Course Content
A. Numbers and Counting
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A.01. Identify place values in whole numbers up to millions
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A.02. Convert between different place values within whole numbers
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A.03. Write numbers up to millions in words and digits
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A.04. Compare whole numbers up to millions using inequality symbols
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A.05. Order a set of whole numbers from least to greatest and greatest to least
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A.06. Round whole numbers to the nearest ten, hundred, thousand, ten thousand, and million
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A.07. Identify even and odd numbers using arithmetic rules
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A.08. Interpret and translate Roman numerals
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A.09. Apply number sense to solve real-world problems
B. Addition and Subtraction
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B.01. Add whole numbers with and without regrouping
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B.02. Subtract whole numbers with and without borrowing
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B.03. Complete addition and subtraction number sentences by finding missing addends or subtrahends
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B.04. Identify and apply the properties of addition (commutative, associative, identity)
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B.05. Estimate sums and differences of whole numbers to the nearest ten, hundred, and thousand
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B.06. Solve one-step word problems involving addition and subtraction of whole numbers
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B.07. Solve multi-step word problems involving addition and subtraction of whole numbers
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B.08. Use inequalities to represent relationships between addition and subtraction expressions
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B.09. Fill in missing digits in addition and subtraction problems
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B.10. Choose numbers that meet a particular sum or difference criterion
C. Multiplication
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C.01. Recall multiplication facts up to 10×10 fluently
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C.02. Solve word problems involving multiplication facts
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C.03. Determine the missing factor in multiplication equations
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C.04. Evaluate the truth of multiplication number sentences
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C.05. Multiply one-digit numbers by three-digit and four-digit numbers using area models
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C.06. Multiply one-digit numbers by multi-digit numbers using partial products
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C.07. Multiply multi-digit numbers by one-digit numbers
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C.08. Solve word problems involving multiplication by one-digit numbers
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C.09. Identify and apply multiplication patterns over increasing place values
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C.10. Multiply numbers ending in zeroes efficiently
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C.11. Apply the properties of multiplication (commutative, associative, identity, zero)
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C.12. Estimate products of multiplication problems
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C.13. Multiply two-digit numbers by two-digit numbers using area models and partial products
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C.14. Apply the distributive property to simplify multiplication problems
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C.15. Use known multiplication facts to deduce other related facts
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C.16. Multiply a two-digit number by a two-digit number
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C.17. Multiply a two-digit number by a larger number
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C.18. Solve word problems involving multiplication by two-digit numbers
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C.19. Multiply three or more numbers up to two digits each
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C.20. Solve word problems involving multiplying three or more numbers
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C.21. Choose numbers that satisfy a specified product
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C.22. Use inequalities to represent relationships between multiplication expressions
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C.23. Apply various multiplication strategies to solve complex problems
D. Division
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D.01. Recall division facts up to 100 ÷ 10 fluently
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D.02. Solve word problems involving division facts
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D.03. Determine the missing number in division equations
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D.04. Evaluate the truth of division number sentences
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D.05. Relate multiplication and division as inverse operations
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D.06. Divide two-digit numbers by one-digit numbers using arrays
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D.07. Apply the distributive property to simplify division problems
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D.08. Divide three-digit numbers by one-digit numbers using area models
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D.09. Divide using partial quotients
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D.10. Divide multi-digit numbers by one-digit numbers
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D.11. Solve word problems involving division by one-digit numbers
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D.12. Interpret remainders in division problems
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D.13. Estimate quotients in division problems
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D.14. Identify and apply division patterns over increasing place values
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D.15. Divide numbers ending in zeroes efficiently
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D.16. Choose numbers that satisfy a specified quotient
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D.17. Divide by two-digit numbers
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D.18. Apply various division strategies to solve complex problems
E. Number Theory
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E.01. Identify factors of a given number
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E.02. Distinguish between prime and composite numbers
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E.03. Determine the prime factorization of a number
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E.04. Apply divisibility rules for 2, 3, 5, 6, 9, and 10
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E.05. Solve word problems involving divisibility rules
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E.06. Determine the highest common factor (HCF) of two or more numbers
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E.07. Identify multiples of a given number
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E.08. Determine the lowest common multiple (LCM) of two or more numbers
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E.09. Solve problems applying prime factorization, HCF and LCM.
F. Fractions and Mixed Numbers
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F.14. Determine fractions of a number
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F.15. Solve word problems involving fractions of a number
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F.16. Round mixed numbers to the nearest whole number
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F.01. Review basic fraction concepts (numerator, denominator, whole)
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F.02. Solve word problems involving fractions of a whole
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F.03. Solve word problems involving fractions of a group
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F.04. Represent unit fractions on number lines
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F.05. Identify equivalent fractions
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F.06. Generate patterns of equivalent fractions
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F.07. Write fractions in lowest terms (simplest form)
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F.08. Define and identify mixed numbers
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F.09. Convert between improper fractions and mixed numbers
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F.10. Compare unit fractions using models and number lines
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F.11. Compare fractions with like denominators using models and number lines
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F.12. Compare fractions with unlike denominators using models and number lines
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F.13. Order fractions with like and unlike denominators
G. Decimals
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G.01. Represent decimals using visual models
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G.02. Relate decimals to fractions
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G.03. Read and interpret decimals expressed in words
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G.04. Identify place values in decimal numbers
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G.05. Describe the relationship between decimal place values
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G.06. Convert decimals between standard and expanded form
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G.07. Identify equivalent decimals
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G.08. Round decimals to the nearest tenth, hundredth, and whole number
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G.09. Represent decimals on number lines
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G.10. Compare decimals using models and number lines
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G.11. Compare decimals numerically
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G.12. Order decimal numbers from least to greatest and greatest to least
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G.13. Solve word problems involving comparing, ordering, and rounding decimals
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G.14. Convert fractions and mixed numbers to decimals
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G.15. Convert decimals to fractions and mixed numbers
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G.16. Compare decimals and fractions on number lines
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G.17. Compare decimals and fractions numerically
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G.18. Order a mix of decimals, fractions, and mixed numbers
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G.19. Convert decimals between standard and expanded form using fractions
H. Add and Subtract Fractions
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H.01. Decompose fractions into unit fractions using models
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H.02. Decompose fractions into unit fractions
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H.03. Decompose fractions in multiple ways
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H.04. Add fractions with like denominators using models and number lines
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H.05. Add fractions with like denominators
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H.06. Subtract fractions with like denominators using models and number lines
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H.07. Subtract fractions with like denominators
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H.08. Add and subtract fractions with like denominators
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H.09. Solve word problems involving adding and subtracting fractions with like denominators
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H.10. Add and subtract mixed numbers with like denominators
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H.11. Solve word problems involving adding and subtracting mixed numbers with like denominators
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H.12. Add fractions with unlike denominators using models
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H.13. Add fractions with unlike denominators
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H.14. Subtract fractions with unlike denominators using models
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H.15. Subtract fractions with unlike denominators
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H.16. Estimate sums and differences of fractions using benchmarks
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H.17. Add and subtract fractions with unlike denominators
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H.18. Solve word problems involving adding and subtracting fractions with unlike denominators
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H.19. Add and subtract mixed numbers with unlike denominators
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H.20. Solve word problems involving adding and subtracting mixed numbers with unlike denominators
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H.21. Add three or more fractions
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H.22. Solve word problems involving adding three or more fractions
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H.23. Complete addition and subtraction number sentences with fractions
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H.24. Use inequalities to represent relationships between addition and subtraction of fractions
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H.25. Estimate sums and differences of mixed numbers
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H.26. Add up to 4 fractions with denominators of 10 and 100
I. Add and Subtract Decimals
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I.01. Add decimal numbers with and without regrouping
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I.02. Subtract decimal numbers with and without borrowing
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I.03. Solve word problems involving addition and subtraction of decimals
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I.04. Choose decimals that result in a particular sum or difference
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I.05. Complete addition and subtraction number sentences with decimals
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I.06. Use inequalities to represent relationships between decimal addition and subtraction
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I.07. Estimate sums and differences of decimals
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I.08. Solve complex problems applying both addition and subtraction of decimals.
J. Multiply and Divide Decimals
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J.01. Estimate products of whole numbers and decimals
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J.02. Multiply a decimal by a power of ten
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J.03. Multiply decimals and whole numbers
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J.04. Solve word problems involving multiplying decimals and whole numbers
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J.05. Use inequalities to represent relationships between decimal multiplication
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J.06. Divide by powers of ten
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J.07. Identify decimal division patterns over increasing place values
K. Percents
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K.01. Represent percentages using visual models
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K.02. Convert fractions to percents using grid models
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K.03. Convert between percents, fractions, and decimals
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K.04. Solve word problems involving converting between percents, fractions, and decimals
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K.05. Compare percents to each other and to fractions
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K.06. Solve word problems comparing percents and fractions
L. Mixed Operations
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L.01. Add, subtract, multiply, and divide whole numbers
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L.02. Solve word problems involving addition, subtraction, multiplication, and division of whole numbers
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L.03. Add, subtract, multiply, and divide decimals
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L.04. Solve word problems involving addition, subtraction, and multiplication of decimals
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L.05. Write numerical expressions to represent mathematical situations
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L.06. Evaluate numerical expressions using the order of operations
M. Problem Solving
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M.01. Write numerical expressions to represent word problems
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M.02. Solve multi-step word problems
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M.03. Solve multi-step word problems involving remainders
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M.04. Evaluate the reasonableness of answers in multi-step word problems
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M.05. Solve word problems with extra or missing information
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M.06. Apply guess-and-check strategies to solve problems
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M.07. Determine the order of events to solve problems
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M.08. Use Venn diagrams to solve problems
N. Money
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N.01. Add and subtract money amounts
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N.02. Solve word problems involving adding and subtracting money
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N.03. Solve word problems involving multiplying money amounts
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N.04. Solve word problems involving multiplying money amounts with decimals
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N.05. Solve word problems involving dividing money amounts
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N.06. Solve word problems involving dividing money amounts with decimals
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N.07. Interpret price lists
O. Number Sequences
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O.01. Use a rule to complete a number sequence
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O.02. Identify and extend arithmetic sequences with whole numbers
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O.03. Identify and extend arithmetic sequences with decimals
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O.04. Identify and extend arithmetic sequences with fractions
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O.05. Identify and extend increasing number sequences
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O.06. Identify and extend geometric number sequences
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O.07. Review mixed number sequence types
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O.08. Solve word problems involving number sequences
P. Data and Graphs
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P.01. Read and interpret data presented in tables
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P.02. Interpret information presented in line graphs
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P.03. Construct line graphs from given data
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P.04. Interpret information presented in bar graphs
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P.05. Construct bar graphs from given data
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P.06. Interpret information presented in picture graphs
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P.07. Construct picture graphs from given data
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P.08. Interpret information presented in dot plots
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P.09. Construct dot plots from given data
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P.10. Organize data into frequency charts
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P.11. Interpret frequency charts to solve one-step problems
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P.12. Determine the most appropriate type of graph for a given data set
Q. Coordinate Plane
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Q.01. Identify the location of objects on a coordinate plane
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Q.02. Graph points on a coordinate plane using ordered pairs
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Q.03. Interpret coordinate planes as maps
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Q.04. Follow directions on a coordinate plane
R. Probability and Statistics
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R.01. Understand the basic concepts of probability
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R.02. Calculate the probability of simple events
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R.03. Make predictions based on probability
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R.04. Differentiate between independent and dependent events
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R.05. Determine possible combinations
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R.06. Find the mode of a data set
S. Time
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S.02. Add and subtract mixed time units
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S.03. Calculate elapsed time
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S.04. Solve word problems involving finding start and end times
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S.05. Convert between 12-hour and 24-hour time
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S.06. Determine time zones using 12-hour time
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S.07. Determine time zones using 24-hour time
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S.08. Interpret schedules and timelines using 12-hour time
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S.09. Interpret schedules using 24-hour time
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S.10. Identify time patterns
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S.01. Convert between different units of time
T. Units of Measurement
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T.01. Choose the appropriate metric unit of measure for length, mass, and volume
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T.02. Compare metric units of length
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T.03. Compare metric units of mass
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T.04. Compare metric units of volume
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T.05. Choose the more reasonable temperature in Celsius
U. Two-Dimensional Figures
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U.01. Identify polygons
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U.02. Classify polygons based on the number of sides
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U.03. Differentiate between regular and irregular polygons
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U.04. Identify angles as greater than, less than, or equal to a right angle
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U.05. Recognize angles of 90, 180, 270, and 360 degrees
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U.06. Classify angles as acute, right, obtuse, and straight
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U.07. Measure angles on a circle
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U.08. Measure angles with a protractor
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U.09. Draw angles with a protractor
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U.10. Estimate angle measurements
V. Symmetry and Transformations
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V.01. Identify lines of symmetry in two-dimensional figures
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V.02. Identify rotational symmetry in two-dimensional figures
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V.03. Recognize and describe reflection, rotation, and translation
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V.04. Identify dilations
W. Three-Dimensional Figures
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W.01. Identify three-dimensional figures
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W.02. Count vertices, edges, and faces of three-dimensional figures
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W.03. Identify the faces of three-dimensional figures
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W.04. Identify nets of three-dimensional figures
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W.05. Recognize three-dimensional figures viewed from different perspectives
X. Geometric Measurement
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X.01. Calculate the perimeter of rectangles
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X.02. Calculate the perimeter of polygons
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X.03. Calculate the area of squares and rectangles
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X.04. Determine area and perimeter of figures on grids
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X.05. Solve word problems involving area and perimeter
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X.06. Apply area and perimeter concepts to determine cost
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X.07. Determine the volume of rectangular prisms
Y. Financial Literacy
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Y.01. Budget a weekly allowance: word problems
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Y.02. Read financial records
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Y.03. Keep financial records
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Y.04. Balance a budget
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Y.05. Adjust a budget
