4th Grade Skills

Whole Numbers

Addition of Whole Numbers

Basic Addition of Whole Numbers
 Add whole numbers, one digit
 Add positive integers, addends from three to nine
 Add positive integers
 Add positive integers, up to two digits
 Add three & fourdigit whole numbers
 Condensed: Add fourdigit & three or fourdigit whole numbers
 Add fourdigit whole numbers

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


Subtraction of Whole Numbers

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

Application of Subtraction of Whole Numbers
 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

Basic Multiplication Facts
 Multiply 1 & onedigit whole numbers
 Multiply 2 & onedigit whole numbers
 Multiply 3 & onedigit whole numbers
 Multiply 4 & onedigit whole numbers
 Multiply 5 & onedigit whole numbers
 Multiply 6 & onedigit whole numbers
 Multiply 7 & onedigit whole numbers
 Multiply 8 & onedigit whole numbers
 Multiply 9 & onedigit whole numbers
 Multiply onedigit whole numbers

Modeling Multiplication of Whole Numbers
 Multiply whole numbers using area models, up to fourdigit & onedigit
 Multiply whole numbers by decomposing factors, up to fourdigit & onedigit
 Condensed: Multiply whole numbers using area models or decomposition, up to fourdigit & onedigit
 Multiply whole numbers using area models, twodigit & twodigit
 Multiply whole numbers by decomposing factors, twodigit & twodigit
 Condensed: Multiply whole numbers using area models or decomposition, twodigit & twodigit

Basic Multiplication of Whole Numbers
 Multiply whole numbers, twodigit & onedigit
 Multiply whole numbers, threedigit & onedigit
 Multiply whole numbers, fourdigit & onedigit
 Condensed: Multiply whole numbers, three or fourdigit & onedigit
 Multiply multiples of 10 & twodigit whole numbers
 Multiply whole numbers, both up to 19
 Multiply whole numbers, twodigit & twodigit

Application of Multiplication of Whole Numbers
 Multiply whole numbers, twodigit & onedigit, realworld context
 Multiply whole numbers, threedigit & onedigit, realworld context
 Multiply whole numbers, fourdigit & onedigit, realworld context
 Condensed: Multiply whole numbers, onedigit & up to fourdigit, realworld context
 Multiply whole numbers, twodigit & twodigit, realworld context
 Condensed: Multiply whole numbers, one or twodigit & up to fourdigit, realworld context
 Multiply whole numbers, up to fourdigit & up to twodigit, realworld context

Products of Ten & One Hundred
 Determine expanded notation or place value representations
 Multiply 10 & twodigit whole numbers
 Multiply multiples of 10 & onedigit whole numbers, realworld context
 Multiply 100 & twodigit whole numbers
 Multiply multiples of 100 & onedigit whole numbers, realworld context
 Condensed: Multiply multiples of 10 or 100 & onedigit whole numbers, realworld context
 Condensed: Multiply whole numbers, twodigit & 10 or 100
 Condensed: Multiply multiples of 10 or 100 & one or twodigit whole numbers, including realworld context

Multiplicative Comparisons
 Solve problems involving multiplicative comparisons
 Solve problems involving multiplicative & additive comparisons


Division of Whole Numbers

Modeling & Application of Division of Whole Numbers, No Remainders
 Determine division equations, realworld context
 Determine equivalence between arrays & division equations
 Determine equivalence between area models & division equations
 Condensed: Determine equivalence between models & division equations
 Divide whole numbers, two to fourdigit dividend, onedigit divisor, realworld context
 Divide positive integers, up to fourdigit dividend, onedigit divisor, realworld context
 Divide whole numbers, up to fivedigit dividend, up to threedigit divisor, realworld context

Basic Division of Whole Numbers, No Remainders
 Apply divisibility rules to twodigit dividends, divisor 2, 5, 10
 Apply divisibility rules to twodigit dividends, divisor 2, 3, 4, 5, 6, 9, 10
 Divide whole numbers, up to twodigit dividend, divisor up to ten
 Divide whole numbers, up to threedigit dividend, onedigit divisor

Basic Division of Whole Numbers, Remainders
 Determine quotient & remainder, onedigit dividend, onedigit divisor
 Determine quotient & remainder as fraction, onedigit dividend, onedigit divisor
 Determine quotient & remainder, twodigit dividend, onedigit divisor
 Determine quotient & remainder as fraction, twodigit dividend, onedigit divisor
 Determine quotient & remainder, threedigit dividend, onedigit divisor
 Determine quotient & remainder as fraction, threedigit dividend, onedigit divisor
 Determine quotient & remainder, fourdigit dividend, onedigit divisor
 Determine quotient & remainder as fraction, fourdigit dividend, onedigit divisor

Application of Division of Whole Numbers, Remainders
 Divide positive integers, up to fourdigit dividend, onedigit divisor, realworld context
 Determine quotient or remainder, up to fourdigit dividend, onedigit divisor, 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

Application of Mixed Operations of Whole Numbers
 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

Equations of Mixed Operations of Whole Numbers
 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


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 to specified place value, up to hundredthousand
 Round whole numbers using frontend rounding
 Estimate sums & differences of whole numbers by rounding to specified place values

Application of Rounding & Estimating 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
 Estimate sums of whole numbers, up to six digits, including realworld context
 Estimate sum of rational numbers, round both to nearest whole, realworld context
 Estimate differences of whole numbers, up to six digits, including realworld context
 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


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


Fractions

Representing Fractions
 Given various models, determine fraction, denominators 2, 3, 4, 6, 8
 Identify fractions on strip diagrams
 Identify fractions or mixed numbers on decimal grid
 Identify common fractions or mixed numbers on number line

Reducing Fractions
 Reduce fractions, denominators less than 20
 Reduce fractions, answer denominators less than 10
 Reduce fractions, answer denominators less than 30

Equivalent Fractions
 Determine equivalent fractions, number lines
 Determine equivalent fractions, strip diagrams
 Determine equivalent fractions, area models
 Determine equivalent fraction equations, area models
 Determine equivalent fraction components
 Identify or determine equivalent fraction components or fractions

Converting Fractions
 Given model, determine fraction & decimal equivalents, unreduced
 Identify decimal equivalent of fractions, realworld context
 Condensed: Determine & identify equivalent fractions & decimals, including models, including realworld context
 Convert improper fractions to unreduced mixed numbers
 Convert mixed numbers to unreduced improper fractions

Comparing & Ordering Fractions
 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
 Compare fractions between onehalf & one
 Compare fractions, denominators less than 30
 Compare fractions, different denominators
 Compare fractions, same numerators, denominators differ by one, denominators less than 10,000
 Order positive fractions

Decomposing Fractions
 Decompose fractions into sum of fractions
 Decompose fractions into sum of fractions, visual models
 Decompose fractions or mixed numbers into sum of fractions, realworld context
 Decompose fractions or mixed numbers into sum of fractions, visual models
 Condensed: Decompose fractions or mixed numbers into sum of fractions, including visual models & realworld context
 Decompose fractions or mixed numbers into sum of fractions & determine equivalent fractions & mixed numbers

Addition of Fractions

Basic Addition of Fractions, Common Denominators
 Add fractions, common denominators, unreduced
 Add fractions, common denominators, proper fraction sum
 Add fractions, common denominators, sums greater than one
 Add fractions, common denominators, mixed number sum
 Add mixed numbers, common denominators

Application of Addition of Fractions, Common Denominators
 Condensed: Add fractions, common denominators, including realworld context
 Add fractions, common denominators, realworld context

Basic Addition of Fractions, Different Denominators
 Given addition expression of two fractions, identify expression using fourths that best estimates sum
 Add fractions, denominators of 10 & 100
 Add fractions, different denominators, unreduced
 Add fractions, one denominator multiple of other, including mixed number 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

Basic Subtraction of Fractions, Common Denominators
 Subtract fractions, common denominators, unreduced
 Subtract fractions, same denominator, positive difference, including unreduced fractions
 Subtract fractions, common denominators, proper fraction difference
 Subtract mixed numbers, common denominators

Application of Subtraction of Fractions, Common Denominators
 Condensed: Subtract fractions, common denominators, including realworld context
 Subtract fractions, common denominators, realworld context

Basic Subtraction of Fractions, Different Denominators
 Given subtraction expression of two fractions, identify expression using fourths that best estimates difference
 Subtract fractions, one denominator multiple of other, proper fraction difference
 Subtract fractions, different denominators, including mixed number differences
 Subtract mixed numbers, different denominators
 Subtract mixed numbers, different denominators, borrowing required


Addition & Subtraction of Fractions

Modeling Addition & Subtraction of Fractions, Common Denominators
 Identify expressions that represent addition or subtraction of unreduced fractions modeled on number lines
 Identify expressions that represent addition or subtraction of unreduced fractions modeled by area models
 Determine & evaluate expressions representing sums & differences of fractions
 Add & subtract fractions, area models
 Add & subtract fractions, various models
 Add & subtract fractions & mixed numbers, area models

Basic Addition & Subtraction of Fractions, Common Denominators
 Condensed: Add fractions, common denominators, including realworld context
 Condensed: Add or subtract fractions, common denominators, unreduced

Modeling Addition & Subtraction of Fractions, Different Denominators
 Add & subtract fractions, fraction strips
 Condensed: Given model, determine or interpret addition & subtraction of fractions

Basic Addition & Subtraction of Fractions, Different Denominators
 Condensed: Add or subtract fractions, different denominators


Multiplication of Fractions

Modeling Multiplication of Fractions
 Identify model representation of multiplication of fraction & whole number

Basic Multiplication of Fractions
 Multiply whole numbers & unit fractions, whole number first
 Multiply whole numbers & unit fractions


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 by unit fractions, number lines
 Divide whole numbers by unit fractions, models
 Divide whole numbers & unit fractions, area models
 Divide whole numbers & unit fractions, fraction strips
 Condensed: Divide whole numbers & fractions, various models
 Identify division models & divide unit fractions by unit fractions

Basic Division of Fractions
 Determine representation of fraction as division expression
 Divide whole numbers by unit fractions
 Divide whole numbers & unit fractions



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

Modeling, Comparing, & Ordering Decimals
 Compare decimal models
 Compare decimal models, up to three models
 Order decimal models
 Condensed: Compare or order decimal models

Basic Comparing & Ordering Decimals
 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 decimals written in word form, up to four decimal places
 Compare numbers, up to fourdigit whole numbers or threedigit decimals
 Order positive decimals
 Order decimals up to 1,000,000,000

Application of Comparing & Ordering Decimals
 Condensed: Compare three to sixdigit whole numbers
 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 up to three decimal places, including realworld context
 Condensed: Compare or order decimals, up to three decimal places, including realworld context
 Compare & order decimals up to 1,000,000,000, realworld context


Converting Decimals
 Convert decimals to fractions, unreduced
 Convert decimals to unreduced fractions, realworld context
 Convert decimals to mixed numbers, unreduced
 Given model, determine fraction & decimal equivalents, unreduced
 Condensed: Determine & identify equivalent fractions & decimals, including models, including realworld context

Addition of Decimals

Basic Addition of Decimals
 Add decimals, positive, up to two 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

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


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


Number Lines
 Given range & increment, identify blank number line
 Identify decimals on number lines, vertical number lines, positive
 Identify common fractions or mixed numbers on number line
 Determine location of rational numbers on number line
 Identify or plot decimals on number lines, increment 0.5
 Identify or plot decimals on number lines, increment 0.1
 Identify or plot decimals on number lines, increment 0.2
 Identify or plot decimals or determine lengths on number line, increment 0.01
 Plot decimals on number lines, increment 0.1 or 0.01
 Condensed: Identify or plot decimals on number lines
 Condensed: Identify or plot decimals or fractions on number lines
 Identify or plot fractions or determine lengths on number line

Number Sense

Place Value

Basic Place Value
 Identify place value of specific digit
 Identify place value of specific digit, decimals
 Determine numerical value of specific digit

Application of Place Value
 Determine values of digit in hundreds place, including comparison to other place values
 Determine values of digit in thousands place, including comparison to other place values
 Determine values of digit in tenthousands place, including comparison to other place values
 Determine values of digit in hundredthousands place, including comparison to other place values
 Condensed: Determine values of specific digits, including comparison to other place values
 Determine product of number & power of 10
 Identify whole numbers with specific digit equal to digit to right divided by 10, expanded notation
 Identify numbers with specific digit equal to digit to right divided by 10, standard notation
 Identify numbers with hundredths value equal to ones value divided by 100
 Identify numbers with specific digit equal to 10 times digit to right
 Identify numbers with ones digit equal to 100 times hundredths digit
 Identify numbers with specific digit equal to digit to right divided by 10, 100, or 1,000


Number Forms

Expanded Number Forms
 Determine equivalent representations of standard & expanded notations, whole numbers
 Convert between standard & expanded notations, whole numbers
 Convert between standard & expanded notations, whole numbers, realworld context
 Condensed: Convert between standard & expanded notations, including place value words
 Determine equivalent representations of standard & expanded notations, decimals
 Convert between standard & expanded notations, up to three decimal places
 Convert between standard & expanded notations, up to three decimal places, realworld context
 Convert between word, standard, & expanded notations, including realworld context

Standard Number Forms
 Given whole number in word form, determine standard notation

Word Number Forms
 Given number in word form, determine standard notation
 Convert numbers to word form, up to 1,000,000

Mixed Number Forms
 Condensed: Convert between word & expanded notations of decimals
 Condensed: Convert between word, standard, & expanded notations
 Convert between standard & expanded notation, fraction expansions, including realworld context
 Convert between word, standard, & expanded notation, fraction expansions, including realworld context



Number Theory

Even & Odd Numbers
 Identify even & odd numbers
 Identify even & odd numbers, realworld context
 Determine even & odd numbers using divisibility

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

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


Patterns & Sequences
 Given pattern of shapes, identify shape that completes pattern
 Given table, determine & extend patterns, addition
 Given table, determine & extend patterns, subtraction
 Given table, determine & extend patterns, multiplication
 Condensed: Given table, determine & extend patterns
 Condensed: Identify shapes that complete patterns or relationship between numeric patterns
 Determine missing elements in tables, subtraction
 Determine specific element from pattern represented in table
 Given description of pattern, determine first five terms
 Given description of patterns, determine first five terms for each pattern

Geometry

Angles, Lines, & Rays

Identify Angles, Lines & Rays
 Identify characteristics of points, lines, segments & rays from diagrams
 Identify characteristics of points, lines, segments & rays from descriptions
 Condensed: Identify characteristics of points, lines, segments & rays
 Classify angles from figure
 Identify types of angles in figures
 Identify angle names
 Identify angles, lines, & segments in figures

Determine Angle Measure
 Measure angles using protractor, realworld context
 Measure angles using protractor
 Identify angles with specified measures
 Given two angle measures in triangle, determine angle measure
 Determine angle measures in figures
 Estimate angle measures
 Identify 90Â°, 180Â°, 270Â°, & 360Â° angles


2D Figures

Lines of Symmetry
 Identify symmetric figures
 Identify lines of symmetry of 2D figures

Parallel & Perpendicular Lines
 Identify intersecting lines in figures, realworld context
 Identify parallel & perpendicular lines in figures
 Identify parallel & perpendicular lines in figures, realworld context

Classifying Figures
 Classify triangle based on given angle measures
 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


Perimeter of Rectangles

Basic Perimeter of Rectangles
 Determine perimeter of rectangles
 Given sides of rectangle, determine perimeter
 Determine side length or perimeter of squares
 Given perimeter & one dimension of rectangle, determine missing dimension
 Given perimeter of rectangle & one side, determine dimension

Application of Perimeter of Rectangles
 Given sides of rectangle, determine perimeter
 Determine perimeter of rectangles, realworld context
 Given model, identify formula & determine perimeter of rectangles
 Condensed: Determine perimeter of rectangles, including realworld context
 Determine perimeter of composite figures containing rectangles & squares, including realworld context


Area of Rectangles

Application & Modeling of Area of Rectangles
 Given model, identify formula & determine area of rectangle
 Given sides of rectangle & cost per square unit, determine area & total cost, realworld context
 Determine area of missing dimension of rectangles, realworld context

Basic Area of Rectangles
 Given sides of rectangle, determine area
 Given area & one dimension of rectangle, determine missing dimension



Measurement & Data

Conversions

Basic Conversions
 Convert between customary units of length
 Convert between customary units of weight & mass
 Convert between customary units of volume & capacity

Application of OneStep Conversions
 Given conversion chart, convert between metric units, realworld context
 Determine equivalent measurements using table
 Convert between customary units, including realworld context
 Convert between metric units, including realworld context
 Convert between metric units, realworld context
 Convert between metric units of length & determine appropriate relative units
 Convert between metric units of weight & determine appropriate relative units

Application of MultiStep Conversions
 Convert between customary units, realworld context
 Convert between customary units of length & determine appropriate relative units
 Convert between metric units of capacity & determine appropriate relative units
 Condensed: Convert between metric units of length, weight, & capacity & determine appropriate relative units
 Convert between customary units to find sums or differences, including realworld context


Measurement Word Problems
 Add, subtract, & multiply integer masses, metric units, realworld context
 Add & subtract decimal distances, metric units, realworld context
 Add & subtract mixed number distances, customary units, realworld context
 Solve problems involving interpretation of various visual diagrams

Time
 Identify digital times before or after hour
 Given time before or after hour, determine digital time
 Identify analog times before or after hour
 Determine time intervals
 Given analog or digital times, determine time passed
 Convert between units of time, days, hours, minutes, & seconds
 Convert between units of time, days, weeks, months, & years
 Condensed: Convert between units of time
 Condensed: Convert between units of time & determine time intervals

Money
 Round money to nearest dollar
 Determine value of collection of coins & bills
 Compare values of collections of coins & bills
 Make change, up to $5 paid


Charts & Graphs

Translating Charts & Graphs

Identify Bar Graph
 Given pictograph, determine equivalent bar graph
 Condensed: Given pictograph, determine equivalent bar graph or table
 Given table, determine equivalent bar graph
 Given table, determine equivalent bar graph, including double bar graphs

Identify Pictograph
 Given bar graph, determine equivalent pictograph
 Given table, determine equivalent pictograph

Identify Table
 Given data, identify frequency table or determine missing element of table
 Given pictograph, determine equivalent table
 Given bar graph, determine equivalent table

MIxed Charts & Graphs
 Given data represented in various ways, identify dot plot
 Given data, identify stemandleaf plot
 Condensed: Given pictograph, determine equivalent bar graph or table
 Condensed: Given bar graph, determine equivalent table or pictograph
 Condensed: Given table, determine equivalent bar graph or pictograph
 Condensed: Determine equivalent visual representations of data


Interpreting Charts & Graphs

Bar & Double Bar Graphs
 Solve onestep problems from bar graphs, realworld context
 Solve problems involving bar graphs
 Solve problems involving interpretation of various graphs
 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

Dot Plots
 Solve onestep problems from dot plots, realworld context
 Solve multistep problems from dot plots, realworld context

Stem&Leaf Plots
 Solve onestep problems from stemandleaf plots, realworld context
 Solve multistep problems from stemandleaf plots, realworld context



Probability
 Determine sample spaces
 Determine probabilities of single events
 Classify probabilities by levels of likelihood
 Determine theoretical probabilities, fraction answers
 Determine experimental probabilities, fraction answers

Financial Literacy
 Identify fixed & variable expenses
 Determine profits
 Determine budget allocations for spending, saving, & giving
 Identify purpose of financial institutions
 Identify advantages & disadvantages of various savings options