plot points on coordinate plane, student selects scales
 Plot rational points on coordinate plane
 Plot rational points on coordinate plane, graph scale at most onehalf
 Condensed: Plot integer points or determine coordinates
 Condensed: Plot or identify points on coordinate plane
 Plot or identify rational points on coordinate plane

Reflections & Distance Between Points
 Determine coordinates of reflected points
 Determine distance between points on coordinate plane, horizontal or vertical
 Determine distance between points on coordinate plane, horizontal or vertical, realworld context



Measurement & Data

Conversions

Basic Customary Conversions
 Convert between customary units of weight & mass
 Convert between customary units of volume & capacity
 Convert between customary units of length
 Convert between customary units of length
 Given unit conversion rate, convert measurement units

Application of Customary Conversions
 Convert between customary units of volume & capacity
 Convert between customary units of weight & mass
 Condensed: Convert between customary units
 Convert between customary units, including realworld context
 Convert between customary units, realworld context
 Convert between customary units to find sums or differences, including realworld context

Basic Metric Conversions
 Convert between metric units of length
 Convert between metric units

Application of Metric Conversions
 Convert between metric units of weight & mass
 Convert between metric units of volume & capacity
 Convert between metric units of length, realworld context
 Convert between metric units of weight & mass, realworld context
 Convert between metric units of volume & capacity, realworld context
 Convert between metric units, including realworld context
 Given conversion chart, convert between metric units, realworld context
 Condensed: Convert between metric units
 Convert between metric units, realworld context
 Condensed: Convert between customary or metric units

Basic Customary & Metric Conversions
 Convert customary to metric units of length, calculator expected
 Convert metric to customary units of length, calculator expected
 Convert customary to metric units of volume & capacity, calculator expected
 Convert metric to customary units of volume & capacity, calculator expected
 Convert customary to metric units of weight & mass, calculator expected
 Convert metric to customary units of weight & mass, calculator expected
 Condensed: Convert between customary & metric, calculator expected

Application of Customary to Metric & Metric to Customary
 Convert customary to metric units of length
 Convert customary to metric units of weight & mass
 Convert customary to metric units of volume & capacity
 Convert metric to customary units of length
 Convert metric to customary units of weight & mass
 Convert metric to customary units of volume & capacity

Application of OneStep Customary & Metric Conversions
 Condensed: Convert between customary & metric
 Convert between customary & metric using conversion graphs
 Convert between customary & metric using unit rates
 Convert between customary & metric using dimensional analysis
 Convert between customary & metric, proportion bias
 Condensed: Convert between customary & metric using multiple representations of conversion factor
 Convert between customary & metric, realworld context
 Convert between customary & metric using scale factors

Application of MultiStep Customary & Metric Conversions
 Convert customary to metric units of length, including multistep
 Convert customary to metric units of weight & mass, including multistep
 Convert customary to metric units of volume & capacity, including multistep
 Convert metric to customary units of length, including multistep
 Convert metric to customary units of weight & mass, including multistep
 Convert metric to customary units of volume & capacity, including multistep
 Condensed: Convert between customary & metric, including multistep


Charts & Graphs

Frequency Tables
 Given data, identify frequency table or determine missing element of table
 Solve onestep problems from frequency tables, realworld context
 Solve problems from frequency tables, realworld context
 Solve onestep problems from frequency & relative frequency tables, realworld context
 Solve multistep problems from frequency tables, realworld context
 Condensed: Interpret twoway frequency tables

Line Plots
 Given data represented in various ways, identify dot plot
 Determine equivalent fraction data sets & line plots
 Solve onestep problems from dot plots, realworld context
 Solve problems involving dot plots
 Solve problems involving line plots & fractions
 Add or subtract fractions from line plots, common denominator
 Solve multistep problems from dot plots, realworld context

Bar & Double Bar Graphs
 Given table, determine equivalent bar graph
 Given bar graph, determine equivalent table
 Given table, determine equivalent bar graph, including double bar graphs
 Condensed: Given bar graph, determine equivalent table or pictograph
 Determine or interpret percentage bar graphs
 Solve problems involving bar graphs
 Solve onestep problems from bar graphs, realworld context
 Solve onestep problems from double bar graphs, realworld context
 Add, subtract, & multiply fractions in bar graphs, common denominator
 Solve multistep problems from bar graphs, realworld context
 Solve multistep problems from double bar graphs, realworld context

Stem&Leaf Plots
 Given data, identify stemandleaf plot
 Given data, identify stemandleaf plot
 Solve onestep problems from stemandleaf plots, realworld context
 Solve multistep problems from stemandleaf plots, realworld context

Scatter Plots
 Given data, determine scatter plot
 Identify equivalent representations of data in tables & scatter plots
 Solve onestep problems from scatter plots, realworld context
 Solve multistep problems from scatter plots, realworld context

Histograms
 Given various representations of data, determine histogram

Pictographs
 Given bar graph, determine equivalent pictograph
 Given pictograph, determine equivalent table
 Given pictograph, determine equivalent bar graph
 Condensed: Given pictograph, determine equivalent bar graph or table

Pie Charts
 Solve problems involving interpretation of pie charts
 Solve problems involving interpretation of pie charts displayed using fractions, decimals, or percents
 Determine percent of category in pie charts

Mixed Charts & Graphs
 Determine unit of measurement for data, various representations
 Determine sample size, various representations
 Condensed: Given table, determine equivalent bar graph or pictograph
 Condensed: Given data, represent with dot plot or stemandleaf plot
 Condensed: Determine equivalent visual representations of data
 Determine solutions to problems involving bar graphs & line graphs
 Condensed: Solve onestep problems from various plots, graphs, & tables, realworld context
 Condensed: Solve multistep problems from various plots, graphs, & tables, realworld context



Probability & Statistics

Measures of Center & Spread

Calculating Measures of Center & Spread
 Determine mean, median, mode, or range
 Determine mean, median, mode, or range from stem&leaf plots
 Determine mean, median, mode, or range from various graphs
 Condensed: Determine mean, median, mode, or range, including graphs
 Given various representations of data, identify mean, median, mode, & range
 Given mean, median, mode, or range, determine missing value in data set
 Given additional value in data set, determine change in mean, median, mode, or range
 Given mean, median, or range, determine missing or additional value in data set
 Determine interquartile range of data
 Determine mean absolute deviation
 Determine mean absolute deviation, realworld context
 Condensed: Solve problems involving interpretation of box plots & stem&leaf plots

Interpretting Measures of Center & Spread
 Given various representations of data, identify outlier
 Solve problems involving interpretation of histograms
 Identify variability in realworld situations
 Determine collection method, distribution shape, & unit of measure for data
 Identify measures of center based on data distribution
 Identify measures of variability based on data distribution
 Identify & interpret measures of center
 Identify & interpret measures of variability
 Determine or interpret shapes & features of graphs
 Determine or interpret measures of center & spread from graphs


Box Plots
 Determine characteristics of boxplots
 Solve problems involving interpretation of box plots
 Solve problems involving interpretation of stacked box plots, realworld context
 Determine fivenumber summary
 Given boxplot, determine values from fivenumber summary
 Condensed: Determine fivenumber summary, including box plots
 Solve problems involving fivenumber summary

Dot Plots
 Determine mean from dot plots
 Determine median from dot plots
 Determine & compare means from two dot plots
 Determine & compare medians from two dot plots
 Determine mean absolute deviation from dot plots
 Compare mean absolute deviations from two dot plots
 Compare characteristics of sidebyside dot plots

Statistical Data
 Determine whether data was counted or measured
 Determine whether data is categorical or numerical
 Identify statistical questions
 Identify biased samples & questions
 Identify samples & populations
 Identify variability in realworld situations
 Determine definitions of data collection & distribution vocabulary, fill in the blank

Basic Probability
 Determine sample spaces
 Classify probabilities by levels of likelihood
 Determine probabilities of single events
 Determine theoretical probabilities
 Determine experimental probabilities
 Determine theoretical probabilities, fraction answers
 Determine experimental probabilities, fraction answers
 Determine probabilities of flipping coins specified number of times
 Determine probabilities & complementary probabilities of single events, including visual models
 Determine predicted values, theoretical probability
 Determine predicted values, experimental probability


Financial Literacy
 Identify positive & negative factors in establishing credit history
 Identify value of credit report
 Determine similarities & differences between debit & credit cards
 Identify methods of college payment
 Balance check register
 Determine budget allocations for spending, saving, & giving
 Solve problems involving information on credit report
 Given features & costs, determine best financial institution based on specified conditions
 Determine annual income
 Determine lifetime income
 Estimate costs of twoyear college education
 Estimate costs of fouryear college education