Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 14 of 22 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 211 - 220 Statements Last Updated: Sep 23, 2013 Goal: Number and Operations Skills and Concepts to Enhance (73% Probability*) 201 - 210 Skills and Concepts to Develop (50% Probability*) 211 - 220 Skills and Concepts to Introduce (27% Probability*) 221 - 230 Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten • Multiplies a 2- or 3-digit number by multiples of 10 or 100 • Multiplies a 3-digit number by a 3-digit number • Divides a 2-digit number by a 1-digit number with no remainder • Divides a 2-digit number or a 3-digit number by a 1-digit number with a remainder • Divides a 3-digit number by a 1-digit number with no remainder • Divides a 4-digit number by a 1-digit number with no remainder • Divides a 3-digit number by a multiple of 10 • Divides a 4-digit number by a 2-digit number • Adds decimals to the thousandths place horizontally with and without regrouping • Subtracts decimals to the hundredths place (same number of digits) with regrouping • Multiplies a decimal by whole number • Divides decimal by a whole number • Divides a 4-digit number by a 1-digit number with no remainder • Divides a 3-digit number by a 2-digit number • Divides a 4-digit number by a 2-digit number • Adds decimals to the hundredths place in horizontal format (not same number of digits) • Adds decimals to the thousandths place horizontally with and without regrouping • Adds decimals through the hundred-thousandths place • Multiplies a decimal by a decimal, vertical form (factors to tenths or hundredths) • Multiplies a decimal by a decimal (factors to hundredths) • Divides decimal by a whole number Number and Operations - Fractions Number and Operations - Fractions Number and Operations - Fractions • Adds fractions with like denominators without reducing • Adds whole numbers and fractions • Uses models to add and subtract fractions and connect the actions to algorithms • Subtracts fractions with like denominators without reducing • Subtracts mixed fractions with like denominators with no regrouping • Solves real-world 1-step problems involving addition and subtraction of fractions with like denominators • Multiplies a fraction by a fraction without reducing to simplest form (simple problem) • Identifies halves of a region using nonadjacent parts • Identifies equivalent fractions using visual representations • Expresses 1 in many different ways (e.g., 3/3, 4/4) • Converts a basic fractional numeral to lowest terms (e.g., halves, thirds, quarters) • Writes mixed numbers as improper fractions and improper fractions as mixed numbers • Compares fractions (e.g., common denominator, 1 in the numerator, denominator is 2, 3, 4, 6, 8, 10) • Orders fractions on a number line • Explains different interpretations of fractions (e.g., parts of a whole, parts of a set, and division of whole numbers by whole numbers) • Writes a terminating decimal as a fraction or mixed number • Adds fractions with like denominators without reducing • Adds fractions with like denominators with reducing or converting to a mixed fraction • Adds fractions with unlike denominators without reducing • Adds simple mixed fractions with unlike denominators (e.g., halves, thirds, fourths, eighths) • Subtracts simple fractions with unlike denominators without reducing (e.g., halves, quarters, thirds, eighths) • Subtracts fractions with unlike denominators without reducing • Subtracts mixed fractions with like denominators with no regrouping • Subtracts mixed fractions with unlike denominators with no regrouping • Solves real-world problems involving addition and subtraction of fractions where converting one denominator is necessary • Uses models to multiply and divide fractions and connect the actions to algorithms • Multiplies a fraction by a fraction where reducing to simplest form is necessary • Multiplies a fraction by a whole number • Solves 1-step real-world problems involving fractions with multiplication and division • Solves 1-step problems involving proportions • Identifies equivalent fractions using visual representations • Identifies a fractions in lowest terms from a region or set • Adds fractions with like denominators with reducing or converting to a mixed fraction • Adds fractions with unlike denominators without reducing • Adds fractions with unlike denominators with reducing or converting to a mixed fraction • Adds simple mixed fractions with unlike denominators (e.g., halves, thirds, fourths, eighths) • Adds mixed fractions where converting from improper fractions is necessary • Subtracts fractions with like denominators with reducing • Subtracts fractions with unlike denominators without reducing • Subtracts fractions with unlike denominators with reducing • Subtracts mixed fractions with unlike denominators with no regrouping • Subtracts whole numbers, fractions, and mixed fractions • Subtracts whole numbers, fractions, and mixed fractions with regrouping • Solves real-world problems involving addition and subtraction of fractions where converting one denominator is necessary • Uses models to multiply and divide fractions and connect the actions to algorithms • Multiplies a fraction by a fraction without reducing to simplest form (complex problem) • Multiplies a fraction by a fraction where reducing to simplest form is necessary Explanatory Notes * At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version. Generated 10/2/13, 9:40:10 AM © 2006-2013 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 15 of 22 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 211 - 220 Statements Last Updated: Sep 23, 2013 Goal: Number and Operations Skills and Concepts to Enhance (73% Probability*) 201 - 210 Skills and Concepts to Develop (50% Probability*) 211 - 220 Skills and Concepts to Introduce (27% Probability*) 221 - 230 Number and Operations - Fractions Number and Operations - Fractions Number and Operations - Fractions • Expresses the equivalent form of a fraction, decimal, and/or percent (simple fraction) • Writes the missing number in a proportion using basic facts • Identifies eighths, reduced to lowest terms, from a region or set • Determines simple equivalent fractions using multiples • Converts fractions to lowest terms • Writes mixed numbers as improper fractions and improper fractions as mixed numbers • Compares fractions on a number line • Compares fractions greater than or less than a given fraction using visual representations • Compares fractions and mixed numbers • Compares fractions and mixed numbers using symbols • Orders fractions on a number line • Explains different interpretations of fractions (e.g., parts of a whole, parts of a set, and division of whole numbers by whole numbers) • Expresses a simple fraction as a decimal • Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 • Expresses the equivalent form of a fraction, decimal, and/or percent (simple fraction) • Multiplies a fraction by a whole number • Multiplies mixed fractions • Divides a mixed fraction by a fraction • Solves 1-step real-world problems involving fractions with multiplication and division • Solves 2- or more step real-world problems involving fractions with multiplication and division • Solves problems involving fractions (e.g., multiple operations, conversions) • Solves 1-step problems involving proportions • Identifies a fractions in lowest terms from a region or set • Determines simple equivalent fractions using multiples • Determines equivalent fractions using multiples • Compares fractions (e.g., comparing numerators and denominators) • Uses alternative algorithms to explain the meaning of fraction • Writes a decimal for a shaded region to the hundredths place • Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 New Vocabulary: biggest, expanded numeral New Signs and Symbols: ¢ cent sign New Vocabulary: lowest term, lowest terms, reduce, triple New Signs and Symbols:
not equal to New Vocabulary: short, ten million New Signs and Symbols: None

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 15 of 22 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 211 - 220 Statements Last Updated: Sep 23, 2013 Goal: Number and Operations Skills and Concepts to Enhance (73% Probability*) 201 - 210 Skills and Concepts to Develop (50% Probability*) 211 - 220 Skills and Concepts to Introduce (27% Probability*) 221 - 230 Number and Operations - Fractions Number and Operations - Fractions Number and Operations - Fractions • Expresses the equivalent form of a fraction, decimal, and/or percent (simple fraction) • Writes the missing number in a proportion using basic facts • Identifies eighths, reduced to lowest terms, from a region or set • Determines simple equivalent fractions using multiples • Converts fractions to lowest terms • Writes mixed numbers as improper fractions and improper fractions as mixed numbers • Compares fractions on a number line • Compares fractions greater than or less than a given fraction using visual representations • Compares fractions and mixed numbers • Compares fractions and mixed numbers using symbols • Orders fractions on a number line • Explains different interpretations of fractions (e.g., parts of a whole, parts of a set, and division of whole numbers by whole numbers) • Expresses a simple fraction as a decimal • Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 • Expresses the equivalent form of a fraction, decimal, and/or percent (simple fraction) • Multiplies a fraction by a whole number • Multiplies mixed fractions • Divides a mixed fraction by a fraction • Solves 1-step real-world problems involving fractions with multiplication and division • Solves 2- or more step real-world problems involving fractions with multiplication and division • Solves problems involving fractions (e.g., multiple operations, conversions) • Solves 1-step problems involving proportions • Identifies a fractions in lowest terms from a region or set • Determines simple equivalent fractions using multiples • Determines equivalent fractions using multiples • Compares fractions (e.g., comparing numerators and denominators) • Uses alternative algorithms to explain the meaning of fraction • Writes a decimal for a shaded region to the hundredths place • Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 New Vocabulary: biggest, expanded numeral New Signs and Symbols: ¢ cent sign New Vocabulary: lowest term, lowest terms, reduce, triple New Signs and Symbols:
not equal to New Vocabulary: short, ten million New Signs and Symbols: None Explanatory Notes * At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version. Generated 10/2/13, 9:40:10 AM © 2006-2013 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 16 of 22 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 221 - 230 Statements Last Updated: Sep 23, 2013 Goal: Number and Operations Skills and Concepts to Enhance (73% Probability*) 211 - 220 Skills and Concepts to Develop (50% Probability*) 221 - 230 Skills and Concepts to Introduce (27% Probability*) 231 - 240 Understand Place Value, Counting, and Cardinality Understand Place Value, Counting, and Cardinality Understand Place Value, Counting, and Cardinality • Predicts the relative size of the answer when computing with 10's, 100's, 1000's • Rounds 4-, 5-, and 6-digit whole numbers to the nearest hundred • Rounds 4-, 5-, and 6-digit whole numbers to the nearest thousand • Rounds 4-, 5-, and 6-digit whole numbers to the nearest ten thousand • Rounds wholes numbers to the nearest billion • Writes whole numbers in standard and expanded form through the hundred thousands • Represents a decimal to the hundredths place (e.g., three hundredths = 0.03) • Compares and orders decimals past the thousandths place • Rounds decimals to the nearest whole number • Rounds decimals to the nearest tenth • Applies base ten place value concepts to solve problems using decimals • Multiplies a decimal by 10, 100, 1000 • Divides a decimal by 10, 100, 1000 • Determines the relative magnitude of whole numbers • Rounds whole numbers to the nearest million • Writes equivalent forms of whole numbers using place value (numbers 100 or greater) (e.g., 253 = 2 hundreds, 5 tens, and 3 ones) • Writes whole numbers in standard and exponential form • Represents a decimal to thousandths place (e.g., three thousandths = 0.003) • Represents a decimal to the hundred thousandths place - (e.g., three hundred thousandths = 0. 00003) • Compares and orders decimals to the hundredths place (not same number of digits after decimal) • Compares and orders decimals to the thousandths place (not same number of digits after decimal) • Compares and orders decimals past the thousandths place • Rounds decimals to the nearest hundredth • Rounds decimals to nearest thousandth • Identifies the place value and value of each digit to the hundredths and thousandths • Applies base ten place value concepts to solve problems using decimals • Divides numbers by powers of 10 • Multiplies a decimal by 10, 100, 1000 • Divides a decimal by 10, 100, 1000 • Determines the relative magnitude of whole numbers • Writes whole numbers in standard and exponential form • Rounds decimals to the nearest hundredth Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten • Uses rounding to estimate answers to difficult multiplication and division problems (whole numbers only) • Subtracts numbers with 5 digits or more with regrouping • Instantly recalls basic multiplication and division facts in a table • Multiplies a 2-digit number by a 2-digit number with regrouping • Multiplies a 3-digit number by a 2-digit number with regrouping • Performs mental computation with multiplication • Uses multiplication strategies to explain computation (e.g., doubles, 9- patterns, decomposing, partial products) • Multiplies a 3-digit number by a 3-digit number • Multiplies a 4- or more digit number by multiples of 100 or 1000 • Multiplies multiple-digit numbers • Divides a 2-digit number or a 3-digit number by a 1-digit number with a remainder • Divides a 4-digit number by a 1-digit number with no remainder • Divides a 3-digit number by a 2-digit number • Multiplies multiple-digit numbers • Divides a 4-digit number by a 2-digit number • Adds decimals to the hundredths place in horizontal format (not same number of digits) • Adds decimals through the hundred-thousandths place • Subtracts decimals to the hundredths place (not same number of digits) • Subtracts a decimal from a whole number, horizontally • Multiplies a decimal by a decimal, vertical form (factors to tenths or hundredths) • Multiplies a decimal by a decimal (factors to hundredths) • Multiplies a decimal by a decimal (factors to thousandths) • Divides a decimal by a decimal • Subtracts a decimal from a whole number, horizontally • Divides a whole number by a decimal • Divides a decimal by a decimal

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 16 of 22 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 221 - 230 Statements Last Updated: Sep 23, 2013 Goal: Number and Operations Skills and Concepts to Enhance (73% Probability*) 211 - 220 Skills and Concepts to Develop (50% Probability*) 221 - 230 Skills and Concepts to Introduce (27% Probability*) 231 - 240 Understand Place Value, Counting, and Cardinality Understand Place Value, Counting, and Cardinality Understand Place Value, Counting, and Cardinality • Predicts the relative size of the answer when computing with 10's, 100's, 1000's • Rounds 4-, 5-, and 6-digit whole numbers to the nearest hundred • Rounds 4-, 5-, and 6-digit whole numbers to the nearest thousand • Rounds 4-, 5-, and 6-digit whole numbers to the nearest ten thousand • Rounds wholes numbers to the nearest billion • Writes whole numbers in standard and expanded form through the hundred thousands • Represents a decimal to the hundredths place (e.g., three hundredths = 0.03) • Compares and orders decimals past the thousandths place • Rounds decimals to the nearest whole number • Rounds decimals to the nearest tenth • Applies base ten place value concepts to solve problems using decimals • Multiplies a decimal by 10, 100, 1000 • Divides a decimal by 10, 100, 1000 • Determines the relative magnitude of whole numbers • Rounds whole numbers to the nearest million • Writes equivalent forms of whole numbers using place value (numbers 100 or greater) (e.g., 253 = 2 hundreds, 5 tens, and 3 ones) • Writes whole numbers in standard and exponential form • Represents a decimal to thousandths place (e.g., three thousandths = 0.003) • Represents a decimal to the hundred thousandths place - (e.g., three hundred thousandths = 0. 00003) • Compares and orders decimals to the hundredths place (not same number of digits after decimal) • Compares and orders decimals to the thousandths place (not same number of digits after decimal) • Compares and orders decimals past the thousandths place • Rounds decimals to the nearest hundredth • Rounds decimals to nearest thousandth • Identifies the place value and value of each digit to the hundredths and thousandths • Applies base ten place value concepts to solve problems using decimals • Divides numbers by powers of 10 • Multiplies a decimal by 10, 100, 1000 • Divides a decimal by 10, 100, 1000 • Determines the relative magnitude of whole numbers • Writes whole numbers in standard and exponential form • Rounds decimals to the nearest hundredth Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten • Uses rounding to estimate answers to difficult multiplication and division problems (whole numbers only) • Subtracts numbers with 5 digits or more with regrouping • Instantly recalls basic multiplication and division facts in a table • Multiplies a 2-digit number by a 2-digit number with regrouping • Multiplies a 3-digit number by a 2-digit number with regrouping • Performs mental computation with multiplication • Uses multiplication strategies to explain computation (e.g., doubles, 9- patterns, decomposing, partial products) • Multiplies a 3-digit number by a 3-digit number • Multiplies a 4- or more digit number by multiples of 100 or 1000 • Multiplies multiple-digit numbers • Divides a 2-digit number or a 3-digit number by a 1-digit number with a remainder • Divides a 4-digit number by a 1-digit number with no remainder • Divides a 3-digit number by a 2-digit number • Multiplies multiple-digit numbers • Divides a 4-digit number by a 2-digit number • Adds decimals to the hundredths place in horizontal format (not same number of digits) • Adds decimals through the hundred-thousandths place • Subtracts decimals to the hundredths place (not same number of digits) • Subtracts a decimal from a whole number, horizontally • Multiplies a decimal by a decimal, vertical form (factors to tenths or hundredths) • Multiplies a decimal by a decimal (factors to hundredths) • Multiplies a decimal by a decimal (factors to thousandths) • Divides a decimal by a decimal • Subtracts a decimal from a whole number, horizontally • Divides a whole number by a decimal • Divides a decimal by a decimal Explanatory Notes * At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version. Generated 10/2/13, 9:40:10 AM © 2006-2013 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 17 of 22 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 221 - 230 Statements Last Updated: Sep 23, 2013 Goal: Number and Operations Skills and Concepts to Enhance (73% Probability*) 211 - 220 Skills and Concepts to Develop (50% Probability*) 221 - 230 Skills and Concepts to Introduce (27% Probability*) 231 - 240 Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten • Divides a 4-digit number by a 2-digit number • Adds decimals to the hundredths place in horizontal format (not same number of digits) • Adds decimals to the thousandths place horizontally with and without regrouping • Adds decimals through the hundred-thousandths place • Multiplies a decimal by a decimal, vertical form (factors to tenths or hundredths) • Multiplies a decimal by a decimal (factors to hundredths) • Divides decimal by a whole number Number and Operations - Fractions Number and Operations - Fractions Number and Operations - Fractions • Adds fractions with like denominators without reducing • Adds fractions with like denominators with reducing or converting to a mixed fraction • Adds fractions with unlike denominators without reducing • Adds simple mixed fractions with unlike denominators (e.g., halves, thirds, fourths, eighths) • Subtracts simple fractions with unlike denominators without reducing (e.g., halves, quarters, thirds, eighths) • Subtracts fractions with unlike denominators without reducing • Subtracts mixed fractions with like denominators with no regrouping • Subtracts mixed fractions with unlike denominators with no regrouping • Solves real-world problems involving addition and subtraction of fractions where converting one denominator is necessary • Uses models to multiply and divide fractions and connect the actions to algorithms • Multiplies a fraction by a fraction where reducing to simplest form is necessary • Multiplies a fraction by a whole number • Solves 1-step real-world problems involving fractions with multiplication and division • Solves 1-step problems involving proportions • Identifies equivalent fractions using visual representations • Identifies a fractions in lowest terms from a region or set • Identifies eighths, reduced to lowest terms, from a region or set • Determines simple equivalent fractions using multiples • Converts fractions to lowest terms • Writes mixed numbers as improper fractions and improper fractions as mixed numbers • Adds fractions with like denominators with reducing or converting to a mixed fraction • Adds fractions with unlike denominators without reducing • Adds fractions with unlike denominators with reducing or converting to a mixed fraction • Adds simple mixed fractions with unlike denominators (e.g., halves, thirds, fourths, eighths) • Adds mixed fractions where converting from improper fractions is necessary • Subtracts fractions with like denominators with reducing • Subtracts fractions with unlike denominators without reducing • Subtracts fractions with unlike denominators with reducing • Subtracts mixed fractions with unlike denominators with no regrouping • Subtracts whole numbers, fractions, and mixed fractions • Subtracts whole numbers, fractions, and mixed fractions with regrouping • Solves real-world problems involving addition and subtraction of fractions where converting one denominator is necessary • Uses models to multiply and divide fractions and connect the actions to algorithms • Multiplies a fraction by a fraction without reducing to simplest form (complex problem) • Multiplies a fraction by a fraction where reducing to simplest form is necessary • Multiplies a fraction by a whole number • Multiplies mixed fractions • Divides a mixed fraction by a fraction • Solves 1-step real-world problems involving fractions with multiplication and division • Adds fractions with unlike denominators with reducing or converting to a mixed fraction • Adds simple mixed fractions with unlike denominators (e.g., halves, thirds, fourths, eighths) • Adds mixed fractions where converting from improper fractions is necessary • Subtracts whole numbers, fractions, and mixed fractions • Subtracts whole numbers, fractions, and mixed fractions with regrouping • Solves real-world problems involving addition and subtraction of fractions where converting both denominators is necessary • Uses models to multiply and divide fractions and connect the actions to algorithms • Multiplies mixed fractions • Uses models to multiply and divide fractions and mixed fractions and connect the actions to algorithms • Divides a fraction by a whole number • Divides a whole number by a fraction • Divides a mixed fraction by a fraction • Solves 2- or more step real-world problems involving fractions with multiplication and division • Solves problems involving fractions (e.g., multiple operations, conversions) • Compares fractions (e.g., comparing numerators and denominators) • Writes a fraction as a decimal and vice versa • Compares and orders decimal and fractional coordinates on a number line

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 17 of 22 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 221 - 230 Statements Last Updated: Sep 23, 2013 Goal: Number and Operations Skills and Concepts to Enhance (73% Probability*) 211 - 220 Skills and Concepts to Develop (50% Probability*) 221 - 230 Skills and Concepts to Introduce (27% Probability*) 231 - 240 Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten • Divides a 4-digit number by a 2-digit number • Adds decimals to the hundredths place in horizontal format (not same number of digits) • Adds decimals to the thousandths place horizontally with and without regrouping • Adds decimals through the hundred-thousandths place • Multiplies a decimal by a decimal, vertical form (factors to tenths or hundredths) • Multiplies a decimal by a decimal (factors to hundredths) • Divides decimal by a whole number Number and Operations - Fractions Number and Operations - Fractions Number and Operations - Fractions • Adds fractions with like denominators without reducing • Adds fractions with like denominators with reducing or converting to a mixed fraction • Adds fractions with unlike denominators without reducing • Adds simple mixed fractions with unlike denominators (e.g., halves, thirds, fourths, eighths) • Subtracts simple fractions with unlike denominators without reducing (e.g., halves, quarters, thirds, eighths) • Subtracts fractions with unlike denominators without reducing • Subtracts mixed fractions with like denominators with no regrouping • Subtracts mixed fractions with unlike denominators with no regrouping • Solves real-world problems involving addition and subtraction of fractions where converting one denominator is necessary • Uses models to multiply and divide fractions and connect the actions to algorithms • Multiplies a fraction by a fraction where reducing to simplest form is necessary • Multiplies a fraction by a whole number • Solves 1-step real-world problems involving fractions with multiplication and division • Solves 1-step problems involving proportions • Identifies equivalent fractions using visual representations • Identifies a fractions in lowest terms from a region or set • Identifies eighths, reduced to lowest terms, from a region or set • Determines simple equivalent fractions using multiples • Converts fractions to lowest terms • Writes mixed numbers as improper fractions and improper fractions as mixed numbers • Adds fractions with like denominators with reducing or converting to a mixed fraction • Adds fractions with unlike denominators without reducing • Adds fractions with unlike denominators with reducing or converting to a mixed fraction • Adds simple mixed fractions with unlike denominators (e.g., halves, thirds, fourths, eighths) • Adds mixed fractions where converting from improper fractions is necessary • Subtracts fractions with like denominators with reducing • Subtracts fractions with unlike denominators without reducing • Subtracts fractions with unlike denominators with reducing • Subtracts mixed fractions with unlike denominators with no regrouping • Subtracts whole numbers, fractions, and mixed fractions • Subtracts whole numbers, fractions, and mixed fractions with regrouping • Solves real-world problems involving addition and subtraction of fractions where converting one denominator is necessary • Uses models to multiply and divide fractions and connect the actions to algorithms • Multiplies a fraction by a fraction without reducing to simplest form (complex problem) • Multiplies a fraction by a fraction where reducing to simplest form is necessary • Multiplies a fraction by a whole number • Multiplies mixed fractions • Divides a mixed fraction by a fraction • Solves 1-step real-world problems involving fractions with multiplication and division • Adds fractions with unlike denominators with reducing or converting to a mixed fraction • Adds simple mixed fractions with unlike denominators (e.g., halves, thirds, fourths, eighths) • Adds mixed fractions where converting from improper fractions is necessary • Subtracts whole numbers, fractions, and mixed fractions • Subtracts whole numbers, fractions, and mixed fractions with regrouping • Solves real-world problems involving addition and subtraction of fractions where converting both denominators is necessary • Uses models to multiply and divide fractions and connect the actions to algorithms • Multiplies mixed fractions • Uses models to multiply and divide fractions and mixed fractions and connect the actions to algorithms • Divides a fraction by a whole number • Divides a whole number by a fraction • Divides a mixed fraction by a fraction • Solves 2- or more step real-world problems involving fractions with multiplication and division • Solves problems involving fractions (e.g., multiple operations, conversions) • Compares fractions (e.g., comparing numerators and denominators) • Writes a fraction as a decimal and vice versa • Compares and orders decimal and fractional coordinates on a number line Explanatory Notes * At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version. Generated 10/2/13, 9:40:10 AM © 2006-2013 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 18 of 22 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 221 - 230 Statements Last Updated: Sep 23, 2013 Goal: Number and Operations Skills and Concepts to Enhance (73% Probability*) 211 - 220 Skills and Concepts to Develop (50% Probability*) 221 - 230 Skills and Concepts to Introduce (27% Probability*) 231 - 240 Number and Operations - Fractions Number and Operations - Fractions Number and Operations - Fractions • Compares fractions on a number line • Compares fractions greater than or less than a given fraction using visual representations • Compares fractions and mixed numbers • Compares fractions and mixed numbers using symbols • Orders fractions on a number line • Explains different interpretations of fractions (e.g., parts of a whole, parts of a set, and division of whole numbers by whole numbers) • Expresses a simple fraction as a decimal • Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 • Expresses the equivalent form of a fraction, decimal, and/or percent (simple fraction) • Solves 2- or more step real-world problems involving fractions with multiplication and division • Solves problems involving fractions (e.g., multiple operations, conversions) • Solves 1-step problems involving proportions • Identifies a fractions in lowest terms from a region or set • Determines simple equivalent fractions using multiples • Determines equivalent fractions using multiples • Compares fractions (e.g., comparing numerators and denominators) • Uses alternative algorithms to explain the meaning of fraction • Writes a decimal for a shaded region to the hundredths place • Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 New Vocabulary: lowest term, lowest terms, reduce, triple New Signs and Symbols:
not equal to New Vocabulary: short, ten million New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: ÷ division

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 18 of 22 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 221 - 230 Statements Last Updated: Sep 23, 2013 Goal: Number and Operations Skills and Concepts to Enhance (73% Probability*) 211 - 220 Skills and Concepts to Develop (50% Probability*) 221 - 230 Skills and Concepts to Introduce (27% Probability*) 231 - 240 Number and Operations - Fractions Number and Operations - Fractions Number and Operations - Fractions • Compares fractions on a number line • Compares fractions greater than or less than a given fraction using visual representations • Compares fractions and mixed numbers • Compares fractions and mixed numbers using symbols • Orders fractions on a number line • Explains different interpretations of fractions (e.g., parts of a whole, parts of a set, and division of whole numbers by whole numbers) • Expresses a simple fraction as a decimal • Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 • Expresses the equivalent form of a fraction, decimal, and/or percent (simple fraction) • Solves 2- or more step real-world problems involving fractions with multiplication and division • Solves problems involving fractions (e.g., multiple operations, conversions) • Solves 1-step problems involving proportions • Identifies a fractions in lowest terms from a region or set • Determines simple equivalent fractions using multiples • Determines equivalent fractions using multiples • Compares fractions (e.g., comparing numerators and denominators) • Uses alternative algorithms to explain the meaning of fraction • Writes a decimal for a shaded region to the hundredths place • Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 New Vocabulary: lowest term, lowest terms, reduce, triple New Signs and Symbols:
not equal to New Vocabulary: short, ten million New Signs and Symbols: None New Vocabulary: None New Signs and Symbols: ÷ division Explanatory Notes * At the range mid-point, this is the probability students would correctly answer items measuring these concepts and skills. Both data from test items and review by NWEA curriculum specialists are used to place Learning Continuum statements into appropriate RIT ranges. Blank cells indicate data are limited or unavailable for this range or document version. Generated 10/2/13, 9:40:10 AM © 2006-2013 Northwest Evaluation Association. All rights reserved. Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 19 of 22 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Sep 23, 2013 Goal: Number and Operations Skills and Concepts to Enhance (73% Probability*) 221 - 230 Skills and Concepts to Develop (50% Probability*) 231 - 240 Skills and Concepts to Introduce (27% Probability*) > 240 Understand Place Value, Counting, and Cardinality Understand Place Value, Counting, and Cardinality Understand Place Value, Counting, and Cardinality • Multiplies a decimal by 10, 100, 1000 • Divides a decimal by 10, 100, 1000 • Determines the relative magnitude of whole numbers • Rounds whole numbers to the nearest million • Writes equivalent forms of whole numbers using place value (numbers 100 or greater) (e.g., 253 = 2 hundreds, 5 tens, and 3 ones) • Writes whole numbers in standard and exponential form • Represents a decimal to thousandths place (e.g., three thousandths = 0.003) • Represents a decimal to the hundred thousandths place - (e.g., three hundred thousandths = 0. 00003) • Compares and orders decimals to the hundredths place (not same number of digits after decimal) • Compares and orders decimals to the thousandths place (not same number of digits after decimal) • Compares and orders decimals past the thousandths place • Rounds decimals to the nearest hundredth • Rounds decimals to nearest thousandth • Identifies the place value and value of each digit to the hundredths and thousandths • Applies base ten place value concepts to solve problems using decimals • Divides numbers by powers of 10 • Multiplies a decimal by 10, 100, 1000 • Divides a decimal by 10, 100, 1000 • Determines the relative magnitude of whole numbers • Writes whole numbers in standard and exponential form • Rounds decimals to the nearest hundredth Number and Operations in Base Ten Number and Operations in Base Ten Number and Operations in Base Ten • Multiplies multiple-digit numbers • Divides a 4-digit number by a 2-digit number • Adds decimals to the hundredths place in horizontal format (not same number of digits) • Adds decimals through the hundred-thousandths place • Subtracts decimals to the hundredths place (not same number of digits) • Subtracts a decimal from a whole number, horizontally • Multiplies a decimal by a decimal, vertical form (factors to tenths or hundredths) • Multiplies a decimal by a decimal (factors to hundredths) • Multiplies a decimal by a decimal (factors to thousandths) • Divides a decimal by a decimal • Subtracts a decimal from a whole number, horizontally • Divides a whole number by a decimal • Divides a decimal by a decimal Number and Operations - Fractions Number and Operations - Fractions Number and Operations - Fractions • Adds fractions with like denominators with reducing or converting to a mixed fraction • Adds fractions with unlike denominators without reducing • Adds fractions with unlike denominators with reducing or converting to a mixed fraction • Solves open sentences with fractions • Identifies the least common multiple of whole numbers