RIT Above 260:• Identifies the contrapositive of a conditional statement
• Uses technology to organize, record, and communicate mathematical ideas
RIT 251-260:• Uses equivalent representations to understand new mathematical content & technology to organize, record, and communicate mathematical ideas • Uses algebraic and graphic representations to model and interpret mathematical and real-world situations• Verifies reasonableness of results of complex problems • Applies the most appropriate problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error
• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models) • Uses the components of mathematical modeling (e.g.: • Problem formulation • Mathematical model • Solution within the model• Interpretation of solution within the model • Validation in original real-world problem situation)
VOCABULARY: • Conditional statement, • Counterexample
SIGNS AND SYMBOLS: • || Absolute value, • Congruent segment symbol, • Parallel symbol, • Right angle marker
RIT 241-250:
• Uses equivalent representations to understand new mathematical content & technology to organize, record, and communicate mathematical ideas
• Uses algebraic representations to model and interpret mathematical and real-world situations
• Uses a number line to determine the distance between a positive and negative number
• Verifies reasonableness of results of complex problems • Applies the most appropriate problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error
• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models) • Uses the components of mathematical modeling (e.g.: • Problem formulation • Mathematical model • Solution within the model• Interpretation of solution within the model • Validation in original real-world problem situation)
VOCABULARY: • Converse
SIGNS AND SYMBOLS: • + Positive number
RIT 231-240:
• Translates a problem to a symbolic expression or equation (analysis)• Analyzes complex problems to separate into simpler parts • Organizes information from a paragraph to solve a problem
• Verifies reasonableness of results of complex problems
• Constructs simple, valid arguments using if ...then statements based on Venn diagrams • Uses equivalent representations to understand new mathematical content & pictures to represent problems
• Uses technology to organize, record, and communicate mathematical ideas
• Uses models to multiply and divide fractions and mixed fractions and connect the actions to algorithms • Uses the components of mathematical modeling (e.g.: • Problem formulation • Mathematical model • Solution within the model• Interpretation of solution within the model • Validation in original real-world problem situation) • Applies the most appropriate problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
SIGNS AND SYMBOLS: • - Negative number, • • Point, • Segment overbar
RIT 221-230:
• Analyzes another student's explanation to understand complex problems
• Restates the problem from various perspectives
• Identifies the question from a problem solving situation
• Determines the required information for solving a difficult problem and whether any further information is needed• Determines the additional information required to solve problems • Uses pictures to represent problems & truth tables to solve simple logic problems & technology to generate and analyze data to solve problems • Uses a number line to determine the midpoint between a positive and negative number
• Translates a problem to a symbolic expression or equation (analysis)• Applies what was learned to a new and/or more complex problem • Organizes information from a paragraph to solve a problem
• Verifies reasonableness of results of more difficult problems
• Looks for a growing pattern to solve a problem
• Solves real-world problems using reasoning strategies• Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations
• Expresses the solution clearly and logically by using the appropriate mathematical terms and notation
• Applies a problem solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness • Applies a variety of problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error
• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
VOCABULARY: • Heaviest, • Lightest, • Shorter
SIGNS AND SYMBOLS: • ft Feet
RIT 211-220:
• Analyzes another student's explanation to understand complex problems
• Restates the problem from various perspectives
• Determines the required information for solving a difficult problem and whether any further information is needed• Determines the additional information required to solve problems & the operation needed from a complex problem • Translates a 2-step problem to a symbolic expression or equation• Verifies reasonableness of results of more difficult problems • Uses pictures, diagrams, and systematic lists to represent problems & manipulatives and models to demonstrate thinking processes • Uses technology to generate and analyze data to solve problems
• Looks for a growing pattern to solve a problem
• Solves real-world problems using reasoning strategies• Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations • Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects)
• Expresses the solution clearly and logically by using the appropriate mathematical terms and notation
• Applies a problem solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness • Applies a variety of problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error
• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
VOCABULARY: • High, • Square meter, • Systematic list
SIGNS AND SYMBOLS: • % Percent
RIT 201-210:
• Analyzes another student's explanation to understand more difficult problems
• Restates the problem in own words
• Selects the information necessary to solve a simple problem and determines whether any further information is needed
• Draws pictures to represent whole number problems
• Uses manipulatives to represent problems & manipulatives and models to demonstrate thinking processes
• Use patterns and their generalizations to make and justify inferences and predictions & a number line to model multiplication
• Uses calculators as problem solving tools (e.g., to explore patterns, to validate solutions)
• Uses technology to gather, analyze, and communicate mathematical information
• Uses models to add and subtract fractions and connect the actions to algorithms
• Writes a number sentence for a simple problem solving situation (analysis)
• Determines the operation needed to solve a real-world problem
• Translates a number sentence to a real-world situation & a 1-step and a 2-step problem problem to a symbolic expression or equation
• Verify reasonableness of results of simple problems
• Looks for a linear pattern to solve a problem & for a repeating pattern to solve a problem
• Solves real-world problems using reasoning strategies• Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations • Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects)
• Relates everyday language to mathematical language and symbols, and progresses toward the use of appropriate terminology (e.g., “repeated addition” becomes “multiplication,” “fair share” becomes “divide,” “balance the equation” becomes “solve the equation")
• Uses a problem solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness •Uses a variety of problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error
• Makes a table or organized list • Works backwards• Makes a problem simpler • Uses models)
VOCABULARY: • Half-dollar, • Mathematical statement, • Meters per second, • Multiplication sentence
SIGNS AND SYMBOLS: • () Order of operations
RIT 191-200:
• Analyzes another student's explanation to understand more difficult problems
• Restates the problem in own words
• Selects the information necessary to solve a simple problem and determines whether any further information is needed
• Draws pictures to represent whole number problems
• Determines the operation needed from a simple problem & the operation needed to solve a real-world problem
• Translates from a diagram to an expression or equation & a 1-step problem to a symbolic expression or equation• Verify reasonableness of results of simple problems
• Looks for a simple linear pattern in a table to solve a problem
• Uses calculators as problem solving tools (e.g., to explore patterns, to validate solutions)
• Uses technology to gather, analyze, and communicate mathematical information
• Uses models to add and subtract fractions and connect the actions to algorithms• Uses a number line to construct subtraction facts with subtrahends and minuends through 20 (whole numbers) • Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated subtraction) • Relates everyday language to mathematical language and symbols, and progresses toward the use of appropriate terminology (e.g., “add more” becomes “plus”)
• Relates everyday language to mathematical language and symbols, and progresses toward the use of appropriate terminology (e.g., “repeated addition” becomes “multiplication,” “fair share” becomes “divide,” “balance the equation” becomes “solve the equation")
• Uses a problem solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness •Uses a variety of problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
VOCABULARY: • Operation, • Regroup, • Rename
SIGNS AND SYMBOLS: • a.m., • ¢ Cent sign, • > Greater than, • < Less than, • oz Ounce, • : Used with time
RIT 181-190:
• Analyzes another student's explanation to understand simple problems
• Draws pictures to represent whole number problems
• Determines the operation needed from a simple problem• Writes a number sentence for a simple problem solving situation • Uses manipulatives to represent whole number problems & to model and justify solutions
• Uses appropriate technology to solve problems & models to calculate differences through 1000 (whole numbers) • Uses a number line to construct subtraction facts with subtrahends and minuends through 20 (whole numbers) • Uses words, pictures, numbers, and technology to explain the solution to problems
• Models multiplication and division algorithms using arrays (whole numbers)
• Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated subtraction)
• Relates everyday language to mathematical language and symbols, and progresses toward the use of appropriate terminology (e.g., “add more” becomes “plus”)• Follows a model of problem solving that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness • Uses a structured model to solve problems using a variety of strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error • Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
VOCABULARY: • Number statement, • Row, • Subtrahend
SIGNS AND SYMBOLS: • ÷ Division, • x Multiplication
RIT 171-180:
• Analyzes another student's explanation to understand simple problems
• Determines the operation needed from a simple problem• Writes a number sentence for a simple problem solving situation
• Uses manipulatives to model and justify solutions & appropriate technology to solve problems & models to calculate whole number sums through 999 • Uses models to calculate differences through 100 (whole numbers) and through 1000 (whole numbers)
• Uses a number line to construct addition facts with sums through 20 (whole numbers)
• Uses words, pictures, numbers, and technology to explain the solution to problems
• Follows a model of problem solving that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness • Uses a structured model to solve problems using a variety of strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)VOCABULARY: • Multiply, • Subtract, • Term, • Total
SIGNS AND SYMBOLS: • $ Dollar sign
RIT 161-170:• Analyzes another student's explanation to understand simple problems
• Uses manipulatives to model and justify solutions & models to construct subtraction facts with differences through 10 (whole numbers) • Uses models to calculate whole number sums through 99 and through 999 & differences through 100 (whole numbers)
• Uses a number line to construct addition facts with sums through 20 (whole numbers)
• Follows a model of problem solving that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness • Uses a structured model to solve problems using a variety of strategies (e.g.:• Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error • Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models) VOCABULARY: • Number line, • Number sentence
SIGNS AND SYMBOLS: • - Subtraction
RIT Below 161:
• Uses models to construct whole number addition facts with addends through 10 and sums through 99SIGNS AND SYMBOLS: • + Addition, • = Is equal to, • Variable
RIT Above 260:• Identifies the contrapositive of a conditional statement
• Uses technology to organize, record, and communicate mathematical ideas
RIT 251-260:• Uses equivalent representations to understand new mathematical content & technology to organize, record, and communicate mathematical ideas
• Uses algebraic and graphic representations to model and interpret mathematical and real-world situations• Verifies reasonableness of results of complex problems
• Applies the most appropriate problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error
• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
• Uses the components of mathematical modeling (e.g.: • Problem formulation • Mathematical model • Solution within the model• Interpretation of solution within the model • Validation in original real-world problem situation)
VOCABULARY: • Conditional statement, • Counterexample
SIGNS AND SYMBOLS: • || Absolute value, • Congruent segment symbol, • Parallel symbol, • Right angle marker
RIT 241-250:
• Uses equivalent representations to understand new mathematical content & technology to organize, record, and communicate mathematical ideas
• Uses algebraic representations to model and interpret mathematical and real-world situations
• Uses a number line to determine the distance between a positive and negative number
• Verifies reasonableness of results of complex problems
• Applies the most appropriate problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error
• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
• Uses the components of mathematical modeling (e.g.: • Problem formulation • Mathematical model • Solution within the model• Interpretation of solution within the model • Validation in original real-world problem situation)
VOCABULARY: • Converse
SIGNS AND SYMBOLS: • + Positive number
RIT 231-240:
• Translates a problem to a symbolic expression or equation (analysis)• Analyzes complex problems to separate into simpler parts
• Organizes information from a paragraph to solve a problem
• Verifies reasonableness of results of complex problems
• Constructs simple, valid arguments using if ...then statements based on Venn diagrams
• Uses equivalent representations to understand new mathematical content & pictures to represent problems
• Uses technology to organize, record, and communicate mathematical ideas
• Uses models to multiply and divide fractions and mixed fractions and connect the actions to algorithms
• Uses the components of mathematical modeling (e.g.: • Problem formulation • Mathematical model • Solution within the model• Interpretation of solution within the model • Validation in original real-world problem situation)
• Applies the most appropriate problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
SIGNS AND SYMBOLS: • - Negative number, • • Point, • Segment overbar
RIT 221-230:
• Analyzes another student's explanation to understand complex problems
• Restates the problem from various perspectives
• Identifies the question from a problem solving situation
• Determines the required information for solving a difficult problem and whether any further information is needed• Determines the additional information required to solve problems
• Uses pictures to represent problems & truth tables to solve simple logic problems & technology to generate and analyze data to solve problems
• Uses a number line to determine the midpoint between a positive and negative number
• Translates a problem to a symbolic expression or equation (analysis)• Applies what was learned to a new and/or more complex problem
• Organizes information from a paragraph to solve a problem
• Verifies reasonableness of results of more difficult problems
• Looks for a growing pattern to solve a problem
• Solves real-world problems using reasoning strategies• Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations
• Expresses the solution clearly and logically by using the appropriate mathematical terms and notation
• Applies a problem solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness
• Applies a variety of problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error
• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
VOCABULARY: • Heaviest, • Lightest, • Shorter
SIGNS AND SYMBOLS: • ft Feet
RIT 211-220:
• Analyzes another student's explanation to understand complex problems
• Restates the problem from various perspectives
• Determines the required information for solving a difficult problem and whether any further information is needed• Determines the additional information required to solve problems & the operation needed from a complex problem
• Translates a 2-step problem to a symbolic expression or equation• Verifies reasonableness of results of more difficult problems
• Uses pictures, diagrams, and systematic lists to represent problems & manipulatives and models to demonstrate thinking processes
• Uses technology to generate and analyze data to solve problems
• Looks for a growing pattern to solve a problem
• Solves real-world problems using reasoning strategies• Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations
• Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects)
• Expresses the solution clearly and logically by using the appropriate mathematical terms and notation
• Applies a problem solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness
• Applies a variety of problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error
• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
VOCABULARY: • High, • Square meter, • Systematic list
SIGNS AND SYMBOLS: • % Percent
RIT 201-210:
• Analyzes another student's explanation to understand more difficult problems
• Restates the problem in own words
• Selects the information necessary to solve a simple problem and determines whether any further information is needed
• Draws pictures to represent whole number problems
• Uses manipulatives to represent problems & manipulatives and models to demonstrate thinking processes
• Use patterns and their generalizations to make and justify inferences and predictions & a number line to model multiplication
• Uses calculators as problem solving tools (e.g., to explore patterns, to validate solutions)
• Uses technology to gather, analyze, and communicate mathematical information
• Uses models to add and subtract fractions and connect the actions to algorithms
• Writes a number sentence for a simple problem solving situation (analysis)
• Determines the operation needed to solve a real-world problem
• Translates a number sentence to a real-world situation & a 1-step and a 2-step problem problem to a symbolic expression or equation
• Verify reasonableness of results of simple problems
• Looks for a linear pattern to solve a problem & for a repeating pattern to solve a problem
• Solves real-world problems using reasoning strategies• Produces a valid conjecture using inductive reasoning by generalizing from a pattern of observations
• Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects)
• Relates everyday language to mathematical language and symbols, and progresses toward the use of appropriate terminology (e.g., “repeated addition” becomes “multiplication,” “fair share” becomes “divide,” “balance the equation” becomes “solve the equation")
• Uses a problem solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness
• Uses a variety of problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error
• Makes a table or organized list • Works backwards• Makes a problem simpler • Uses models)
VOCABULARY: • Half-dollar, • Mathematical statement, • Meters per second, • Multiplication sentence
SIGNS AND SYMBOLS: • () Order of operations
RIT 191-200:
• Analyzes another student's explanation to understand more difficult problems
• Restates the problem in own words
• Selects the information necessary to solve a simple problem and determines whether any further information is needed
• Draws pictures to represent whole number problems
• Determines the operation needed from a simple problem & the operation needed to solve a real-world problem
• Translates from a diagram to an expression or equation & a 1-step problem to a symbolic expression or equation• Verify reasonableness of results of simple problems
• Looks for a simple linear pattern in a table to solve a problem
• Uses calculators as problem solving tools (e.g., to explore patterns, to validate solutions)
• Uses technology to gather, analyze, and communicate mathematical information
• Uses models to add and subtract fractions and connect the actions to algorithms• Uses a number line to construct subtraction facts with subtrahends and minuends through 20 (whole numbers)
• Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated subtraction)
• Relates everyday language to mathematical language and symbols, and progresses toward the use of appropriate terminology (e.g., “add more” becomes “plus”)
• Relates everyday language to mathematical language and symbols, and progresses toward the use of appropriate terminology (e.g., “repeated addition” becomes “multiplication,” “fair share” becomes “divide,” “balance the equation” becomes “solve the equation")
• Uses a problem solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness
• Uses a variety of problem solving strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
VOCABULARY: • Operation, • Regroup, • Rename
SIGNS AND SYMBOLS: • a.m., • ¢ Cent sign, • > Greater than, • < Less than, • oz Ounce, • : Used with time
RIT 181-190:
• Analyzes another student's explanation to understand simple problems
• Draws pictures to represent whole number problems
• Determines the operation needed from a simple problem• Writes a number sentence for a simple problem solving situation
• Uses manipulatives to represent whole number problems & to model and justify solutions
• Uses appropriate technology to solve problems & models to calculate differences through 1000 (whole numbers)
• Uses a number line to construct subtraction facts with subtrahends and minuends through 20 (whole numbers)
• Uses words, pictures, numbers, and technology to explain the solution to problems
• Models multiplication and division algorithms using arrays (whole numbers)
• Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated subtraction)
• Relates everyday language to mathematical language and symbols, and progresses toward the use of appropriate terminology (e.g., “add more” becomes “plus”)• Follows a model of problem solving that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness
• Uses a structured model to solve problems using a variety of strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error • Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
VOCABULARY: • Number statement, • Row, • Subtrahend
SIGNS AND SYMBOLS: • ÷ Division, • x Multiplication
RIT 171-180:
• Analyzes another student's explanation to understand simple problems
• Determines the operation needed from a simple problem• Writes a number sentence for a simple problem solving situation
• Uses manipulatives to model and justify solutions & appropriate technology to solve problems & models to calculate whole number sums through 999
• Uses models to calculate differences through 100 (whole numbers) and through 1000 (whole numbers)
• Uses a number line to construct addition facts with sums through 20 (whole numbers)
• Uses words, pictures, numbers, and technology to explain the solution to problems
• Follows a model of problem solving that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness
• Uses a structured model to solve problems using a variety of strategies (e.g.: • Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error• Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)VOCABULARY: • Multiply, • Subtract, • Term, • Total
SIGNS AND SYMBOLS: • $ Dollar sign
RIT 161-170:• Analyzes another student's explanation to understand simple problems
• Uses manipulatives to model and justify solutions & models to construct subtraction facts with differences through 10 (whole numbers)
• Uses models to calculate whole number sums through 99 and through 999 & differences through 100 (whole numbers)
• Uses a number line to construct addition facts with sums through 20 (whole numbers)
• Follows a model of problem solving that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness
• Uses a structured model to solve problems using a variety of strategies (e.g.:• Draws a picture • Uses process of elimination • Looks for patterns • Uses trial and error • Makes a table or organized list • Works backwards • Makes a problem simpler • Uses models)
VOCABULARY: • Number line, • Number sentence
SIGNS AND SYMBOLS: • - Subtraction
RIT Below 161:
• Uses models to construct whole number addition facts with addends through 10 and sums through 99SIGNS AND SYMBOLS: • + Addition, • = Is equal to, • Variable