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 rule

If 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 rule

If 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 tables

If 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 prime

If 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 problems

If 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 problems

If 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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