Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 31 of 40 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 Goal: The Real and Complex Number Systems 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*) 241 - 250 Ratios and Proportional Relationships Ratios and Proportional Relationships Ratios and Proportional Relationships • Solves real-world problems involving decimals (not money) using multiplication • Solves problems involving ratios • Solves 1-step problems involving proportions • Calculates basic percents of a number (e.g., 10%, 20%, 25%, 50%, 100%) • Calculates a percent of a number (e.g., 6% of 30) • Calculates a number from a percent (e.g., 4 is 9% of what) • Solves problems involving percents • Solves problems involving tax and tips • Converts between inches, feet, and yards • Converts between millimeters, centimeters, meters, and kilometers • Uses dimensional analysis for unit conversions (length) • Solves problems involving length in the customary system and converts to larger or smaller units • Converts between ounces and pounds • Converts between ounces, pounds, and tons • Converts between cups, pints, quarts, and gallons • Converts within the metric system • Apply dimensional analysis to simple real-world problems (capacity) • Solves problems involving capacity in the customary system and converts to larger or smaller units • Computes 2-step conversions between units of time • Applies dimensional analysis to simple real-world problems (time) • Solves complex problems involving miles per gallon • Solves complex problems involving miles/kilometers per hour • Solves problems involving rates • Solves problems involving perimeter and converts to larger or smaller units • Interprets data given in circle graphs to solve complex problems (with percents) • Expresses a percent as a fraction and vice versa • Writes a ratio as a percent and vice versa • Uses concrete and pictorial models to represent ratios • Writes the missing number in a proportion with numbers other than basic facts (e.g., 5/13=?/117) • Uses estimation to solve problems involving proportional reasoning (decimals only) • Solves real-world problems involving decimals (not money) using multiplication • Solves problems involving equivalent fractions (analysis) • Solves problems involving ratios • Solves multiple-step problems involving proportions • Calculates a percent of a number (e.g., 6% of 30) • Calculates the percent one number is of another (e.g., 20 is what % of 90) • Solves problems involving percents • Solves problems involving percents (analysis) • Solves problems involving simple percent discounts (e.g., finding sale price) • Solves problems involving percent increase and decrease • Solves problems involving tax and tips • Calculates commission/deductions and total pay • Converts between millimeters, centimeters, meters, and kilometers • Uses dimensional analysis for unit conversions (length) • Converts between the customary and metric system given conversion ratios (2-step, length) • Apply dimensional analysis to simple real-world problems (length) • Solves problems involving length in the customary system and converts to larger or smaller units • Converts between grams and kilograms • Solves problems involving weight in the customary system and converts to larger or smaller units • Converts within the metric system • Apply dimensional analysis to simple real-world problems (capacity) • Solves problems involving capacity in the customary system and converts to larger or smaller units • Solves complex problems involving miles per gallon • Solves problems comparing unit prices • Solves problems involving rates • Interprets data given in circle graphs to solve complex problems (with percents) • Expresses a percent as a fraction and vice versa • Writes a ratio as a percent and vice versa • Identifies the ratio from a given real-world situation • Solves real-world problems involving decimals (not money) using multiplication • Solves multiple-step problems involving proportions • Solves problems involving a fractional increase • Calculates the percent one number is of another (e.g., 20 is what % of 90) • Calculates a percent of a rational number (e.g., 6% of 0.78) • Solves problems involving percents (analysis) • Solves problems involving simple percent discounts (e.g., finding sale price) • Solves problems involving complex percent discounts (e.g., finding percent discount, regular price) • Calculates commission/deductions and total pay • Solves problems involving successive discounts • Uses dimensional analysis for unit conversions (length) • Apply dimensional analysis to simple real-world problems (length) • Solves problems involving weight in the customary system and converts to larger or smaller units • Uses dimensional analysis for unit conversions (time) • Solves problems involving rate conversions (e.g., mi/hr to ft/sec) • Identifies the ratio from a given real-world situation 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 8/7/14, 9:48:57 PM © 2006-2014 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 32 of 40 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 Goal: The Real and Complex Number Systems 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*) 241 - 250 Perform Operations Perform Operations Perform Operations • Uses rounding to estimate answers to real-world problems involving multiplication and division of numbers less than 100 (whole numbers only) • Uses rounding to estimate answers to real-world problems involving numbers less than 1000 with multiplication and division (whole numbers only) • Uses rounding to estimate answers to real-world problems involving numbers 1000 or greater using multiplication and division (whole numbers only) • Multiplies multiple-digit numbers • Divides a 4-digit number by a 2-digit number • Divides multiple-digit numbers • Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) • Solves real-world multiple-step problems involving whole numbers • Demonstrates an understanding of multiple properties • 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 multiple-digit numbers • Divides numbers by powers of 10 • 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 fraction • Divides a fraction by a whole number • Divides a whole number by a fraction • Divides a mixed fraction by a whole number • Divides a whole number by a mixed fraction • Divides a mixed fraction by a fraction • Divides a fraction by a mixed fraction • Divides a mixed fraction by a mixed fraction • Solves 2- or more step real-world problems involving fractions with multiplication and division • Solves problems involving fractions (e.g., multiple operations, conversions) • Subtracts a decimal from a whole number, horizontally • Multiplies a decimal by 10, 100, 1000 • Divides a whole number by a decimal • Divides a decimal by 10, 100, 1000 • Divides a decimal by a decimal • Adds integers with unlike signs • Adds several positive and negative integers • Subtracts integers • Solves problems involving addition and subtraction of integers • Multiplies integers with like signs • Uses a number line to determine the distance between a positive and negative number • Subtracts integers • Uses the multiplicative inverse property with rational numbers • Uses factor and multiple concepts to solve difficult problems • Identifies the least common multiple of whole numbers

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 32 of 40 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 Goal: The Real and Complex Number Systems 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*) 241 - 250 Perform Operations Perform Operations Perform Operations • Uses rounding to estimate answers to real-world problems involving multiplication and division of numbers less than 100 (whole numbers only) • Uses rounding to estimate answers to real-world problems involving numbers less than 1000 with multiplication and division (whole numbers only) • Uses rounding to estimate answers to real-world problems involving numbers 1000 or greater using multiplication and division (whole numbers only) • Multiplies multiple-digit numbers • Divides a 4-digit number by a 2-digit number • Divides multiple-digit numbers • Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) • Solves real-world multiple-step problems involving whole numbers • Demonstrates an understanding of multiple properties • 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 multiple-digit numbers • Divides numbers by powers of 10 • 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 fraction • Divides a fraction by a whole number • Divides a whole number by a fraction • Divides a mixed fraction by a whole number • Divides a whole number by a mixed fraction • Divides a mixed fraction by a fraction • Divides a fraction by a mixed fraction • Divides a mixed fraction by a mixed fraction • Solves 2- or more step real-world problems involving fractions with multiplication and division • Solves problems involving fractions (e.g., multiple operations, conversions) • Subtracts a decimal from a whole number, horizontally • Multiplies a decimal by 10, 100, 1000 • Divides a whole number by a decimal • Divides a decimal by 10, 100, 1000 • Divides a decimal by a decimal • Adds integers with unlike signs • Adds several positive and negative integers • Subtracts integers • Solves problems involving addition and subtraction of integers • Multiplies integers with like signs • Uses a number line to determine the distance between a positive and negative number • Subtracts integers • Uses the multiplicative inverse property with rational numbers • Uses factor and multiple concepts to solve difficult problems • Identifies the least common multiple of whole numbers 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 8/7/14, 9:48:57 PM © 2006-2014 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 33 of 40 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 Goal: The Real and Complex Number Systems 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*) 241 - 250 Perform Operations Perform Operations Perform Operations • Divides a fraction by a fraction • 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) • 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 decimals to the thousandths place, horizontally, with and without regrouping • Subtracts decimals through the hundred-thousandths place, horizontally • 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 10, 100, 1000 • Multiplies a decimal by a decimal (factors to thousandths) • Divides a decimal by 10, 100, 1000 • Divides a decimal by a decimal • Computes with dollars and cents over $5.00 and converts to decimals (multiplication/division) • Computes the value of multiple bills and coins (multiplication/division) • Calculate the sum of integers using a number line • Adds integers with unlike signs • Adds several positive and negative integers • Uses models to add and subtract integers and connect the actions to algorithms • Subtracts integers • Solves real-world problems involving addition and subtraction of integers • Solves problems involving addition and subtraction of integers • Multiplies integers with unlike signs • Divides integers with unlike signs • Divides integers with like signs • Adds rational expressions in decimal form • Divides integers with like signs • Subtracts rational expressions in decimal form • Multiplies rational expressions • Identifies the additive inverse property • Interprets data given in tables to solve problems • Writes a fraction as a decimal and vice versa • Writes a fraction as a mixed decimal and vice versa

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 33 of 40 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 Goal: The Real and Complex Number Systems 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*) 241 - 250 Perform Operations Perform Operations Perform Operations • Divides a fraction by a fraction • 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) • 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 decimals to the thousandths place, horizontally, with and without regrouping • Subtracts decimals through the hundred-thousandths place, horizontally • 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 10, 100, 1000 • Multiplies a decimal by a decimal (factors to thousandths) • Divides a decimal by 10, 100, 1000 • Divides a decimal by a decimal • Computes with dollars and cents over $5.00 and converts to decimals (multiplication/division) • Computes the value of multiple bills and coins (multiplication/division) • Calculate the sum of integers using a number line • Adds integers with unlike signs • Adds several positive and negative integers • Uses models to add and subtract integers and connect the actions to algorithms • Subtracts integers • Solves real-world problems involving addition and subtraction of integers • Solves problems involving addition and subtraction of integers • Multiplies integers with unlike signs • Divides integers with unlike signs • Divides integers with like signs • Adds rational expressions in decimal form • Divides integers with like signs • Subtracts rational expressions in decimal form • Multiplies rational expressions • Identifies the additive inverse property • Interprets data given in tables to solve problems • Writes a fraction as a decimal and vice versa • Writes a fraction as a mixed decimal and vice versa 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 8/7/14, 9:48:57 PM © 2006-2014 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 34 of 40 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 Goal: The Real and Complex Number Systems 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*) 241 - 250 Perform Operations Perform Operations Perform Operations • Identifies the additive inverse property • Solves difficult problems involving elapsed time, with the conversion of hours • Interprets data given in tables to solve problems • Writes a simple mixed fraction as a decimal and vice versa • Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 • Determines factors of whole numbers • Uses multiple number theory concepts to solve problems (e.g., factors, digits, odd/even, divisibility) • Uses factor and multiple concepts to solve simple problems • Identifies common factors of two or more numbers • Identifies the greatest common factor of whole numbers Extend and Use Properties Extend and Use Properties Extend and Use Properties • Graphs ordered pairs in all quadrants • Computes and interprets distance, given a set of ordered pairs (horizontal and vertical lines) • 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 • 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 • 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) • Writes a decimal for a shaded region to the hundredths place • 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 • Simplifies rational expressions with absolute value • Graphs ordered pairs in all quadrants • Computes and interprets distance, given a set of ordered pairs (horizontal and vertical lines) • Determines the relative magnitude of whole numbers • Writes whole numbers in standard and exponential form • Compares fractions (e.g., comparing numerators and denominators) • Rounds decimals to the nearest hundredth • Compares and orders decimal and fractional coordinates on a number line • Estimates the square roots of numbers • Simplifies expressions containing square roots • Uses expressions with absolute value to represent situations • Computes and interprets distance, given a set of ordered pairs (horizontal and vertical lines)

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 34 of 40 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 Goal: The Real and Complex Number Systems 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*) 241 - 250 Perform Operations Perform Operations Perform Operations • Identifies the additive inverse property • Solves difficult problems involving elapsed time, with the conversion of hours • Interprets data given in tables to solve problems • Writes a simple mixed fraction as a decimal and vice versa • Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 • Determines factors of whole numbers • Uses multiple number theory concepts to solve problems (e.g., factors, digits, odd/even, divisibility) • Uses factor and multiple concepts to solve simple problems • Identifies common factors of two or more numbers • Identifies the greatest common factor of whole numbers Extend and Use Properties Extend and Use Properties Extend and Use Properties • Graphs ordered pairs in all quadrants • Computes and interprets distance, given a set of ordered pairs (horizontal and vertical lines) • 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 • 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 • 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) • Writes a decimal for a shaded region to the hundredths place • 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 • Simplifies rational expressions with absolute value • Graphs ordered pairs in all quadrants • Computes and interprets distance, given a set of ordered pairs (horizontal and vertical lines) • Determines the relative magnitude of whole numbers • Writes whole numbers in standard and exponential form • Compares fractions (e.g., comparing numerators and denominators) • Rounds decimals to the nearest hundredth • Compares and orders decimal and fractional coordinates on a number line • Estimates the square roots of numbers • Simplifies expressions containing square roots • Uses expressions with absolute value to represent situations • Computes and interprets distance, given a set of ordered pairs (horizontal and vertical lines) 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 8/7/14, 9:48:57 PM © 2006-2014 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 35 of 40 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 Goal: The Real and Complex Number Systems 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*) 241 - 250 Extend and Use Properties Extend and Use Properties Extend and Use Properties • 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 • Compares two integers • Orders integers on a number line • Orders integers • Locates rational numbers on a number line • Orders rational numbers, in a/b form • Orders fractions and decimals to the hundred thousandths New Vocabulary: real number, ten million New Signs and Symbols: ( ) parenthesis around an integer, cm centimeter/centimetre, °C degrees Celsius, km kilometer/kilometre, mL milliliter/millilitre, # number, / per, + positive number, : ratio New Vocabulary: discount, equality New Signs and Symbols: || absolute value, oz ounce New Vocabulary: feet per second, least common multiple New Signs and Symbols: LCM lowest common multiple, sec second, square root symbol

Please refer to the DesCartes Use Agreement for terms of use. Educational Standard: Common Core Mathematics K-12: 2010 Page 35 of 40 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 231 - 240 Statements Last Updated: Aug 4, 2014 Goal: The Real and Complex Number Systems 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*) 241 - 250 Extend and Use Properties Extend and Use Properties Extend and Use Properties • 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 • Compares two integers • Orders integers on a number line • Orders integers • Locates rational numbers on a number line • Orders rational numbers, in a/b form • Orders fractions and decimals to the hundred thousandths New Vocabulary: real number, ten million New Signs and Symbols: ( ) parenthesis around an integer, cm centimeter/centimetre, °C degrees Celsius, km kilometer/kilometre, mL milliliter/millilitre, # number, / per, + positive number, : ratio New Vocabulary: discount, equality New Signs and Symbols: || absolute value, oz ounce New Vocabulary: feet per second, least common multiple New Signs and Symbols: LCM lowest common multiple, sec second, square root symbol 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 8/7/14, 9:48:57 PM © 2006-2014 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 36 of 40 DesCartes: A Continuum of Learning® Mathematics RIT Score Range: 241 - 250 Statements Last Updated: Aug 4, 2014 Goal: The Real and Complex Number Systems Skills and Concepts to Enhance (73% Probability*) 231 - 240 Skills and Concepts to Develop (50% Probability*) 241 - 250 Skills and Concepts to Introduce (27% Probability*) 251 - 260 Ratios and Proportional Relationships Ratios and Proportional Relationships Ratios and Proportional Relationships • Uses estimation to solve problems involving proportional reasoning (decimals only) • Solves real-world problems involving decimals (not money) using multiplication • Solves problems involving equivalent fractions (analysis) • Solves problems involving ratios • Solves multiple-step problems involving proportions • Calculates a percent of a number (e.g., 6% of 30) • Calculates the percent one number is of another (e.g., 20 is what % of 90) • Solves problems involving percents • Solves problems involving percents (analysis) • Solves problems involving simple percent discounts (e.g., finding sale price) • Solves problems involving percent increase and decrease • Solves problems involving tax and tips • Calculates commission/deductions and total pay • Converts between millimeters, centimeters, meters, and kilometers • Uses dimensional analysis for unit conversions (length) • Converts between the customary and metric system given conversion ratios (2-step, length) • Apply dimensional analysis to simple real-world problems (length) • Solves problems involving length in the customary system and converts to larger or smaller units • Converts between grams and kilograms • Solves problems involving weight in the customary system and converts to larger or smaller units • Converts within the metric system • Apply dimensional analysis to simple real-world problems (capacity) • Solves problems involving capacity in the customary system and converts to larger or smaller units • Solves complex problems involving miles per gallon • Solves problems comparing unit prices • Solves problems involving rates • Interprets data given in circle graphs to solve complex problems (with percents) • Expresses a percent as a fraction and vice versa • Writes a ratio as a percent and vice versa • Identifies the ratio from a given real-world situation • Solves real-world problems involving decimals (not money) using multiplication • Solves multiple-step problems involving proportions • Solves problems involving a fractional increase • Calculates the percent one number is of another (e.g., 20 is what % of 90) • Calculates a percent of a rational number (e.g., 6% of 0.78) • Solves problems involving percents (analysis) • Solves problems involving simple percent discounts (e.g., finding sale price) • Solves problems involving complex percent discounts (e.g., finding percent discount, regular price) • Calculates commission/deductions and total pay • Solves problems involving successive discounts • Uses dimensional analysis for unit conversions (length) • Apply dimensional analysis to simple real-world problems (length) • Solves problems involving weight in the customary system and converts to larger or smaller units • Uses dimensional analysis for unit conversions (time) • Solves problems involving rate conversions (e.g., mi/hr to ft/sec) • Identifies the ratio from a given real-world situation • Solves problems involving complex percent discounts (e.g., finding percent discount, regular price) • Solves problems involving successive discounts • Uses dimensional analysis for unit conversions (time) • Solves problems involving rate conversions (e.g., mi/hr to ft/sec)