DesCartes: A Continuum of Learning
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1 Mathematics RIT Score Range: < 161 < 161 Add & Subtract: Represent and Solve Problems Uses models to construct whole number addition facts with addends through 10 Multiply & Divide: Represent and Solve Problems Solve Problems & Analyze Patterns & Relationships Add & Subtract: Represent and Solve Problems Uses models to construct facts with differences through 10 (whole numbers) Multiply & Divide: Represent and Solve Problems Solve Problems & Analyze Patterns & Relationships New Signs and Symbols: + addition, = is equal to, -, variable Page 1 of 17
2 Mathematics RIT Score Range: < Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Uses models to construct whole number addition facts with addends through 10 Uses models to construct facts with differences through 10 (whole numbers) New Signs and Symbols: + addition, = is equal to, -, variable Writes equivalent forms of whole number expressions (e.g., = ) Reads a chart or table - comparisons (start unknown) Solves real-world whole number addition problems with sums to 100 Represents a basic facts addition problem with a number sentence numbers under 20 Recognizes addition and fact families through 18 New Vocabulary: fact family New Signs and Symbols: ( ) order of operations, multiplication, tally mark Page 2 of 17
3 Mathematics RIT Score Range: Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Uses models to construct facts with differences through 10 (whole numbers) Writes equivalent forms of whole number expressions (e.g., = ) Reads a chart or table - comparisons (start unknown) Solves real-world whole number addition problems with sums to 100 Represents a basic facts addition problem with a number sentence numbers under 20 Recognizes addition and fact families through 18 Solves real-world whole number addition problems with sums to 100 Instantly recalls basic addition facts with sums to 18 in a table - with extraneous information given numbers under 20 numbers 100 and under Solves real-world whole number problems involving addition and Recognizes addition and fact families through 18 Solves basic facts addition and open sentences using diagrams and models (e.g., using balances) Solves 1-step open sentences with missing addends (numbers 100 and under) Solves simple problems based on data from tally charts Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Counts by 2's to 100 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 Distinguishes between odd and even numbers Uses counting by multiples for multiplication Solves word problems involving basic whole number multiplication facts to 10 x 10 Uses manipulatives to divide a small set of objects into groups of equal size Uses sharing for division Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated ) Extends a growing arithmetic pattern, defined by numbers Writes a number sentence for a simple problem solving situation Analyzes a growing, arithmetic pattern with numbers to determine the rule Page 3 of 17
4 Mathematics RIT Score Range: New Signs and Symbols: + addition, = is equal to, -, variable Adds 1-digit numbers with sums to 18 (with parentheses) Analyzes a growing, arithmetic pattern with numbers to determine the rule New Vocabulary: fact family New Signs and Symbols: ( ) order of operations, multiplication, tally mark Interprets a chart or table - calculation required Extends a growing arithmetic pattern, defined by numbers Writes a number sentence for a simple problem solving situation addition of numbers less than 100 (whole numbers numbers under 1000 New Vocabulary: gave, left, row, unifix cubes New Signs and Symbols: division, $ dollar sign Page 4 of 17
5 Mathematics RIT Score Range: Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Writes equivalent forms of whole number expressions (e.g., = ) Reads a chart or table - comparisons (start unknown) Solves real-world whole number addition problems with sums to 100 Represents a basic facts addition problem with a number sentence numbers under 20 Recognizes addition and fact families through 18 Solves real-world whole number addition problems with sums to 100 Instantly recalls basic addition facts with sums to 18 in a table - with extraneous information given numbers under 20 numbers 100 and under Solves real-world whole number problems involving addition and Recognizes addition and fact families through 18 Solves basic facts addition and open sentences using diagrams and models (e.g., using balances) Solves 1-step open sentences with missing addends (numbers 100 and under) Solves simple problems based on data from tally charts - with extraneous information given (change unknown) numbers 100 and under Solves 1-step open sentences with missing addends (numbers 100 and under) Solves 2-step open sentences with missing addends Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Counts by 2's to 100 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 Distinguishes between odd and even numbers Uses counting by multiples for multiplication Solves word problems involving basic whole number multiplication facts to 10 x 10 Uses manipulatives to divide a small set of objects into groups of equal size Uses sharing for division Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated ) Solves word problems with whole number division facts with dividend and divisors less than 11 Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated ) 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 Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) Uses manipulatives to divide a small set of objects into groups of equal size Demonstrates an understanding of the zero property of multiplication Solves simple open sentences with missing factors (numbers 100 and under) Distinguishes between odd and even numbers Extends a growing arithmetic pattern, defined by numbers Extends a growing arithmetic pattern, defined by objects or diagrams Page 5 of 17
6 Mathematics RIT Score Range: Writes a number sentence for a simple problem solving situation Adds 1-digit numbers with sums to 18 (with parentheses) Analyzes a growing, arithmetic pattern with numbers to determine the rule New Vocabulary: fact family New Signs and Symbols: ( ) order of operations, multiplication, tally mark Analyzes a growing, arithmetic pattern with numbers to determine the rule Interprets a chart or table - calculation required Extends a growing arithmetic pattern, defined by numbers Writes a number sentence for a simple problem solving situation addition of numbers less than 100 (whole numbers numbers under 1000 New Vocabulary: gave, left, row, unifix cubes New Signs and Symbols: division, $ dollar sign Solves problems involving measurement of temperature Identifies numbers as composite numbers under 1000 Evaluates numerical expressions using grouping symbols (whole numbers Solves whole number word problems with numbers over 1000 Interprets a chart or table - calculation required Solves problems using tables numbers less than 1000 with addition and (whole numbers Completes a simple function table based on real-life situations (e.g., the number of tricycles related to the number of wheels) Analyzes a growing, arithmetic pattern with numbers to determine the rule New Vocabulary: composite number, each, prime number New Signs and Symbols: F degrees Fahrenheit, lb pound Page 6 of 17
7 Mathematics RIT Score Range: Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Solves real-world whole number addition problems with sums to 100 Instantly recalls basic addition facts with sums to 18 in a table - with extraneous information given numbers under 20 numbers 100 and under Solves real-world whole number problems involving addition and Recognizes addition and fact families through 18 Solves basic facts addition and open sentences using diagrams and models (e.g., using balances) Solves 1-step open sentences with missing addends (numbers 100 and under) Solves simple problems based on data from tally charts - with extraneous information given (change unknown) numbers 100 and under Solves 1-step open sentences with missing addends (numbers 100 and under) Solves 2-step open sentences with missing addends Solves 2-step open sentences with missing addends Solves open sentences with basic-facts calculations on both sides of the sentence numbers 100 and under (analysis) Understands equivalence and extends the concept to number sentences involving variables (e.g., = [] + 2) Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems 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 Distinguishes between odd and even numbers Uses counting by multiples for multiplication Solves word problems involving basic whole number multiplication facts to 10 x 10 Uses manipulatives to divide a small set of objects into groups of equal size Uses sharing for division Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated ) Solves word problems with whole number division facts with dividend and divisors less than 11 Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated ) 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 Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) Uses manipulatives to divide a small set of objects into groups of equal size Demonstrates an understanding of the zero property of multiplication Solves simple open sentences with missing factors (numbers 100 and under) Distinguishes between odd and even numbers Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) Solves word problems with whole number division facts with dividend and divisors less than 11 Solves simple open sentences with missing factors (numbers 100 and under) Describes a realistic situation using information given in a linear equation Solves whole number word problems with division over 10 x 10 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) Extends a growing arithmetic pattern, defined by objects or diagrams Predicts from simple charts and tables Page 7 of 17
8 Mathematics RIT Score Range: Analyzes a growing, arithmetic pattern with numbers to determine the rule Interprets a chart or table - calculation required Extends a growing arithmetic pattern, defined by numbers Writes a number sentence for a simple problem solving situation addition of numbers less than 100 (whole numbers numbers under 1000 New Vocabulary: gave, left, row, unifix cubes New Signs and Symbols: division, $ dollar sign Solves problems involving measurement of temperature Identifies numbers as composite numbers under 1000 Evaluates numerical expressions using grouping symbols (whole numbers Solves whole number word problems with numbers over 1000 Interprets a chart or table - calculation required Solves problems using tables numbers less than 1000 with addition and (whole numbers Completes a simple function table based on real-life situations (e.g., the number of tricycles related to the number of wheels) Analyzes a growing, arithmetic pattern with numbers to determine the rule New Vocabulary: composite number, each, prime number New Signs and Symbols: F degrees Fahrenheit, lb pound Uses simple linear equations to represent problem situations Completes a simple function table based on real-life situations (e.g., the number of tricycles related to the number of wheels) Completes a function table given a simple rule (e.g., x + 2) Determines the rule and completes a simple function machine output Solves problems using tables numbers 1000 or greater with addition and (whole numbers Solves whole number word problems with numbers over 1000 Determines the remainder in a real-world problem (whole numbers) Uses division for multiple-step real-world problems (whole numbers) Evaluates numerical expressions using grouping symbols (whole numbers Solves real-world problems involving 2-step multiple operations, whole numbers only Extends a growing arithmetic pattern, defined by objects or diagrams New Vocabulary: minimum, plus New Signs and Symbols: cent sign, = is equal to, + positive number Page 8 of 17
9 Mathematics RIT Score Range: Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems - with extraneous information given (change unknown) numbers 100 and under Solves 1-step open sentences with missing addends (numbers 100 and under) Solves 2-step open sentences with missing addends Solves 2-step open sentences with missing addends Solves open sentences with basic-facts calculations on both sides of the sentence numbers 100 and under (analysis) Understands equivalence and extends the concept to number sentences involving variables (e.g., = [] + 2) Solves open sentences with calculations on both sides of the sentence Understands equivalence and extends the concept to number sentences involving variables (e.g., = [] + 2) Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Solves word problems with whole number division facts with dividend and divisors less than 11 Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated ) 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 Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) Uses manipulatives to divide a small set of objects into groups of equal size Demonstrates an understanding of the zero property of multiplication Solves simple open sentences with missing factors (numbers 100 and under) Distinguishes between odd and even numbers Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) Solves word problems with whole number division facts with dividend and divisors less than 11 Solves simple open sentences with missing factors (numbers 100 and under) Describes a realistic situation using information given in a linear equation Solves whole number word problems with division over 10 x 10 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) Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects) Solves simple open sentences with missing factors (numbers over 100) Demonstrates an understanding of the associative property of multiplication Predicts the relative size of the answer when multiplying whole numbers Solves whole number word problems with division over 10 x 10 Extends a growing arithmetic pattern, defined by objects or diagrams Solves problems involving measurement of temperature Identifies numbers as composite numbers under 1000 Evaluates numerical expressions using grouping symbols (whole numbers Predicts from simple charts and tables Uses simple linear equations to represent problem situations Completes a simple function table based on real-life situations (e.g., the number of tricycles related to the number of wheels) Completes a function table given a simple rule (e.g., x + 2) Determines the rule and completes a simple function machine output Determines factors of whole numbers multiplication and division of numbers less than 100 (whole numbers numbers less than 1000 with multiplication and division (whole numbers Page 9 of 17
10 Mathematics RIT Score Range: Solves whole number word problems with numbers over 1000 Interprets a chart or table - calculation required Solves problems using tables numbers less than 1000 with addition and (whole numbers Completes a simple function table based on real-life situations (e.g., the number of tricycles related to the number of wheels) Analyzes a growing, arithmetic pattern with numbers to determine the rule New Vocabulary: composite number, each, prime number New Signs and Symbols: F degrees Fahrenheit, lb pound Solves problems using tables numbers 1000 or greater with addition and (whole numbers Solves whole number word problems with numbers over 1000 Determines the remainder in a real-world problem (whole numbers) Uses division for multiple-step real-world problems (whole numbers) Evaluates numerical expressions using grouping symbols (whole numbers Solves real-world problems involving 2-step multiple operations, whole numbers only Extends a growing arithmetic pattern, defined by objects or diagrams New Vocabulary: minimum, plus New Signs and Symbols: cent sign, = is equal to, + positive number Uses rounding to estimate answers to difficult multiplication and division problems (whole numbers Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) Solves real-world problems involving 2-step multiple operations, whole numbers only Solves real-world multiple-step problems involving whole numbers Solves 1-step problems involving proportions Uses simple linear equations to represent problem situations Applies algebraic methods to solve theoretical problems Completes a function table given a simple rule (e.g., x + 2) Determines the rule given a simple real-world function table (e.g., # Dogs compared to # Legs) Determines the rule and completes a simple function machine output Looks for a growing pattern to solve a problem Identifies numbers as prime New Signs and Symbols: ( ) parenthesis around an integer, { } set notation Page 10 of 17
11 Mathematics RIT Score Range: Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Solves 2-step open sentences with missing addends Solves open sentences with basic-facts calculations on both sides of the sentence numbers 100 and under (analysis) Understands equivalence and extends the concept to number sentences involving variables (e.g., = [] + 2) Solves open sentences with calculations on both sides of the sentence Understands equivalence and extends the concept to number sentences involving variables (e.g., = [] + 2) Solves open sentences with calculations on both sides of the sentence Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) Solves word problems with whole number division facts with dividend and divisors less than 11 Solves simple open sentences with missing factors (numbers 100 and under) Describes a realistic situation using information given in a linear equation Solves whole number word problems with division over 10 x 10 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) Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects) Solves simple open sentences with missing factors (numbers over 100) Demonstrates an understanding of the associative property of multiplication Predicts the relative size of the answer when multiplying whole numbers Solves whole number word problems with division over 10 x 10 Models algorithms using place value concepts (multiplication and division with whole numbers) Demonstrates an understanding of multiple properties Predicts from simple charts and tables Uses simple linear equations to represent problem situations Completes a simple function table based on real-life situations (e.g., the number of tricycles related to the number of wheels) Completes a function table given a simple rule (e.g., x + 2) Determines the rule and completes a simple function machine output Solves problems using tables numbers 1000 or greater with addition and (whole numbers Solves whole number word problems with numbers over 1000 Determines the remainder in a real-world problem (whole numbers) Uses division for multiple-step real-world problems (whole numbers) Determines factors of whole numbers multiplication and division of numbers less than 100 (whole numbers numbers less than 1000 with multiplication and division (whole numbers Uses rounding to estimate answers to difficult multiplication and division problems (whole numbers Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) Solves real-world problems involving 2-step multiple operations, whole numbers only Solves real-world multiple-step problems involving whole numbers Solves 1-step problems involving proportions multiplication and division of numbers less than 100 (whole numbers numbers less than 1000 with multiplication and division (whole 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 Solves 1-step problems involving proportions Applies algebraic methods to solve theoretical problems Extends a growing pattern of triangular numbers, defined by objects or diagrams Uses factor and multiple concepts to solve simple problems Page 11 of 17
12 Mathematics RIT Score Range: Evaluates numerical expressions using grouping symbols (whole numbers Solves real-world problems involving 2-step multiple operations, whole numbers only Extends a growing arithmetic pattern, defined by objects or diagrams New Vocabulary: minimum, plus New Signs and Symbols: cent sign, = is equal to, + positive number Uses simple linear equations to represent problem situations Applies algebraic methods to solve theoretical problems Completes a function table given a simple rule (e.g., x + 2) Determines the rule given a simple real-world function table (e.g., # Dogs compared to # Legs) Determines the rule and completes a simple function machine output Looks for a growing pattern to solve a problem Identifies numbers as prime Uses multiple number theory concepts to solve problems (e.g., factors, digits, odd/even, divisibility) Determines factors of whole numbers Looks for a growing pattern to solve a problem New Signs and Symbols: ( ) parenthesis around an integer, { } set notation Page 12 of 17
13 Mathematics RIT Score Range: Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Add & Subtract: Represent and Solve Problems Solves open sentences with calculations on both sides of the sentence Understands equivalence and extends the concept to number sentences involving variables (e.g., = [] + 2) Solves open sentences with calculations on both sides of the sentence Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects) Solves simple open sentences with missing factors (numbers over 100) Demonstrates an understanding of the associative property of multiplication Predicts the relative size of the answer when multiplying whole numbers Solves whole number word problems with division over 10 x 10 Models algorithms using place value concepts (multiplication and division with whole numbers) Demonstrates an understanding of multiple properties Models algorithms using place value concepts (multiplication and division with whole numbers) Determines factors of whole numbers multiplication and division of numbers less than 100 (whole numbers numbers less than 1000 with multiplication and division (whole numbers Uses rounding to estimate answers to difficult multiplication and division problems (whole numbers Solves complex word problems involving whole number division with remainder (e.g., 2-step, 2-digit divisor) Solves real-world problems involving 2-step multiple operations, whole numbers only Solves real-world multiple-step problems involving whole numbers Solves 1-step problems involving proportions Uses simple linear equations to represent problem situations Applies algebraic methods to solve theoretical problems Completes a function table given a simple rule (e.g., x + 2) Determines the rule given a simple real-world function table (e.g., # Dogs compared to # Legs) Determines the rule and completes a simple function machine output Looks for a growing pattern to solve a problem Identifies numbers as prime multiplication and division of numbers less than 100 (whole numbers numbers less than 1000 with multiplication and division (whole 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 Solves 1-step problems involving proportions Applies algebraic methods to solve theoretical problems Extends a growing pattern of triangular numbers, defined by objects or diagrams Uses factor and multiple concepts to solve simple problems Uses multiple number theory concepts to solve problems (e.g., factors, digits, odd/even, divisibility) Determines factors of whole numbers Looks for a growing pattern to solve a problem Evaluates numerical expressions using the order of operations (whole numbers Evaluates numerical expressions using the order of operations (using integers) Solves problems comparing unit prices Page 13 of 17
14 Mathematics RIT Score Range: New Signs and Symbols: ( ) parenthesis around an integer, { } set notation Page 14 of 17
15 Mathematics RIT Score Range: Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Models algorithms using place value concepts (multiplication and division with whole numbers) Demonstrates an understanding of multiple properties Models algorithms using place value concepts (multiplication and division with whole numbers) multiplication and division of numbers less than 100 (whole numbers numbers less than 1000 with multiplication and division (whole 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 Solves 1-step problems involving proportions Applies algebraic methods to solve theoretical problems Extends a growing pattern of triangular numbers, defined by objects or diagrams Uses factor and multiple concepts to solve simple problems Uses multiple number theory concepts to solve problems (e.g., factors, digits, odd/even, divisibility) Determines factors of whole numbers Looks for a growing pattern to solve a problem Evaluates numerical expressions using the order of operations (whole numbers Evaluates numerical expressions using the order of operations (using integers) Solves problems comparing unit prices Evaluates numerical expressions using the order of operations (using integers) Uses reasoning strategies to solve problems Page 15 of 17
16 Mathematics RIT Score Range: > 250 Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Models algorithms using place value concepts (multiplication and division with whole numbers) Evaluates numerical expressions using the order of operations (whole numbers Evaluates numerical expressions using the order of operations (using integers) Solves problems comparing unit prices Evaluates numerical expressions using the order of operations (using integers) Uses reasoning strategies to solve problems Uses reasoning strategies to solve problems Page 16 of 17
17 Mathematics RIT Score Range: > Add & Subtract: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Solve Problems & Analyze Patterns & Relationships Evaluates numerical expressions using the order of operations (using integers) Uses reasoning strategies to solve problems > 250 Add & Subtract: Represent and Solve Problems Multiply & Divide: Represent and Solve Problems Solve Problems & Analyze Patterns & Relationships Uses reasoning strategies to solve problems Page 17 of 17
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