Math 2-5

Operations and Algebraic Thinking (2-5)

Math: Operations and Algebraic Thinking: Add & Subtract: Represent and Solve Problems ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Operations and Algebraic Thinking: Add & Subtract: Represent and Solve ProblemsRIT 221-230: Solves open sentences with calculations on both sides of the sentence

RIT 211-220: Demonstrates an understanding of the inverse relationship between addition and subtraction Uses algebraic reasoning to solve problems involving equality relationships Solves open sentences with calculations on both sides of the sentence

RIT 201-210: Solves real-world whole number problems involving subtraction with numbers 100 and under (analysis) Solves whole number subtraction word problems with numbers over 1000 Demonstrates an understanding of the commutative property of addition Demonstrates an understanding of the zero property of addition (identity) Uses algebraic reasoning to solve problems involving equality relationships Solves 1-step open sentences with missing addends (numbers over 100) Solves 2-step open sentences with missing addends Solves open sentences with basic-facts calculations on both sides of the sentence

RIT 191-200: Determines the operation needed from a simple problem Solves real-world whole number addition problems with sums to 20 (result unknown) - with extraneous information given Solves whole number addition word problems with sums over 1000 Solves real-world whole number problems involving subtraction w/ numbers 100 and under, and under 1000 Solves whole number subtraction word problems with numbers over 1000 Uses algebraic reasoning to solve problems involving equality relationships Solves basic facts addition & subtraction open sentences using diagrams and models (e.g., using balances) Solves 1-step open sentences with missing addends (numbers 100 and under) Solves 1-step open sentences with missing addends (numbers over 100) Solves 2-step open sentences with missing addends

RIT 181-190: Determines the operation needed from a simple problem Writes a number sentence for a simple problem solving situation Solves real-world whole number addition problems with sums to 20 (result unknown) - with extraneous information given Solves real-world whole number addition problems with sums to 20 (start unknown) Solves real-world whole number addition problems with sums to 100 (result unknown) Solves real-world whole number addition problems with sums to 1000 Solves real-world whole number problems involving subtraction with numbers under 20 Solves real-world whole number problems involving subtraction with numbers 100 and under Solves real-world whole number problems involving subtraction with numbers under 1000 Solves real-world whole number problems involving addition and subtraction Solves basic facts addition & subtraction open sentences using diagrams and models (e.g., using balances) Solves 1-step open sentences with missing addends (numbers 100 and under)

RIT 171-180: Determines the operation needed from a simple problem Writes a number sentence for a simple problem solving situation Solves real-world whole number addition problems with sums to 20 (result unknown) Solves real-world whole number addition problems with sums to 20 (start unknown) Solves real-world whole number addition problems with sums to 20 (change unknown) Solves real-world whole number addition problems with sums to 100 (result unknown)

Solves real-world whole number addition problems with sums to 1000 Solves real-world whole number problems involving subtraction with numbers under 20 Demonstrates an understanding that vertical and horizontal representations are equivalent Solves basic-facts open sentences - addition and subtraction

RIT Below 171: Solves real-world whole number addition problems with sums to 20 (result unknown) Solves basic-facts open sentences - addition and subtraction

Math: Operations and Algebraic Thinking: Multiply & Divide: Represent and Solve Problems ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Operations and Algebraic Thinking: Multiply & Divide: Represent, Solve Problems Students:RIT 221-230: Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) Describes and uses a variable with whole numbers, multiplication, and division in a contextual situation Solves 2-step open sentences with missing factors

RIT 211-220: Uses number sense strategies to solve problems (multiplication/division) Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects) Solves problems using the inverse relationship between multiplication and division Solves whole number word problems with division over 10 x 10 Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) Uses simple linear equations to represent problem situations Solves simple open sentences with missing factors (numbers over 100) Solves 2-step open sentences with missing factors

RIT 201-210: Determines the operation needed to solve a real-world problem Solves word problems involving whole number multiplication with numbers greater than 10 x 10 Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects) Solves word problems with whole number division facts with dividend and divisors less than 11 Solves whole number word problems with division over 10 x 10 Uses simple linear equations to represent problem situations Solves simple open sentences with missing factors (numbers 100 and under)

RIT 191-200: Determines the operation needed to solve a real-world problem Distinguishes between odd and even numbers Solves word problems involving basic whole number multiplication facts to 10 x 10 Solves word problems involving whole number multiplication with numbers greater than 10 x 10 Uses repeated subtraction for division Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated subtraction) Solves word problems with whole number division facts with dividend and divisors less than 11 Demonstrates an understanding of the zero property of multiplication Solves simple open sentences with missing factors (numbers 100 and under)

RIT 181-190: Distinguishes between odd and even numbers Solves word problems involving basic whole number multiplication facts to 10 x 10 Uses sharing for division Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated subtraction) Models multiplication and division algorithms using arrays (whole numbers) Demonstrates an understanding of the zero property of multiplication Demonstrates an understanding of the inverse relationship between multiplication and division

Math: Operations and Algebraic Thinking: Solve Problems & Analyze Patterns & Relationships ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 2

Math: Operations and Algebraic Thinking: Solve Problems & Analyze Patterns & Relationships Students:RIT Above 250: Uses factor and multiple concepts to solve difficult problems

RIT 241-250: Uses factor and multiple concepts to solve difficult problems Applies algebraic methods to solve real-world problems

RIT 231-240: Evaluates numerical expressions using the order of operations (whole numbers only) Applies algebraic methods to solve real-world problems Completes a function table according to a rule

RIT 221-230: Looks for a growing pattern to solve a problem Solves real-world problems using reasoning strategies Determines factors of whole numbers Uses factor and multiple concepts to solve simple problems Divides numbers by powers of 10 Solves real-world multiple-step problems involving whole numbers Extends a growing pattern of triangular numbers, defined by objects or diagrams Applies algebraic methods to solve theoretical problems Applies algebraic methods to solve real-world problems Completes a function table according to a rule

RIT 211-220: Looks for a growing pattern to solve a problem Solves real-world problems using reasoning strategies Determines factors of whole numbers Identifies numbers as prime Solves real-world problems involving 2-step multiple operations, whole numbers only Solves real-world multiple-step problems involving whole numbers Extends a repeating pattern of geometric shapes in a grid Extends a growing geometric pattern - using numbers Extends a pattern formed by two arithmetic growing patterns - odd and even terms (such as 1,5,4,8,7,...) Extends, or completes, growing patterns defined by equations or number facts Extends a growing pattern of numbers - explicit quadratic rule - recursive rule is to add x more each time (such as 1,2,4,7,...) Identifies rules and applies them to new patterns Applies algebraic methods to solve theoretical problems

RIT 201-210: Looks for a linear pattern to solve a problem Solves real-world problems using reasoning strategies Use patterns and their generalizations to make and justify inferences and predictions Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) Evaluates numerical expressions using grouping symbols (whole numbers only) Solves real-world problems involving 2-step multiple operations, whole numbers only Solves problems using tables Predicts from simple charts and tables Extends a growing arithmetic pattern, defined by objects or diagrams Extends a pattern formed by two arithmetic growing patterns - odd and even terms (such as 1,5,4,8,7,...) Extends a growing pattern of numbers - explicit quadratic rule - recursive rule is to add x more each time (such as 1,2,4,7,...) Extends a pattern formed by rotating a geometric figure

Math: Operations and Algebraic Thinking: Vocabulary and Signs & Symbols ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Operations and Algebraic Thinking: Vocabulary and Signs & Symbols Students:RIT 231-240: Vocabulary: none Signs and Symbols: • multiplication symbol (dot), - negative number

RIT 221-230: Vocabulary: none Signs and Symbols: none

RIT 211-220: Vocabulary: proof Signs and Symbols: ? a variable, long division symbol, ? next in sequence, R remainder

RIT 201-210: Vocabulary: half-dollar, minimum, plus Signs and Symbols: ¢ cent sign, + positive number, = is equal to

RIT 191-200: Vocabulary: capacity, composite number, each, prime number Signs and Symbols: ( ) order of operations, ° degress Fahrenheit, $ dollar sign, ft feet, g gram, min minute

RIT 181-190: Vocabulary: gave, left, odd number, row, symmetrical, unifix cubes Signs and Symbols: { } set notation, ÷ division, x multiplication

RIT 171-180: Vocabulary: none Signs and Symbols: lb pound

RIT Below 171: Vocabulary: none Signs and Symbols: + addition, = is equal to, - subtraction, variable

Numbers and Operations in Base Ten (2-5)

Math: Number & Operations in Base Ten: Understand Place Value, Counting & Cardinality ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 2

Math: Number & Operations in Base Ten: Understand Place Value, Counting & Cardinality Students:RIT Above 230: Rounds decimals to the nearest hundredth Rounds decimals to nearest ten-thousandth

RIT 221-230: Determines the relative magnitude of whole numbers Orders whole numbers a million or greater using < or > symbols Rounds whole numbers to the nearest million Rounds wholes numbers to the nearest billion Writes equivalent forms of whole numbers using place value (numbers 100 or greater) (e.g., 253 = 2 hundreds, 5 tens, and 3 ones) Represents a decimal to thousandths place (e.g., three thousandths = 0.003) 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 Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 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)

RIT 211-220: Identifies whole numbers 100 - 999 using 2-D and 3-D models Identifies whole numbers over 999 using 2- and 3-D models 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 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) Rounds decimals to the nearest whole number Rounds decimals to the nearest tenth Writes a fraction or mixed number as a decimal when the denominator is a multiple of 10 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 difficult multiplication and division problems (whole numbers only)

RIT 201-210: Identifies whole numbers over 999 using base-10 blocks Identifies the numeral and written name for whole numbers with a zero between digits to the ten thousands place Identifies the numeral and written name for whole numbers over 100,000 Compares whole numbers through 999,999 Compares whole numbers through the billions using the symbols <, >, or = Rounds 4-, 5-, and 6-digit whole numbers to the nearest ten 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 whole numbers to the nearest hundred thousand Explains the rules for rounding Writes equivalent forms of whole numbers using place value (e.g., 54 = 4 tens and 14 ones) Identifies the place value and value of each digit in whole numbers through the billions Writes whole numbers in standard and expanded form through the hundred thousands Applies base ten place value concepts with whole numbers to solve problems Writes whole numbers using place value terms and vice versa Rounds decimals to the nearest whole number Uses rounding to estimate answers to real-world problems involving numbers 1000 or greater with addition and subtraction (whole numbers only) Uses rounding to estimate answers to addition and subtraction problems (whole numbers only) Identifies the missing symbol to compare 2 expressions (e.g., < or >)

Math: Number & Operations in Base Ten: Operations with Multi-Digit Whole Numbers ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 2

Math: Number & Operations in Base Ten: Operations with Multi-Digit Whole NumbersRIT 221-230: Uses multiplication strategies to explain computation (e.g., doubles, 9-patterns, decomposing, partial products) Multiplies multiple-digit numbers Divides a 4-digit number by a 2-digit number

RIT 211-220: Subtracts numbers with 5 digits or more with regrouping Instantly recalls basic multiplication and division facts in a table Multiplies a 3-digit number by a 2-digit number with regrouping Performs mental computation with multiplication 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 Divides a 4-digit number by a 2-digit number Recognizes multiplication and division fact families

RIT 201-210: Uses front end estimation for multiplication and division computations (whole numbers only) Instantly recalls basic addition facts with sums to 18 in a table Adds multiple-digit numbers, with regrouping, with sums over 1000 Performs mental computation with more than 4 addends Subtracts 3- or 4-digit numbers with regrouping Subtracts numbers with 5 digits or more with regrouping Instantly recalls basic multiplication facts where one factor is 6-12 and the other factor is 0-12 Instantly recalls basic multiplication and division facts in a table Multiplies a 2-digit number by a 1-digit number with regrouping Multiplies a 3- or 4-digit number by a 1-digit number Multiplies multiple 1-digit numbers Multiplies a 2-digit number by a 2-digit number with no regrouping Multiplies a 3-digit number by a 2-digit number with regrouping Performs mental computation with multiplication Multiplies a 2- or 3-digit number by multiples of 10 or 100 Multiplies a 3-digit number by a 3-digit number Instantly recalls division facts with dividend and divisors less than 13 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 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 Recognizes multiplication and division fact families

RIT 191-200: Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) Uses number sense strategies to determine the correct answer for an addition computation Adds two 3- and/or 4-digit numbers, with regrouping, with sums over 1000 Adds multiple-digit numbers, with regrouping, with sums over 1000 Subtracts 1-digit number from a 2-digit number with regrouping Subtracts a 2-digit number from a 2-digit number, with regrouping Uses strategies for sums and differences with 2-digit numbers (e.g., decomposing, compatible, compensation, partial sums, counting on) Subtracts a 2-digit number from a 3-digit number with a single regrouping Subtracts 3- or 4-digit numbers with regrouping Performs mental subtraction with numbers under 1000 Subtracts multiple-digit numbers with no regrouping Instantly recalls basic multiplication facts where one factor is 6-12 and the other factor is 0-12 Multiplies a 2- or 3-digit number by a 1-digit number with no regrouping Multiplies a 2-digit number by a 1-digit number with regrouping

Math: Number and Operations Base Ten: Operations with Decimals ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Number and Operations in Base Ten: Operations with Decimals Students:RIT Above 230: 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

RIT 221-230: 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

RIT 211-220: 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 Subtracts decimals to the thousandths place, vertically, with the zero missing in the ones place Subtracts decimals to the thousandths place, horizontally, with and without regrouping 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

RIT 201-210: Adds decimals to the hundredths place in vertical format (not same number of digits) Adds decimals to the thousandths place horizontally with and without regrouping Adds decimals through the hundred-thousandths place Subtracts decimals to the thousandths place, vertically, with the zero missing in the ones place Subtracts decimals to the thousandths place, horizontally, with and without regrouping 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

RIT 191-200: Adds decimals to the hundredths place (same number of digits) Adds decimals to the hundredths place in vertical format (not same number of digits) Subtracts decimals to the hundredths place (same number of digits) with regrouping Subtracts decimals to the thousandths place, vertically, with and without regrouping Subtracts decimals through the hundred-thousandths place, vertically Multiplies a decimal by whole number Divides decimal by a whole number

RIT 181-190: Adds decimals to the hundredths place (same number of digits) Subtracts decimals to the hundredths place (same number of digits) without regrouping Adds decimals to the thousandths place vertically with and without regrouping Subtracts decimals to the hundredths place (same number of digits) without regrouping Subtracts decimals to the hundredths place (same number of digits) with regrouping Subtracts decimals to the thousandths place, vertically, with and without regrouping Solves real-world problems involving decimals (not money) using addition and subtraction Multiplies a decimal by whole number

Math: Number and Operations Base Ten: Vocabulary and Signs & Symbols ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Numbers and Operations Base Ten: Vocabulary and Signs & Symbols Students:RIT 221-230: Vocabulary: ten million Signs and Symbols: none

RIT 211-220: Vocabulary: none Signs and Symbols: none

RIT 201-210: Vocabulary: compatible numbers, expanded numeral, twice Signs and Symbols: ÷ division, missing operations, ∅ null or empty set

RIT 191-200: Vocabulary: billion, hundred million, longer, quintillion, standard numeral, trillion Signs and Symbols: $ dollar sign, > greater than, < less than, R remainder

RIT 181-190: Vocabulary: closest, digit, million, nearest, one, ten thousand Signs and Symbols: { } set notation, long division, symbol

RIT 171-180: Vocabulary: fact family, hundred, thousand Signs and Symbols: ( ) order of operations

RIT 161-170: Vocabulary: none Signs and Symbols: + addition, = is equal to, x multiplication, - subtraction, variable

Math: Number & Operations: Fractions: Develop Understanding of Fractions as Numbers ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Number & Operations: Fractions: Develop Understanding of Fractions as Numbers Students:RIT 231-240: 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

RIT 221-230: 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) Orders fractions on a number line

RIT 211-220: Identifies a fractions in lowest terms from a region or set Identifies eighths, reduced to lowest terms, from a region or set Expresses "1" in many different ways (e.g., 3/3, 4/4) 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 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 Solves problems involving equivalent fractions

RIT 201-210: Identifies halves of a region using nonadjacent parts 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) Writes a terminating decimal as a fraction or mixed number Writes the missing number in a proportion using basic facts

RIT 191-200: Identifies one-half from a region or set Identifies 1/4 from a region or set Identifies 1/3 from a region or set Identifies 2/3 or 3/3 from a region or set Identifies a fraction (denominators other than 2, 3, 4, 8, 10) from a region or set Matches numeric and visual representation of equivalent fractions Writes the missing number in a proportion using basic facts

RIT 181-190: Represents 1/4 with a diagram or model Represents 3/4 with a diagram or model Identifies equal parts by using models Identifies 1/2 from a region or set Identifies 1/4 from a region or set Identifies 2/3 or 3/3 from a region or set Identifies eighths from a region or set Identifies a fraction (denominators other than 2, 3, 4, 8, 10) from a region or set

RIT Below 181: Represents 1/2 with a diagram or model Identifies equivalent fractions using visual representations

Math: Number & Operations: Fractions: Add, Subtract, Multiply, Divide ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 2

Math: Number & Operations: Fractions: Add, Subtract, Multiply & Divide RIT Above 240: Solves open sentences with fractions

RIT 231-240: Adds fractions with unlike denominators with reducing or converting to a mixed fraction Adds mixed fractions where converting from improper fractions is necessary 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 Divides a 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)

RIT 221-230: Uses alternative algorithms to explain the meaning of "fraction" 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 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 with regrouping Solves real-world problems involving addition and subtraction of fractions where converting one denominator is necessary 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 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)

RIT 211-220: 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

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

RIT 201-210: Adds fractions with like denominators without reducing Adds simple mixed fractions with unlike denominators (e.g., halves, thirds, fourths, eighths) 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

Math: Number & Operations: Fractions: Add, Subtract, Multiply & Divide ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Number & Operations: Fractions: Add, Subtract, Multiply & Divide Students:RIT 221-230: Vocabulary: cord, short Signs and Symbols: ÷ division, $ dollar sign

RIT 211-220: Vocabulary: lowest term, lowest terms, reduce, triple Signs and Symbols: > greater than, < less than, ≠ not equal to, % percent

RIT 201-210: Vocabulary: biggest, mixed number Signs and Symbols: + addition, ¢ cent sign, x multiplication

RIT 191-200: Vocabulary: none Signs and Symbols: - subtraction, variable

RIT 181-190: Vocabulary: fourths, thirds Signs and Symbols: = is equal to

Math: Geometry: Reason with Shapes and Their Attitudes ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Geometry: Reason with Shapes and Their Attributes Students:RIT Above 240: Identifies and names a rhombus

RIT 231-240: Compares polygons by properties

RIT 221-230: Identifies and names a trapezoid Identifies and names a quadrilateral Compares polygons by properties Identifies properties of quadrilaterals Identifies the number of edges on rectangular prisms

RIT 211-220: Identifies properties of angles Identifies and names a quadrilateral

Identifies corners (vertices) of cubes Identifies and names a rectangular prism Predicts and verifies the effects of combining or subdividing basic shapes Compares simple plane figures to solid figures (e.g., circle/sphere, square/cube, rectangle/rectangular solid)

RIT 201-210: Identifies and names a parallelogram Identifies and names a polygon Classifies cubes by their properties (e.g., edges with equal lengths, faces with equal areas and congruent shapes, right angle corners) Identifies and names a cylinder

RIT 191-200: Identifies and names a polygon Identifies the number of faces on rectangular prisms Identifies and names a cylinder Identifies and names a sphere Sorts 2-D shapes and objects according to their attributes Creates a new shape by combining different shapes, or identifies the different shapes that were used to make the original shape Identifies position of shapes (e.g., inside, outside, between)

RIT 181-190: Compares squares (larger, smaller) Identifies and names multiple shapes (e.g., square, rectangle, triangle, circle) Classifies polygons by sides and vertices Identifies and names a cube Identifies and names a sphere

RIT 171-180: Identifies and names a triangle Identifies and names a square Identifies and names a rectangle Identifies and names a circle Identifies and names a cube Recognizes geometric shapes in real-world objects Identifies spatial sense concepts (e.g., outside, inside, between, over, under, above, below, behind, in front, middle)

RIT Below 171: Identifies and names a triangle, a circle, a square, a circle Identifies sides and vertices of polygons Identifies and names a cone Compares open and closed figures Sorts solid figures and objects according to attributes

Math: Geometry: Identify Lines and Angles and Graph Points ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Geometry: Identify Lines & Angles and Graph Points Students:RIT Above 250: Determines which lines are perpendicular (analysis) Classifies isosceles triangles Classifies scalene triangles

RIT 241-250: Classifies right triangles by defining properties

RIT 231-240: Determines which lines are perpendicular (analysis) Classifies isosceles triangles; classifies scalene triangles

RIT 221-230: Identifies rays Determines which lines are perpendicular (analysis) Identifies acute angles Classifies equilateral triangles Classifies polygons by type of angle Predicts changes necessary to create symmetry in basic plane shapes Determines coordinates of geometric figures in the first quadrant Determines the distance between points, following grid lines, in the first quadrant on a coordinate graph (as in city blocks)

RIT 211-220: Identifies rays Identifies perpendicular lines Identifies acute angles Identifies obtuse angles Classifies polygons by type of angle Classifies polygons by number of sides Classifies plane figures by the number of lines of symmetry Determines the distance between horizontal and vertical lines in the first quadrant of a rectangular coordinate system Locates the origin on a coordinate grid

RIT 201-210: Identifies parallel lines Identifies angles Identifies right angles Classifies polygons by sides and angles Classifies plane figures by the number of lines of symmetry Graphs ordered pairs in the first quadrant Determines, names locations in first quadrant on labeled grid or coordinate system (e.g., map or graph) Determines the distance between horizontal and vertical lines in the first quadrant of a rectangular coordinate system Locates the origin on a coordinate grid

RIT 191-200: Identifies lines; identifies parallel lines Identifies angles Identifies plane figures with line symmetry Identifies the number of lines of symmetry in plane figures Determines, names locations in first quadrant on labeled grid or coordinate system (e.g., map or graph)

RIT 181-190: Identifies points on a line Identifies plane figures with line symmetry Determines, names locations in first quadrant on labeled grid or coordinate system (e.g., map or graph)

Math: Geometry: Vocabulary and Signs and Symbols ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Geometry: Vocabulary and Signs and Symbols Students:RIT 231-240: Vocabulary: acute triangle Signs/Symbols: congruent segment symbol

RIT 221-230: Vocabulary: equilateral triangle, isosceles triangle, obtuse triangle, scalene triangle Signs/Symbol: in. inch, ∟ right angle marker, segment overbar

RIT 211-220: Vocabulary: acute angle, congruent angle, geometric solid, obtuse angle, straight angle, union Signs/Symbols: < angle, angle marker (arc), ° degrees

RIT 201-210: Vocabulary: coordinate, coordinate point, edge, origin, parallel line, regular polygon, trapezoid Signs/Symbols: none

RIT 191-200: Vocabulary: face, intersect, kite, large, oval, parallel, plane, rhombus, straight, vertical line Signs/Symbols: = is equal to

RIT 181-190: Vocabulary: grid, smallest, symmetry Signs/Symbols: ( ) ordered pair, •point

RIT 171-180: Vocabulary: ray Signs/Symbols: none

RIT Below 171: Vocabulary: corner, flat Signs/Symbols: none

Math 6+

Math: Algebra, Functions, Expressions & Equations: Expressions & Properties of Operations ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 2

Math: Algebra, Functions, Expressions & Equations: Expressions & Properties of Operations Students:RIT Above 260: Simplifies monomials Simplifies polynomial expressions using power laws Factors polynomials by identifying a common monomial and then factoring the trinomial

RIT 251-260: Uses the additive inverse property with rational numbers Solves problems with scientific notation Uses expressions to represent situations that involve variable quantities with exponents Uses expressions with absolute value to represent situations Evaluates expressions by substituting with rational numbers Simplifies monomials Simplifies polynomial expressions Multiplies binomials Multiplies a polynomial by a polynomial Divides a polynomial by a monomial Factors polynomials by identifying common factors Factors trinomials in the form x^2 + bx + c Factors polynomials using difference of squares

RIT 241-250: Writes a number expressed in scientific notation in standard form Writes a whole number in scientific notation Writes a decimal in scientific notation Evaluates expressions using the order of operations, including exponents (whole numbers only) Evaluates numerical expressions using the order of operations (using integers) Evaluates expressions using the order of operations, including exponents (using integers) Simplifies rational expressions with scientific notation Solves problems with scientific notation Uses expressions to represent situations that involve variable quantities with exponents

Evaluates expressions by substituting with rational numbers Simplifies polynomial expressions Multiplies binomials Factors trinomials in the form x^2 + bx + c Factors polynomials using difference of squares

RIT 231-240: Translates a problem to a symbolic expression or equation (analysis) Writes whole numbers in standard and exponential form Writes a number expressed in scientific notation in standard form Writes a whole number in scientific notation Writes a decimal in scientific notation Evaluates numerical expressions using the order of operations (whole numbers only) Evaluates expressions using the order of operations, including exponents (whole numbers only) Evaluates numerical expressions using the order of operations (using integers) Uses the distributive property Solves problems with scientific notation Uses expressions to represent situations that involve variable quantities with exponents Uses basic operations on algebraic expressions (substituting for unknowns) Recognizes commutative, associative, distributive, symmetric, transitive, and reflexive properties Uses basic operations on algebraic expressions (combining like terms) Uses basic operations on algebraic expressions (expanding - monomial by a binomial) Writes equivalent forms of algebraic expressions (e.g., (x + 3)/2 = x/2 + 3/2) Represents relationships of quantities in the form of an expression

RIT 221-230: Translates a problem to a symbolic expression or equation (analysis) Writes whole numbers in standard and exponential form Uses the distributive property Describes and uses a variable with whole numbers, multiplication, and division in a contextual situation Uses basic operations on algebraic expressions (substituting for unknowns)

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Math: Algebra, Functions, Expressions & Equations: Solve Problems and Use Equations & Inequalities Students:RIT Above 260: Uses the compound interest equation to solve problems Rewrites a complex formula to solve for a specific variable Solves quadratic equations using the quadratic formula Solves quadratic equations by completing the square Solves logarithmic equations Solves real-world systems of linear equations Solves polynomial inequalities

RIT 251-260: Uses reasoning strategies to solve problems Solves linear equations using rational numbers Applies algebraic methods to solve complex real-world and theoretical problems Solves problems involving consecutive numbers Rewrites a complex formula to solve for a specific variable Writes linear equations, given two points on a line Solves quadratic equations by factoring Solves quadratic equations by completing the square Uses polynomial equations to solve complex theoretical problems (e.g., using distributive property, variables on both sides) Uses polynomial equations to solve area and perimeter problems Solves logarithmic equations Uses the Multiplication Property of Equality as a first step in solving systems of linear equations Uses substitution as a first step in solving systems of linear equations Uses algebraic methods to solve systems of linear equations Uses graphs to solve systems of linear equations in real-world situations Solves real-world systems of linear equations Solves single variable linear inequalities with variable in both members using number lines

RIT 241-250: Uses reasoning strategies to solve problems Solves problems involving simple interest rates without the formula Uses linear equations to represent situations involving variable quantities Solves 2-step open sentences with missing factors (variables on both sides of the sentence) Solves linear equations with fractions Solves linear equations using rational numbers Solves open sentences with fractions Applies algebraic methods to solve real-world problems Applies algebraic methods to solve a variety of real-world and theoretical problems Solves problems involving consecutive numbers Writes linear equations when given ordered pairs Uses polynomial equations to solve complex real-world problems (e.g., using distributive property, variables on both sides) Uses the Multiplication Property of Equality as a first step in solving systems of linear equations Uses algebraic methods to solve systems of linear equations Uses graphs to solve systems of linear equations in real-world situations Solves linear inequalities using graphs

RIT 231-240: Solves real-world problems involving addition and subtraction of fractions where converting both denominators is necessary Solves 2- or more step real-world problems involving fractions with multiplication and division Solves problems involving fractions (e.g., multiple operations, conversions) Solves real-world problems involving rate of pay Solves real-world problems involving rate of pay with time and a half Solves difficult real-world problems involving decimals (e.g., multiple multiplications, conversions) Expresses a simple linear equation from a contextual situation Solves 2-step open sentences with missing factors (variables on both sides of the sentence) Solves 2-step linear equations Solves linear equations with decimals Solves linear equations with integers

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Math: Algebra, Functions, Expressions & Equations: Use Functions to Model Relationships Students:RIT Above 260: Writes the equation of the line when given the graph of the line Determines the minimum and maximum of a quadratic function

RIT 251-260: Writes the equation of the line when given the graph of the line Determines the graph of a line when given the equation Determines slope from graphs Determines slope from ordered pairs and tables Interprets the meaning of slope and intercepts in problem solving situations Identifies discriminants and roots Uses graphs to solve systems of linear equations Represents a real-world function using a complex equation (e.g., variables on both sides, distributive, rational) Models real life functions using function notation Distinguishes between linear and nonlinear functions (analysis) Uses graphs to represent functions and interpret slope Determines the vertex of a parabola Investigates, describes, and predicts the effects of parameter changes on the graphs of exponential functions Determines the effects of parameter changes on functions Determines the domain and range of a function

RIT 241-250: Uses an algebraic expression to represent a triangular number pattern Identifies and describes situations with varying rates of change Uses tables to determine function equations Represents a real-world function using a complex equation (e.g., variables on both sides, distributive, rational) Models real life functions using function notation Determines the x- and/or y-intercept of an equation of a function

Performs operations on functions Solves problems involving complex functions Determines the domain and range of a function

RIT 231-240: Predicts from charts and tables Recognizes and extends arithmetic sequences (predicts nth term) Recognizes and extends the Fibonacci sequence Represents real-world functions using an equation Uses tables to determine function equations Completes a function table according to a rule Models real life functions using function notation Identifies the graph type, given equations of linear and nonlinear functions Solves problems involving complex functions

RIT 221-230: Looks for a growing pattern to solve a problem Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations Extends a growing pattern of triangular numbers, defined by objects or diagrams Represents geometric sequences using written descriptions in recursive terms (present term, next term) Uses mapping diagrams to represent functions Completes a function table according to a rule

RIT 211-220: Looks for a growing pattern to solve a problem Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations Extends a repeating pattern of geometric shapes in a grid Extends a growing geometric pattern - using numbers Extends a pattern formed by two arithmetic growing patterns - odd and even terms (such as 1,5,4,8,7,...)

Math: Algebra, Functions, Expressions & Equations: Vocabulary and Signs & Symbols ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Algebra, Functions, Expressions & Equations: Vocabulary and Signs & SymbolsRIT Above 260: Vocabulary: semi-annual Signs and Symbols: P principal, r rate, t time

RIT 251-260: Vocabulary: coordinate plane, quadratic equation, undefined, wider, x-coordinate, y-coordinate Signs and Symbols: { } set notation, || absolute value, P perimeter

RIT 241-250: Vocabulary: polynomial, solution set, y-intercept Signs and Symbols: % percent

RIT 231-240: Vocabulary: algebraic sentence, arithmetic progression, depreciate, is less than, regression equation, successive, time-and-a-half Signs and Symbols: -, f(x) the value of the function f at x, ≥ greater than or equal to,

km kilometer/kilometre, ≤ less than or equal to, m meter/metre, • multiplication symbol (dot)RIT 221-230: Vocabulary: algebra, cord, expanded notation, net, reflexive, short, transitive Signs and Symbols: < less than, + positive number, repeating decimal overbar, Δ triangle

RIT 211-220: Vocabulary: coin, triple Signs and Symbols: ( ) parentheses around an integer, $ dollar sign, ? next in sequence

RIT 201-210: Vocabulary: expanded numeral, half-dollar, minimum, plus Signs and Symbols: ( ) ordered pair, a.m., °C degrees Celsius, °F degrees Fahrenheit, - negative number, p.m., + positive number, = is equal to

RIT 191-200: Vocabulary: capacity, deposit, each, longer Signs and Symbols: ( ) order of operations, ÷ division, ft feet, x multiplication

RIT 181-190: Vocabulary: changed, gave left, pennies Signs and Symbols: none

RIT 171-180: Vocabulary: none Signs and Symbols: ¢ cent sign, lb pound

RIT Below 171: Vocabulary: none Signs and Symbols: + addition, $ dollar sign, = is equal to, - subtraction, variable

Math: The Real and Complex Number Systems: Ratios and Proportional Relationships ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 3

Math: The Real and Complex Number Systems: Ratios and Proportional Relationships Students:RIT Above 260: Solves problems involving rate conversions (e.g., mi/hr to ft/sec) Solves problems involving rates

RIT 251-260: Solves problems involving complex percent discounts (e.g., finding percent discount, regular price) Solves complex real-world problems involving capacity Uses dimensional analysis for unit conversions (time) Solves problems involving rate conversions (e.g., mi/hr to ft/sec)

RIT 241-250: Identifies the ratio from a given real-world situation 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 weight in the customary system and converts to larger or smaller units Solves problems involving capacity in the metric system and converts to larger or smaller units Uses dimensional analysis for unit conversions (time) Converts from Celsius to Fahrenheit, given conversion ratios Solves problems involving rate conversions (e.g., mi/hr to ft/sec)

RIT 231-240: Writes a ratio as a percent and vice versa Identifies the ratio from a given real-world situation Uses estimation to solve problems involving proportional reasoning (decimals only) 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)

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 Solves problems involving capacity in the customary system and converts to larger or smaller units Converts from Celsius to Fahrenheit, given conversion ratios Solves complex problems involving miles per gallon Solves problems comparing unit prices Explores maps and relates them to measurements of real distances, using proportional reasoning Uses similar triangles to construct ratios and solve for a missing side

RIT 221-230: Identifies a fractions in lowest terms from a region or set Determines simple equivalent fractions using multiples Determines equivalent fractions using multiples Writes a decimal for a shaded region to the hundredths place Writes a ratio as a percent and vice versa

Math: Algebra, Functions, Expressions & Equations: Solve Problems and Use Equations & Inequalities ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 2

Math: Algebra, Functions, Expressions & Equations: Use Functions to Model Relationships Students:RIT Above 260: Writes the equation of the line when given the graph of the line Determines the minimum and maximum of a quadratic function

RIT 251-260: Writes the equation of the line when given the graph of the line Determines the graph of a line when given the equation Determines slope from graphs Determines slope from ordered pairs and tables Interprets the meaning of slope and intercepts in problem solving situations Identifies discriminants and roots Uses graphs to solve systems of linear equations Represents a real-world function using a complex equation (e.g., variables on both sides, distributive, rational) Models real life functions using function notation Distinguishes between linear and nonlinear functions (analysis) Uses graphs to represent functions and interpret slope Determines the vertex of a parabola Investigates, describes, and predicts the effects of parameter changes on the graphs of exponential functions Determines the effects of parameter changes on functions Determines the domain and range of a function

RIT 241-250: Uses an algebraic expression to represent a triangular number pattern Identifies and describes situations with varying rates of change Uses tables to determine function equations Represents a real-world function using a complex equation (e.g., variables on both sides, distributive, rational) Models real life functions using function notation Determines the x- and/or y-intercept of an equation of a function Performs operations on functions Solves problems involving complex functions Determines the domain and range of a function

RIT 231-240: Predicts from charts and tables Recognizes and extends arithmetic sequences (predicts nth term) Recognizes and extends the Fibonacci sequence Represents real-world functions using an equation Uses tables to determine function equations Completes a function table according to a rule Models real life functions using function notation Identifies the graph type, given equations of linear and nonlinear functions

Solves problems involving complex functions

RIT 221-230: Looks for a growing pattern to solve a problem Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations Extends a growing pattern of triangular numbers, defined by objects or diagrams Represents geometric sequences using written descriptions in recursive terms (present term, next term) Uses mapping diagrams to represent functions Completes a function table according to a rule

RIT 211-220: Looks for a growing pattern to solve a problem Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations Extends a repeating pattern of geometric shapes in a grid Extends a growing geometric pattern - using numbers Extends a pattern formed by two arithmetic growing patterns - odd and even terms (such as 1,5,4,8,7,...)

Math: Algebra, Functions, Expressions & Equations: Vocabulary and Signs & Symbols ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Algebra, Functions, Expressions & Equations: Vocabulary and Signs & SymbolsRIT Above 260: Vocabulary: semi-annual Signs and Symbols: P principal, r rate, t time

RIT 251-260: Vocabulary: coordinate plane, quadratic equation, undefined, wider, x-coordinate, y-coordinate Signs and Symbols: { } set notation, || absolute value, P perimeter

RIT 241-250: Vocabulary: polynomial, solution set, y-intercept Signs and Symbols: % percent

RIT 231-240: Vocabulary: algebraic sentence, arithmetic progression, depreciate, is less than, regression equation, successive, time-and-a-half Signs and Symbols: -, f(x) the value of the function f at x, ≥ greater than or equal to,

km kilometer/kilometre, ≤ less than or equal to, m meter/metre, • multiplication symbol (dot)RIT 221-230: Vocabulary: algebra, cord, expanded notation, net, reflexive, short, transitive Signs and Symbols: < less than, + positive number, repeating decimal overbar, Δ triangle

RIT 211-220: Vocabulary: coin, triple Signs and Symbols: ( ) parentheses around an integer, $ dollar sign, ? next in sequence

RIT 201-210: Vocabulary: expanded numeral, half-dollar, minimum, plus Signs and Symbols: ( ) ordered pair, a.m., °C degrees Celsius, °F degrees Fahrenheit, - negative number, p.m., + positive number, = is equal to

RIT 191-200: Vocabulary: capacity, deposit, each, longer Signs and Symbols: ( ) order of operations, ÷ division, ft feet, x multiplication

RIT 181-190: Vocabulary: changed, gave left, pennies Signs and Symbols: none

RIT 171-180: Vocabulary: none Signs and Symbols: ¢ cent sign, lb pound

RIT Below 171: Vocabulary: none Signs and Symbols: + addition, $ dollar sign, = is equal to, - subtraction, variable

Math: The Real and Complex Number Systems: Ratios and Proportional Relationships ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 3

Math: The Real and Complex Number Systems: Ratios and Proportional Relationships Students:RIT Above 260: Solves problems involving rate conversions (e.g., mi/hr to ft/sec) Solves problems involving rates

RIT 251-260: Solves problems involving complex percent discounts (e.g., finding percent discount, regular price) Solves complex real-world problems involving capacity Uses dimensional analysis for unit conversions (time) Solves problems involving rate conversions (e.g., mi/hr to ft/sec)

RIT 241-250: Identifies the ratio from a given real-world situation 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 weight in the customary system and converts to larger or smaller units Solves problems involving capacity in the metric system and converts to larger or smaller units Uses dimensional analysis for unit conversions (time) Converts from Celsius to Fahrenheit, given conversion ratios Solves problems involving rate conversions (e.g., mi/hr to ft/sec)

RIT 231-240: Writes a ratio as a percent and vice versa Identifies the ratio from a given real-world situation Uses estimation to solve problems involving proportional reasoning (decimals only) 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) 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 Solves problems involving capacity in the customary system and converts to larger or smaller units Converts from Celsius to Fahrenheit, given conversion ratios Solves complex problems involving miles per gallon Solves problems comparing unit prices Explores maps and relates them to measurements of real distances, using proportional reasoning Uses similar triangles to construct ratios and solve for a missing side

RIT 221-230: Identifies a fractions in lowest terms from a region or set Determines simple equivalent fractions using multiples Determines equivalent fractions using multiples Writes a decimal for a shaded region to the hundredths place Writes a ratio as a percent and vice versa

Math: The Real and Complex Number Systems: Perform Operations ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 5

Math: The Real and Complex Number Systems: Perform Operations Students:RIT Above 260: Performs operations on complex numbers and expresses the results in simplest form

RIT 251-260: Uses factor and multiple concepts to solve difficult problems Performs operations on complex numbers and expresses the results in simplest form Performs basic operations on matrices

RIT 241-250: Uses factor and multiple concepts to solve difficult problems Identifies the least common multiple of whole numbers Uses a number line to determine the distance between a positive and negative number Subtracts integers Performs basic operations on matrices

RIT 231-240: Divides multiple-digit numbers Adds fractions with unlike denominators with reducing or converting to a mixed fraction Adds mixed fractions where converting from improper fractions is necessary Subtracts whole numbers, fractions, and mixed fractions with regrouping 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 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 Multiplies integers with like signs Divides integers with like signs Subtracts rational expressions in decimal form Performs basic operations on matrices

RIT 221-230: 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 Uses multiplication strategies to explain computation (e.g., doubles, 9-patterns, decomposing, partial products)

Multiplies multiple-digit numbers Divides a 4-digit number by a 2-digit number Divides multiple-digit numbers Divides numbers by powers of 10 Adds fractions with like denominators with reducing or converting to a mixed fraction Adds fractions with unlike denominators without reducing

Math: The Real and Complex Number Systems: Extend and Use Properties ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 4

Math: The Real and Complex Number Systems: Extend and Use Properties Students:RIT Above 260: Defines "irrational numbers" Simplifies rational expressions with negative exponents

RIT 251-260: Uses fractional and negative exponents as optional ways of representing problem situations (e.g., 27^2/3 = (27^1/3)^2 = 9) Simplifies rational expressions with exponents

RIT 241-250: Uses the multiplicative inverse property with rational numbers Simplifies rational expressions with exponents Estimates the square roots of numbers Computes and interprets distance, given a set of ordered pairs (horizontal and vertical lines)

RIT 231-240: Compares fractions (e.g., comparing numerators and denominators) Rounds decimals to the nearest hundredth Rounds decimals to nearest ten-thousandth Orders rational numbers, in a/b form Writes a fraction as a decimal and vice versa Writes a fraction as a mixed decimal and vice versa Compares and orders decimal and fractional coordinates on a number line Uses powers of 10 to represent numbers (e.g., 8 x 10^3 = 8000) Models algorithms using place value concepts (multiplication and division with whole numbers) Evaluates expressions containing powers (e.g., 3^2 x 2^3) Applies rules for multiplying and dividing powers 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)

RIT 221-230: Determines the relative magnitude of whole numbers Orders whole numbers a million or greater using < or > symbols Rounds whole numbers to the nearest million Rounds wholes numbers to the nearest billion Writes equivalent forms of whole numbers using place value (numbers 100 or greater) (e.g., 253 = 2 hundreds, 5 tens, and 3 ones) Compares fractions (e.g., comparing numerators and denominators) Orders fractions on a number line Uses alternative algorithms to explain the meaning of "fraction" Represents a decimal to thousandths place (e.g., three thousandths = 0.003) 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 Compares two integers Orders integers Locates rational numbers on a number line Orders rational numbers, in a/b form 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 Expresses the equivalent form of a fraction, decimal, and/or percent (simple fraction) Writes a power as a product of multiplied numbers and vice versa (e.g., 2^4 = 2 x 2 x 2 x 2) Uses powers of 10 to represent numbers (e.g., 8 x 10^3 = 8000) Uses powers to represent 10, 100, 1000, 10,000, and 100,000

Uses rounding to estimate answers to real-world problems involving multiplication and division of numbers

Math: The Real and Complex Number System: Vocabulary and Signs & Symbols ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: The Real and Complex Number System: Vocabulary and Signs & Symbols Students:RIT 251-260: Vocabulary: none Signs and Symbols: i square root of -1

RIT 241-250: Vocabulary: feet per second, least common multiple Signs and Symbols: [ ] square brackets, LCM lowest common multiple, sec second, square root symbol

RIT 231-240: Vocabulary: discount, equality, matrix, representative sample Signs and Symbols: || absolute value, hr hour, km kilometer/kilometre, oz ounce, / per, segment overbar

RIT 221-230: Vocabulary: real number, ten million Signs and Symbols: ( ) parentheses around an integer, cm centimeter/centimetre, °C degrees Celsius,

dm decimeter/decimetre, m meter/metre, mL milliliter/millilitre, mm millimeter/millimetre,+ positive number, : ratioRIT 211-220: Vocabulary: common factor, decimal form, greatest common factor, lowest term, lowest terms, proof, reduce Signs and Symbols: ? a variable, kg kilogram, - negative sign, ≠ not equal to, yd yard

RIT 201-210: Vocabulary: biggest, compatible numbers, coordinate, coordinate point, integer, larger, miles per gallon, mixed number, origin, twice Signs and Symbols: ¢ cent sign, ' feet, ft feet, in. inch, " inches, missing operation, mpg miles per gallon,

- negative number, ∅ null or empty setRIT 191-200: Vocabulary: billion, composite number, decade, hundred million, miles per hour, prime number, quintillion, scale, standard numeral, trillion Signs and Symbols: °F degrees Fahrenheit degrees Fahrenheit, $ dollar sign, g gram, > greater than,

lb pound, < less than, min minute, mph miles per hour, % percent, R remainderRIT 181-190: Vocabulary: closest, cup, digit, fourths, grid, millimeter, million, nearest, odd number, one, pint, row, smallest, symmetrical, tablespoon, teaspoon, ten thousand, thirds, unifix cubes Signs and Symbols: ( ) ordered pair, { } set notation, c cup, ÷ division, gal gallon, long division symbol,

• point, pt pint, qt quart, tsp teaspoonRIT 171-180: Vocabulary: fact family, hundred, thousand Signs and Symbols: ( ) order of operations

RIT Below 171: Vocabulary: none Signs and Symbols: + addition, = is equal to, × multiplication, − subtraction, variable

Math: Geometry: Geometric Measurement and Dimension ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 4

Math: Geometry: Geometric Measurement and Dimension Students:RIT Above 260: Solves real-world problems involving surface area Uses properties of angles to solve mathematical problems Uses the properties of 30-60-90 triangles to solve problems

RIT 251-260: Determines the area of a figure when plotting ordered pairs without a grid Determines the length of the side of a square, given the area Determines the area of a parallelogram, given a labeled diagram Calculate the height of a trapezoid, given the area, without the formula given (metric) Determines the diameter or radius when given the area of a circle (metric units) Solves problems involving complex figures (e.g., triangle, parallelogram) Solves complex problems involving inscribed figures Solves problems comparing area to perimeter (analysis) Solves real-world problems involving surface area Calculates the length of one side of a cube, given the volume (customary units) Determines the volume of a cylinder Calculates the radius of a sphere, given the volume and formula (metric units) Solves real-world problems comparing volumes of figures Uses reasoning to verify properties of parallel and perpendicular lines Uses properties of angles and figures to solve algebraic problems Uses properties of angles to solve mathematical problems Recognizes that the sum of the measures of two sides of a triangle must be greater than the measure of the third side Recognizes the exterior angle relationships of triangles Classifies right triangles by defining properties Solves problems involving properties of triangles Identifies and names a rhombus Classifies polygons by properties Uses the Pythagorean theorem to solve problems

RIT 241-250: Solves problems involving the perimeter of squares, rectangles, or triangles (analysis) Determines the circumference when given the diameter or radius (or vice versa) Determines the circumference when given the area of a circle (or vice versa) Determines the area of a triangle without the formula Solves problems involving area of a rectangle and converts to larger or smaller units (customary) Describes the change in area of a rectangle when dimensions of an object are altered Determines the area of a parallelogram, given a labeled diagram Solves problems involving area of a circle Determines the diameter or radius when given the area of a circle (metric units) Determines the area of irregular shapes (customary units) Calculates the area of irregular shapes (metric units) Solves complex problems involving inscribed figures Determines the surface area of rectangular solids Calculates the length of one side of a cube, given the volume (customary units) Determines the effects of changing dimensions on volume (no units) Identifies and determines missing angle measures for complementary angles Uses properties of angles and figures to solve algebraic problems Recognizes that the sum of the measures of two sides of a triangle must be greater than the measure of the third side Recognizes the exterior angle relationships of triangles Classifies right triangles by defining properties Identifies and names a rhombus Uses the Pythagorean theorem to solve problems Using the slope of an equation, identifies parallel and perpendicular lines Determines the distance between two points Determines the figure when plotting ordered pairs

Math: Geometry: Congruence, Similarity, Transformations & Trig ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Geometry: Congruence, Similarity, Transformations & Trig Students:RIT Above 260: Determines sine of an angle in a given right triangle Determines tangent of an angle in a given triangle

RIT 251-260: Identifies properties of congruent angles Identifies corresponding and alternate exterior/interior angles Verifies congruency of triangles using ASA, SAS, SSS, or AAS Solves problems involving properties of similar triangles (e.g., using geometric mean, Triangle Proportionality Theorem) Uses picture representations to identify corresponding parts of symmetric plane figures Uses picture representations to identify symmetry of plane figures with respect to a point or line

RIT 241-250: Uses an indirect method to measure the height of an inaccessible object Identifies properties of congruent angles Identifies and determines a missing angle measure in corresponding, vertical, and alternate exterior/interior angles Identifies corresponding and alternate exterior/interior angles Constructs congruent figures Determines the new coordinates of a transformed geometric figure

RIT 231-240: Identifies and determines a missing angle measure in corresponding, vertical, and alternate exterior/interior angles Solves problems involving properties of congruent triangles Determines an appropriate scale for representing an object in a scale drawing Identifies geometric transformations (dilations)

RIT 221-230: Predicts changes necessary to create symmetry in basic plane shapes Identifies geometric transformations (rotations) Identifies geometric transformations (reflections)

RIT 211-220: Identifies similar and congruent triangles Identifies congruent polygons and their corresponding sides and angles Classifies plane figures by the number of lines of symmetry Identifies geometric transformations (rotations) Identifies geometric transformations (reflections)

RIT 201-210: Classifies plane figures by the number of lines of symmetry Defines transformations

RIT 191-200: Identifies congruent figures Identifies plane figures with line symmetry Identifies the number of lines of symmetry in plane figures Identifies transformations of plane figures (reflections/flips)

RIT 181-190: Identifies congruent line segments Identifies congruent figures Identifies figures that are similar Identifies plane figures with line symmetry Identifies transformations of plane figures (rotations/turns)

RIT 171-180: Identifies figures that are similar

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Math: Statistics and Probability: Interpreting Categorical and Quantitative Data Students:RIT Above 260: Reads and interprets interquartile range in box-and-whisker plots

RIT 251-260: Solves complex problems involving mean Computes and compares mean, median, mode, and range in simple examples to demonstrate that they may differ for a given set of data Uses the regression line method to make predictions

RIT 241-250: Reads and interprets data in tables Reads and interprets data in box-and-whisker plots Determines the correlation for a set of data Predicts from an analysis of data and statistical measures

RIT 231-240: Interprets data given in tables to solve problems Determines appropriate intervals and/or scale for a bar graph Interprets data given in horizontal and vertical bar graphs to solve problems Interprets data given in line graphs to solve problems Reads and interprets data in box-and-whisker plots Determines the mean of a complex set of data (e.g., fractions, integers, many data points) Estimates the mean from a set of data Solves problems with missing data when the mean is known Determines the median from a complex set of data (e.g., not in order, many data points) Estimates line of best fit to make predictions Identifies outliers on a data display (e.g., uses interquartile range to identify outliers on a box-and-whisker plot) Predicts from an analysis of data and statistical measures

RIT 221-230: Interprets data given in tables to solve problems Determines the average (mean) of a simple set of data Determines the mean of a complex set of data (e.g., fractions, integers, many data points) Estimates the mean from a set of data Solves simple problems involving mean Solves problems with missing data when the mean is known Determines the middle value (median) from a simple set of data Predicts from plotted data

RIT 211-220: Solves problems using pictographs Solves problems using bar graphs Interprets data in line graphs (e.g., change over time) Reads and interprets data in scatter plots Reads and interprets data in line plots Determines the average (mean) of a simple set of data Solves simple problems involving mean Predicts from pictographs and bar graphs Predicts from plotted data

RIT 201-210: Reads and interprets tables Organizes data to create simple bar graphs Solves problems using bar graphs Draws conclusions from data - bar graphs Predicts from pictographs and bar graphs Predicts from simple charts and tables

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Math: Statistics and Probability: Using Sampling and Probability to Make Decisions Students:RIT Above 260: Determines the probabilities of compound events (dependent)

RIT 251-260: Uses random sampling techniques Determines the probabilities of complex compound events (independent)

RIT 241-250: Determines probability using counting procedures Determines probability using tables Determines probability using an area model Uses multiplication principle of counting to determine possibilities Uses theoretical probability to predict future events

RIT 231-240: Determines probability - must determine size of sample space Modifies sample space to change the probability of an event Determines the probability of independent simple compound events

RIT 221-230: Determines the most accurate sample for a situation Determines likelihood using tree diagrams Determines probability - must determine size of sample space Determines the possible outcomes for a simple probability experiment using spinners Determines the possible outcomes for a simple probability experiment using dart boards Solves problems involving combinations Determines the number of possible combinations of given items Determines the outcome of simple multiple events Uses previous results to predict future events Computes probability as a fraction, given equivalent forms

RIT 211-220: Determines the probability for a simple experiment using one die Determines probability from a real-world situation - number of possible outcomes given Determines the probabilities for a simple experiment using a frequency table - must determine size of sample space Determines probability when drawing objects from containers - must determine size of sample space Determines the possible outcomes for a simple probability experiment using spinners Solves problems involving permutations Determines the number of possible combinations of given items Predicts the sample space, based on the outcome of an experiment - tally sheet Uses the results of probability experiments or events to predict future events

RIT 201-210: Recognizes events that are certain, likely, unlikely, possible, or impossible Uses the concept of chance to determine the likelihood of an event Determines the probability for a simple experiment using one or more coins Determines the probability for a simple experiment using objects - must determine size of sample space

RIT 191-200: Investigates probability of "more likely" or "less likely" using a spinner

RIT 181-190: Investigates probability of "more likely" or "less likely" using a spinner Investigates probability of "more likely" or "less likely" with objects hidden in containers

Math: Statistics and Probability: Vocabulary and Signs & Symbols ©2011 NWEA. DesCartes: A Continuum of Learning is the exclusive copyrighted property of NWEA. www.fortheteachers.org | Page 1 of 1

Math: Statistics and Probability: Vocabulary and Signs & Symbols Students:RIT 251-260: Vocabulary: none Signs and Symbols: + addition

RIT 241-250: Vocabulary: correlation, hyperbolic, mileage table Signs and Symbols: ° degrees, E east, x multiplication, NE northeast, NNE north northeast, NW northwest, S south, W west

RIT 231-240:

Vocabulary: average salary, box-and-whisker plot, data point, interquartile, middle, outlier, percentile, quartile, sample, upper quartile Signs and Symbols: ( ) ordered pair, $ dollar sign, • outlier

RIT 221-230: Vocabulary: frequency table, median, survey Signs and Symbols: oz ounce, P( ) probability, % percent

RIT 211-220: Vocabulary: combinations, fastest, fitted line, line of best fit, line plot, mean, number cube, outcome, positive linear relationship, scatter plot, tails Signs and Symbols: { } set notation, d distance, mph miles per hour, t time

RIT 201-210: Vocabulary: bar graph, below, chance, less likely, probability, random Signs and Symbols: °F Fahrenheit, ft feet, lb pound, min minute

RIT 191-200: Vocabulary: none Signs and Symbols: | tally mark

RIT 181-190: Vocabulary: lowest, most likely, most often Signs and Symbols: none

RIT 171-180: Vocabulary: fewer, taller Signs and Symbols: cm centimeter/centimetre

RIT Below 171: Vocabulary: dollar, shortest Signs and Symbols: $ dollar sign, = is equal to