
Course Content
A. Number Sense
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A.01. Identify place value names (ones, tens, hundreds, thousands).
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A.02. Understand the relationship between place values.
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A.03. Convert between standard and expanded form.
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A.04. Determine the value of a digit based on its place value.
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A.05. Convert between different place values (e.g., tens to hundreds).
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A.06. Represent numbers using place value models.
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A.07. Write word names for numbers.
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A.08. Round numbers to the nearest ten, hundred, and thousand.
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A.09. Identify and apply rounding in real-world scenarios (e.g., estimating costs).
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A.10. Use rounding to estimate sums and differences.
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A.11. Determine if a number is even or odd.
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A.12. Explain the rules for determining even and odd numbers through arithmetic.
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A.13. Understand and use inequalities (, =) to compare numbers.
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A.14. Order a set of numbers from least to greatest or greatest to least.
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A.15. Identify and generate skip-counting sequences.
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A.16. Recognize and interpret Roman numerals.
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A.17. Identify prime and composite numbers.
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A.18. Represent inequalities on a number line.
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A.19. Understand and compare integers.
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A.20. Solve problems involving number patterns and sequences.
B. Addition
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B.01. Recall basic addition facts up to 20.
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B.02. Solve addition word problems involving facts up to 20.
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B.03. Complete addition sentences with missing addends (up to 20).
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B.04. Add two-digit numbers.
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B.05. Solve addition word problems involving two-digit numbers.
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B.06. Complete addition sentences with missing addends (up to two digits).
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B.07. Add three-digit numbers.
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B.08. Solve addition word problems involving three-digit numbers.
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B.09. Complete addition sentences with missing addends (up to three digits).
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B.10. Add four-digit numbers.
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B.11. Solve addition word problems involving four-digit numbers.
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B.12. Complete addition sentences with missing addends (up to four digits).
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B.13. Add three or more numbers.
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B.14. Apply the properties of addition (commutative and associative) to simplify calculations.
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B.15. Identify and correct errors in addition problems.
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B.16. Solve addition problems involving missing digits.
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B.17. Recognize and explain addition patterns across increasing place values.
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B.18. Estimate sums.
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B.19. Estimate sums in word problems.
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B.20. Solve multi-step word problems involving addition.
C. Subtraction
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C.01. Recall basic subtraction facts up to 18.
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C.02. Solve subtraction word problems involving facts up to 18.
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C.03. Complete subtraction sentences with missing subtrahends or differences (up to 18).
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C.04. Subtract two-digit numbers.
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C.05. Solve subtraction word problems involving two-digit numbers.
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C.06. Complete subtraction sentences with missing subtrahends or differences (up to two digits).
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C.07. Subtract three-digit numbers.
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C.08. Solve subtraction word problems involving three-digit numbers.
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C.09. Complete subtraction sentences with missing subtrahends or differences (up to three digits).
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C.10. Subtract four-digit numbers.
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C.11. Solve subtraction word problems involving four-digit numbers.
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C.12. Complete subtraction sentences with missing subtrahends or differences (up to four digits).
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C.13. Solve subtraction problems involving missing digits.
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C.14. Recognize and explain subtraction patterns across increasing place values.
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C.15. Estimate differences.
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C.16. Estimate differences in word problems.
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C.17. Solve multi-step word problems involving subtraction.
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C.18. Apply subtraction to solve real-world problems.
D. Understanding Multiplication
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D.01. Count equal groups of objects.
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D.02. Write multiplication sentences to represent equal groups.
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D.03. Relate addition to multiplication using equal groups.
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D.04. Represent multiplication using arrays.
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D.05. Write multiplication sentences to represent arrays.
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D.06. Create arrays to model multiplication problems.
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D.07. Use number lines to model multiplication.
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D.08. Understand the concept of factors and products.
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D.09. Identify multiplication as repeated addition.
E. Multiplication
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E.01. Recall basic multiplication facts up to 10.
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E.02. Find missing factors in multiplication sentences (up to 10).
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E.03. Identify multiples of a given number (up to 12).
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E.04. Find numbers with a given product.
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E.05. Identify factors of a number.
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E.06. Find all factor pairs of a number.
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E.07. Determine the prime factorization of a number.
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E.08. Multiply one-digit numbers by teen numbers using grids.
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E.09. Multiply one-digit numbers by two-digit numbers using area models.
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E.10. Multiply one-digit numbers by two-digit numbers using the standard algorithm.
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E.11. Solve multiplication word problems involving one-digit numbers and two-digit numbers.
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E.12. Multiply one-digit numbers by three-digit numbers using area models.
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E.13. Multiply one-digit numbers by three-digit numbers using the standard algorithm.
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E.14. Multiply one-digit numbers by multi-digit numbers using partial products.
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E.15. Multiply one-digit numbers by larger numbers.
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E.16. Multiply by 10 or 100.
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E.17. Recognize and explain multiplication patterns across increasing place values.
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E.18. Apply the properties of multiplication (commutative, associative, distributive) to simplify calculations.
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E.19. Use the distributive property to find missing factors or solve multiplication problems.
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E.20. Use one multiplication fact to find another related fact.
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E.21. Estimate products (multiplying by one-digit or larger numbers).
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E.22. Estimate products in word problems.
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E.23. Multiply numbers ending in zeros.
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E.24. Solve multiplication word problems involving numbers ending in zeros.
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E.25. Multiply three or more numbers.
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E.26. Solve multiplication word problems involving three or more numbers.
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E.27. Use inequalities to compare products.
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E.28. Solve multi-step word problems involving multiplication.
F. Multiplicative Relationships
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F.01. Compare numbers using multiplication.
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F.02. Solve comparison word problems using multiplication.
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F.03. Understand and solve problems involving unit rates and equivalent rates.
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F.04. Apply multiplicative reasoning to solve real-world problems.
G. Understanding Division
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G.01. Divide by counting equal groups.
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G.02. Write division sentences to represent groups.
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G.03. Relate multiplication and division using groups.
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G.04. Write division sentences to represent arrays.
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G.05. Relate multiplication and division using arrays.
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G.06. Relate multiplication and division facts.
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G.07. Divide using arrays.
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G.08. Divide using area models.
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G.09. Divide using repeated subtraction.
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G.10. Divide using the distributive property.
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G.11. Understand the concept of quotients and remainders.
H. Division
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H.01. Recall basic division facts up to 10.
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H.02. Solve division word problems involving facts up to 10.
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H.03. Divide two-digit numbers.
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H.04. Solve division word problems involving two-digit numbers.
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H.05. Divide two-digit numbers with remainders.
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H.06. Interpret remainders in division problems.
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H.07. Divide three-digit numbers.
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H.08. Solve division word problems involving three-digit numbers.
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H.09. Divide three-digit numbers with remainders.
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H.10. Interpret remainders in division problems involving three-digit numbers.
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H.11. Complete division tables.
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H.12. Find numbers with a given quotient.
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H.13. Divide numbers ending in zeros.
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H.14. Estimate quotients using compatible numbers.
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H.15. Use inequalities to compare estimated quotients.
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H.16. Estimate quotients in word problems.
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H.17. Apply divisibility rules.
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H.18. Solve word problems involving divisibility rules.
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H.19. Recognize and explain division patterns across increasing place values.
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H.20. Use inequalities to compare quotients.
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H.21. Solve multi-step word problems involving division.
I. Mixed Operations
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I.01. Complete number sentences involving addition, subtraction, multiplication, or division.
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I.02. Solve problems involving a mix of addition, subtraction, multiplication, and division.
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I.03. Solve addition, subtraction, multiplication, and division word problems.
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I.04. Estimate sums, differences, products, and quotients in word problems.
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I.05. Identify and solve word problems with extra or missing information.
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I.06. Solve word problems using guess-and-check strategies.
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I.07. Solve multi-step word problems involving subtraction.
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I.08. Use strip diagrams to represent and solve multi-step word problems.
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I.09. Solve multi-step word problems involving addition and subtraction.
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I.10. Solve multi-step word problems.
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I.11. Solve multi-step word problems involving remainders.
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I.12. Identify reasonable answers in multi-step word problems.
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I.13. Write numerical expressions involving one operation.
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I.14. Find numbers with a particular sum, difference, product, or quotient.
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I.15. Mentally add and subtract numbers ending in zeros.
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I.16. Use inequalities involving addition, subtraction, multiplication, and division.
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I.17. Solve real-world problems involving mixed operations.
J. Variable Expressions
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J.01. Write variable expressions to represent word problems.
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J.02. Write variable expressions.
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J.03. Evaluate variable expressions.
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J.04. Write variable equations to represent word problems.
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J.05. Solve variable equations involving addition and subtraction.
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J.06. Solve variable equations involving multiplication and division.
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J.07. Solve variable equations.
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J.08. Understand the concept of variables and their use in mathematical expressions.
K. Logical Reasoning
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K.03. Find two numbers based on their sum, difference, product, and quotient.
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K.04. Determine the order of numbers or objects based on given clues.
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K.05. Sort shapes into a Venn diagram.
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K.06. Use Venn diagrams to solve problems.
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K.07. Apply logical reasoning to solve a variety of problems.
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K.01. Solve place value word problems.
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K.02. Find two numbers based on their sum and difference.
L. Patterns and Sequences
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L.01. Identify and extend repeating patterns of shapes.
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L.02. Create repeating patterns of shapes.
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L.03. Identify and extend growing patterns of shapes.
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L.04. Use a rule to complete a number pattern.
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L.05. Analyze number patterns and determine the rule governing them.
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L.06. Compare different number patterns.
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L.07. Complete increasing number patterns.
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L.08. Complete geometric number patterns.
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L.09. Solve number pattern word problems.
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L.10. Solve mixed review problems involving number patterns.
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L.11. Create input/output tables involving addition, subtraction, multiplication, and division.
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L.12. Analyze and identify patterns in shapes.
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L.13. Apply pattern recognition to solve problems.
M. Coordinate Plane
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M.01. Identify objects located on a coordinate plane.
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M.02. Graph points on a coordinate plane.
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M.03. Follow directions on a coordinate plane.
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M.04. Use coordinate planes as maps.
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M.05. Understand the concept of coordinates and their use in locating points.
N. Data and Graphs
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N.01. Read and interpret data from a table.
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N.02. Interpret pictographs.
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N.03. Create pictographs.
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N.04. Interpret line graphs.
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N.05. Create line graphs.
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N.06. Interpret bar graphs.
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N.07. Interpret double bar graphs.
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N.08. Create bar graphs.
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N.09. Interpret line plots.
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N.10. Create line plots.
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N.11. Interpret frequency charts.
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N.12. Create frequency charts.
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N.13. Interpret stem-and-leaf plots.
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N.14. Create stem-and-leaf plots.
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N.15. Interpret circle graphs.
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N.16. Choose the best type of graph to represent data.
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N.17. Analyze and interpret data presented in various graphical formats.
O. Money
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O.01. Count coins and bills up to $100.
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O.02. Compare money amounts.
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O.03. Order money amounts.
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O.04. Round money amounts.
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O.05. Add and subtract money amounts.
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O.06. Solve addition and subtraction word problems involving money.
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O.07. Make change.
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O.08. Find the change, price, or amount paid.
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O.09. Work with price lists.
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O.10. Apply money skills to real-world situations.
P. Units of Measurement
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P.01. Read a thermometer and determine temperature.
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P.02. Determine reasonable temperatures for different situations.
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P.03. Measure length using a centimeter ruler.
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P.04. Identify appropriate units of length for different measurements.
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P.05. Compare different units of length.
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P.06. Convert units of length.
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P.07. Identify appropriate units of mass for different measurements.
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P.08. Compare different units of mass.
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P.09. Convert units of mass.
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P.10. Identify appropriate units of volume for different measurements.
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P.11. Compare different units of volume.
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P.12. Convert units of volume.
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P.13. Apply measurement skills to real-world problems.
Q. Time
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Q.01. Match clocks and times.
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Q.02. Match analog and digital clocks.
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Q.03. Read clocks and write times.
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Q.04. Convert between different units of time.
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Q.05. Add and subtract mixed units of time.
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Q.06. Work with fractions of time units.
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Q.07. Calculate elapsed time.
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Q.08. Find start and end times in multi-step word problems.
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Q.09. Convert between 12-hour and 24-hour time.
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Q.10. Understand and use time zones (12-hour and 24-hour time).
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Q.11. Interpret and use transportation schedules (12-hour and 24-hour time).
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Q.12. Identify and solve problems involving time patterns.
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Q.13. Apply time skills to real-world scenarios.
R. Geometry
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R.01. Identify two-dimensional figures based on descriptions.
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R.02. Identify three-dimensional figures.
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R.03. Count vertices, edges, and faces of three-dimensional figures.
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R.04. Identify faces of three-dimensional figures.
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R.05. Identify three-dimensional figures based on descriptions.
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R.06. Identify nets of three-dimensional figures.
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R.07. Determine if a figure is a polygon.
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R.08. Count the number of sides in polygons.
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R.09. Identify regular and irregular polygons.
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R.10. Identify and define lines, line segments, and rays.
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R.11. Identify parallel, perpendicular, and intersecting lines.
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R.12. Identify acute, right, obtuse, and straight angles.
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R.13. Understand angles as fractions of a circle.
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R.14. Understand angles of 90, 180, 270, and 360 degrees.
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R.15. Identify types of triangles (equilateral, isosceles, scalene, right, acute, obtuse).
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R.16. Identify parallel sides in quadrilaterals.
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R.17. Identify parallelograms.
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R.18. Identify trapezoids.
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R.19. Identify rectangles.
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R.20. Identify rhombuses.
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R.21. Classify quadrilaterals.
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R.22. Identify all possible names for a quadrilateral.
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R.23. Draw quadrilaterals.
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R.24. Identify congruent figures.
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R.25. Identify reflection, rotation, and translation.
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R.26. Identify lines of symmetry.
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R.27. Draw lines of symmetry.
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R.28. Count lines of symmetry.
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R.29. Identify rotational symmetry.
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R.30. Apply geometric concepts to solve problems.
S. Geometric Measurement
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S.01. Calculate perimeter.
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S.02. Calculate perimeter of figures on grids.
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S.03. Calculate perimeter when given some side lengths.
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S.04. Find the area of figures made of unit squares.
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S.05. Select figures with a given area.
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S.06. Select two figures with the same area.
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S.07. Tile a rectangle and find the area.
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S.08. Multiply to find the area of a rectangle.
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S.09. Create figures with a given area.
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S.10. Create rectangles with a given area.
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S.11. Find the area or missing side length of a rectangle.
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S.12. Find the area of complex figures by dividing them into rectangles.
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S.13. Find the areas of complex figures.
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S.14. Solve word problems involving area and perimeter.
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S.15. Solve word problems relating perimeter and area of rectangles.
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S.16. Understand and calculate volume.
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S.17. Understand and calculate surface area.
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S.18. Apply geometric measurement skills to solve real-world problems.
T. Understanding Fractions
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T.01. Identify halves, thirds, and fourths.
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T.02. Create models of halves, thirds, and fourths.
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T.03. Create models of sixths and eighths.
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T.04. Create models of halves, thirds, fourths, sixths, and eighths.
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T.05. Understand fractions using fraction bars.
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T.06. Understand fractions using area models.
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T.07. Show fractions using fraction bars.
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T.08. Show fractions using area models.
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T.09. Match fractions to models (halves, thirds, fourths).
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T.10. Match unit fractions to models.
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T.11. Match fractions to models.
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T.12. Identify unit fractions on number lines.
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T.13. Identify fractions on number lines (halves, fourths, eighths).
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T.14. Identify fractions on number lines.
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T.15. Graph unit fractions on number lines.
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T.16. Graph fractions on number lines.
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T.17. Graph smaller or larger fractions on number lines.
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T.18. Solve unit fraction word problems using models.
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T.19. Solve unit fraction word problems.
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T.20. Solve word problems involving fractions of a whole using models.
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T.21. Solve word problems involving fractions of a whole.
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T.22. Solve word problems involving fractions of a group.
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T.23. Decompose fractions into unit fractions using models.
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T.24. Decompose fractions into unit fractions.
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T.25. Understand the concept of fractions and their representation.
U. Equivalent Fractions
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U.01. Find equivalent fractions using area models.
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U.02. Identify equivalent fractions on number lines.
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U.03. Find equivalent fractions using number lines.
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U.04. Graph equivalent fractions on number lines.
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U.05. Identify equivalent fractions.
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U.06. Work with fractions with denominators of 10 and 100.
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U.07. Identify and explain patterns of equivalent fractions.
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U.08. Write fractions in lowest terms.
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U.09. Understand the concept of equivalent fractions.
V. Compare and Order Fractions
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V.01. Compare fractions with like denominators using models.
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V.02. Compare fractions with like numerators or denominators using models.
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V.03. Compare fractions using models.
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V.04. Graph and compare fractions with like denominators on number lines.
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V.05. Graph and compare fractions with like numerators or denominators on number lines.
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V.06. Compare fractions using ½ as a benchmark.
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V.07. Compare fractions using ½ as a benchmark: find the missing numerator.
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V.08. Compare fractions with like denominators.
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V.09. Compare fractions with like numerators or denominators.
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V.10. Compare fractions.
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V.11. Compare fractions with like denominators in recipes.
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V.12. Order fractions with like denominators.
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V.13. Order fractions with like numerators or denominators.
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V.14. Order fractions.
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V.15. Identify smaller or larger fractions.
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V.16. Understand comparing and ordering fractions.
W. Decimals Up to Tenths
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W.01. Model decimals and fractions up to tenths.
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W.02. Understand decimals expressed in words (up to tenths).
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W.03. Identify place values in decimal numbers (up to tenths).
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W.04. Graph decimals on number lines (up to tenths).
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W.05. Use decimal number lines (up to tenths).
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W.06. Graph fractions as decimals on number lines (up to tenths).
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W.07. Convert fractions to decimals (up to tenths).
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W.08. Convert decimals to fractions (up to tenths).
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W.09. Convert decimals between standard and expanded form using fractions (up to tenths).
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W.10. Compare decimals on number lines (up to tenths).
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W.11. Compare decimal numbers (up to tenths).
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W.12. Order decimal numbers (up to tenths).
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W.13. Compare decimals and fractions on number lines (up to tenths).
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W.14. Compare decimals and fractions (up to tenths).
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W.15. Work with number sequences involving decimals (up to tenths).
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W.16. Understand the concept of decimals up to tenths.
X. Decimals Up to Hundredths
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X.01. Identify decimal numbers illustrated in models.
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X.02. Model decimals and fractions up to hundredths.
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X.03. Understand decimals expressed in words (up to hundredths).
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X.04. Identify place values in decimal numbers (up to hundredths).
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X.05. Determine one-tenth or one-hundredth more or less.
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X.06. Identify equivalent decimals (up to hundredths).
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X.07. Graph decimals on number lines (up to hundredths).
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X.08. Use decimal number lines (up to hundredths).
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X.09. Graph fractions as decimals on number lines (up to hundredths).
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X.10. Convert fractions to decimals (denominators of 10 and 100).
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X.11. Convert fractions to decimals (up to hundredths).
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X.12. Convert decimals to fractions (up to hundredths).
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X.13. Convert decimals between standard and expanded form using fractions (up to hundredths).
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X.14. Round decimals (up to hundredths).
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X.15. Compare decimals using models (up to hundredths).
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X.16. Compare decimals on number lines (up to hundredths).
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X.17. Compare decimal numbers (up to hundredths).
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X.18. Order decimal numbers (up to hundredths).
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X.19. Compare decimals and fractions on number lines (up to hundredths).
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X.20. Compare decimals and fractions (up to hundredths).
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X.21. Work with number sequences involving decimals (up to hundredths).
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X.22. Understand the concept of decimals up to hundredths.
Y. Add and Subtract Decimals Up to Tenths
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Y.01. Add decimal numbers (up to tenths).
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Y.02. Subtract decimal numbers (up to tenths).
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Y.03. Solve addition and subtraction word problems involving decimals (up to tenths).
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Y.04. Find decimals with a particular sum or difference (up to tenths).
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Y.05. Add three or more decimals (up to tenths).
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Y.06. Solve word problems involving adding three or more decimals (up to tenths).
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Y.07. Complete decimal addition or subtraction sentences (up to tenths).
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Y.08. Use inequalities with decimal addition and subtraction (up to tenths).
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Y.09. Estimate sums and differences of decimals (up to tenths).
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Y.10. Solve decimal problems using diagrams (up to tenths).
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Y.11. Understand adding and subtracting decimals up to tenths.
Z. Add and Subtract Decimals Up to Hundredths
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Z.01. Add decimal numbers (up to hundredths).
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Z.02. Subtract decimal numbers (up to hundredths).
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Z.03. Solve addition and subtraction word problems involving decimals (up to hundredths).
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Z.04. Find decimals with a particular sum or difference (up to hundredths).
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Z.05. Add three or more decimals (up to hundredths).
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Z.06. Solve word problems involving adding three or more decimals (up to hundredths).
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Z.07. Complete addition or subtraction sentences (up to hundredths).
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Z.08. Use inequalities with addition and subtraction (up to hundredths).
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Z.09. Estimate sums and differences of decimals (up to hundredths).
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Z.10. Understand adding and subtracting decimals up to hundredths.
AA. Probability and Statistics
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AA.08. Interpret line plots to find the mode.
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AA.09. Interpret line plots to find the mean.
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AA.10. Interpret line plots to find the median.
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AA.11. Interpret charts to find mean and mode.
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AA.12. Understand and apply basic statistical concepts.
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AA.01. Identify events as certain, probable, unlikely, or impossible.
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AA.02. Understand probability.
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AA.03. Find the probability of an event.
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AA.04. Make predictions based on probability.
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AA.05. Find the mode of a data set.
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AA.06. Find the mean of a data set.
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AA.07. Find the median of a data set.