### Operations & Algebraic Thinking

 If your goal is 180 or less:  • Uses a number line to construct addition facts with sums through 20 (whole numbers) • 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 100 (result unknown) • Represents a basic facts addition problem with a number sentence • Subtracts a 1-digit number from a 2-digit number that is less than 20 (whole numbers only) • Solves real-world whole number problems involving subtraction with numbers under 20 • Instantly recalls basic multiplication facts where one factor is 0-5 and the other factor is 0-12 • Multiplies basic facts to 10 x 10 vertically • Adds 1-digit numbers with sums to 18 (with parentheses) • Recognizes addition and subtraction fact families through 18 • Solves basic-facts open sentences - addition and subtraction • Solves basic facts open sentences - multiplication and division • Determines the operation needed from a simple problem • Writes a number sentence for a simple problem solving situation • Counts by 2's to 100 • Writes equivalent forms of whole number expressions (e.g., 15 + 5 = 10 + 10)• Extends a growing arithmetic pattern, defined by numbers • Analyzes a growing, arithmetic pattern with numbers to determine the ruleIf your goal is between 181 and 190:  • Uses rounding to estimate answers to real-world problems involving addition of numbers less than 100 (whole numbers only) • Instantly recalls basic addition facts with sums to 18 in a table • 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 100 (result unknown) • Instantly recalls basic subtraction facts with minuend less than 10 • 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 problems using the inverse relationship between addition and subtraction • Uses counting by multiples for multiplication • Instantly recalls basic multiplication facts where one factor is 6-12 and the other factor is 0-12 • Multiplies basic facts to 10 x 10 vertically • 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 subtraction) • Models multiplication and division algorithms using arrays (whole numbers) • Instantly recalls division facts with dividend and divisors less than 10 • Solves real-world whole number problems involving addition and subtraction • Recognizes addition and subtraction fact families through 18 • Demonstrates an understanding of the zero property of multiplication • Demonstrates an understanding of the inverse relationship between multiplication and division • Solves basic facts addition and subtraction open sentences using diagrams and models (e.g., using balances) • Solves 1-step open sentences with missing addends (numbers 100 and under) • Determines the operation needed from a simple problem• Extends a growing arithmetic pattern, defined by numbers • Analyzes a growing, arithmetic pattern with numbers to determine the ruleIf your goal is between 191 and 200: • Uses rounding to estimate answers to real-world problems involving numbers less than 1000 with addition and subtraction (whole numbers only) • 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 (change unknown) • 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 whole number subtraction word problems with numbers over 1000 • Solves problems using the inverse relationship between addition and subtraction • Instantly recalls basic multiplication facts where one factor is 6-12 and the other factor is 0-12 • 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 manipulatives to divide a small set of objects into groups of equal size • Models whole number multiplication and division algorithms (e.g., shows multiplication as repeated addition and division as repeated subtraction) • Instantly recalls division facts with dividend and divisors less than 10 • Instantly recalls division facts with dividend and divisors less than 13 • Solves word problems with whole number division facts with dividend and divisors less than 11 • 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) • Demonstrates an understanding of the commutative property of multiplication with simple problems • Demonstrates an understanding of the zero property of multiplication • Uses algebraic reasoning to solve problems involving equality relationships • Solves 1-step open sentences with missing addends (numbers 100 and under) • Solves simple open sentences with missing factors (numbers 100 and under)• Solves 2-step open sentences with missing addends • Determines the operation needed from a simple problem • Translates a 1-step problem to a symbolic expression or equation • Interprets a chart or table - calculation required • Solves problems using tables • Writes equivalent forms of whole numbers 11 to 20 using addition (e.g., 14 = 7 + 7) • Distinguishes between odd and even numbers• Extends a growing arithmetic pattern, defined by objects or diagrams • Analyzes a growing, arithmetic pattern with numbers to determine the rule • Completes a simple function table based on real-life situations (e.g., the number of tricycles related to the number of wheels) • Identifies numbers as composite If your goal is between 201 and 210: • Uses rounding to estimate answers to real-world problems involving numbers 1000 or greater with addition and subtraction (whole numbers only) • Solves real-world whole number problems involving subtraction with numbers 100 and under (analysis) • Solves whole number subtraction word problems with numbers over 1000 • Solves problems using the inverse relationship between addition and subtraction • 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) • Instantly recalls division facts with dividend and divisors less than 13 • Performs mental computation with division • Solves word problems with whole number division facts with dividend and divisors less than 11 • Solves simple word problems involving whole number division with remainder (e.g., 1-step, 1-digit divisor) • Solves whole number word problems with division over 10 x 10 • 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 only) • Solves real-world problems involving 2-step multiple operations, whole numbers only • Demonstrates an understanding of the commutative property of multiplication with simple problems • Understands equivalence and extends the concept to number sentences involving variables (e.g., 8 + 2 = [] + 2) • Uses algebraic reasoning to solve problems involving equality relationships • Uses simple linear equations to represent problem situations • Describes a realistic situation using information given in a linear equation • Solves simple open sentences with missing factors (numbers 100 and under) • Solves 2-step open sentences with missing addends • Solves open sentences with basic-facts calculations on both sides of the sentence • Translates a 1-step problem to a symbolic expression or equation • Translates a 2-step problem to a symbolic expression or equation• Solves problems using tables • Uses number sense strategies to solve problems (addition/subtraction only)Extends a growing arithmetic pattern, defined by objects or diagrams • 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 • Predicts from simple charts and tablesIf your goal is between 211 and 220: • 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) • Models whole number multiplication and division algorithms (e.g., uses physical materials to show 4 groups of 3 objects) • Performs mental computation with 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) • Solves real-world problems involving 2-step multiple operations, whole numbers only • Solves real-world multiple-step problems involving whole numbers • Predicts the relative size of the answer when multiplying whole numbers • Demonstrates an understanding of the inverse relationship between addition and subtraction • Demonstrates an understanding of the commutative property of multiplication with simple problems • Demonstrates an understanding of the associative property of multiplication • Demonstrates an understanding of the distributive property of multiplication by decomposing a term • Understands equivalence and extends the concept to number sentences involving variables (e.g., 8 + 2 = [] + 2) • Uses algebraic reasoning to solve problems involving equality relationships • Uses simple linear equations to represent problem situations • Solves simple open sentences with missing factors (numbers over 100) • Solves open sentences using the distributive property • Solves open sentences with calculations on both sides of the sentence • Applies algebraic methods to solve theoretical problems • Uses pictures to represent problems • Translates a 2-step problem to a symbolic expression or equation• 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 • Determines factors of whole numbers • Identifies numbers as primeIf your goal is between 221 and 230: • 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) • Models algorithms using place value concepts (multiplication and division with 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 • Demonstrates an understanding of multiple properties • Represents relationships of quantities in the form of an expression • Solves open sentences with calculations on both sides of the sentence • Applies algebraic methods to solve theoretical problems • Applies algebraic methods to solve real-world problems • Uses pictures to represent problems • Uses multiple number theory concepts to solve problems (e.g., factors, digits, odd/even, divisibility • Extends a growing pattern of triangular numbers, defined by objects or diagrams • Looks for a growing pattern to solve a problem • Determines factors of whole numbers• Uses factor and multiple concepts to solve simple problemsIf your goal is between 231 and 240: • Models algorithms using place value concepts (multiplication and division with whole numbers) • Evaluates numerical expressions using the order of operations (whole numbers only) • Solves multiple-step problems involving proportions • Represents relationships of quantities in the form of an expression • Applies algebraic methods to solve real-world problems • Solves problems comparing unit prices • Uses pictures to represent problemsIf your goal is greater than 240: • Solves multiple-step problems involving proportions• Applies algebraic methods to solve real-world problems • Uses reasoning strategies to solve problems
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