
Course Content
A. Numbers and Counting
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A.01. Recognize and identify place values in whole numbers up to ten million
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A.02. Convert numbers up to one million from digits to words and vice versa
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A.03. Convert numbers up to ten million from digits to words and vice versa
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A.04. Convert numbers between standard and expanded form up to ten million
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A.05. Round whole numbers to the nearest thousands place
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A.06. Compare whole numbers up to one million
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A.07. Compare whole numbers up to ten million
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A.08. Arrange whole numbers in ascending or descending order up to one million
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A.09. Arrange whole numbers in ascending or descending order up to ten million
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A.10. Round whole numbers to the nearest millions place
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A.11. Determine if a number is even or odd based on arithmetic rules
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A.12. Understand and apply Roman numerals
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A.13. Explore the historical context and usage of different number systems
B. Addition and Subtraction
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B.01. Recognize and apply the properties of addition (commutative, associative, identity)
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B.02. Complete simple addition and subtraction sentences with missing numbers
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B.03. Add and subtract whole numbers up to millions
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B.04. Choose numbers that yield a particular sum or difference
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B.05. Estimate sums and differences of whole numbers up to four digits
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B.06. Estimate sums and differences of whole numbers up to six digits
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B.07. Solve inequalities involving addition and subtraction
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B.08. Solve word problems involving addition and subtraction of whole numbers
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B.09. Estimate sums and differences in real-world word problems involving up to six-digit numbers
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B.10. Apply addition and subtraction properties to solve problems
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B.11. Fill in missing digits in addition and subtraction problems
C. Multiplication Fluency
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C.07. Apply multiplication facts to solve real-world problems quickly
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C.01. Recall multiplication facts up to 10
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C.02. Identify multiples of a given number up to 10
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C.03. Recall multiplication facts up to 12
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C.04. Identify multiples of a given number up to 12
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C.05. Determine the missing factor in multiplication facts up to 10
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C.06. Determine the missing factor in multiplication facts up to 12
D. Division Fluency
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D.01. Recall division facts up to 10
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D.02. Solve word problems involving division facts up to 10
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D.03. Recall division facts up to 12
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D.04. Solve word problems involving division facts up to 12
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D.05. Apply division facts to solve real-world problems efficiently
E. Multiplication
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E.01. Multiply numbers by multiples of ten
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E.02. Use one multiplication fact to deduce another
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E.03. Multiply by 1-digit numbers
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E.04. Estimate products of multiplication problems
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E.05. Use area models to multiply 2-digit numbers by 2-digit numbers
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E.06. Multiply 2-digit numbers by 2-digit numbers using partial products
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E.07. Complete missing steps in multi-digit multiplication problems
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E.08. Multiply 2-digit numbers by 2-digit numbers accurately
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E.09. Multiply by 1-digit numbers: word problems
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E.10. Apply properties of multiplication to simplify calculations
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E.11. Multiply 2-digit numbers by 3-digit or 4-digit numbers
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E.12. Multiply three or more numbers up to 2 digits each
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E.13. Solve inequalities involving multiplication
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E.14. Multiply numbers ending in zeroes
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E.15. Use box multiplication to find products
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E.16. Use lattice multiplication to find products
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E.17. Solve word problems involving multiplication of multi-digit numbers
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E.18. Choose numbers that result in a particular product
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E.19. Explore the relationship between multiplication and area calculations
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E.20. Analyze and correct errors in multi-digit multiplication problems
F. Division
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F.01. Relate multiplication and division facts
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F.02. Estimate quotients in division problems
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F.03. Divide by 1-digit numbers
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F.04. Estimate quotients using compatible numbers
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F.05. Divide numbers ending in zeroes
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F.06. Divide by 2-digit numbers using models
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F.07. Divide by 2-digit numbers using partial quotients
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F.08. Complete division sentences with 2-digit divisors
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F.09. Divide 2-digit and 3-digit numbers by 2-digit numbers
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F.10. Divide 4-digit numbers by 2-digit numbers
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F.11. Divide by 1-digit numbers: word problems
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F.12. Solve multi-step word problems involving multiplicative comparison
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F.13. Adjust quotients to ensure accurate division
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F.14. Divide numbers ending in zeroes: word problems
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F.15. Estimate quotients: word problems
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F.16. Choose numbers that result in a particular quotient
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F.17. Solve word problems involving division of multi-digit numbers
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F.18. Analyze and correct errors in multi-digit division problems
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F.19. Investigate the relationship between division and fractions
G. Number Theory
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G.01. Identify factors of a given number
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G.02. List all factor pairs of a given number
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G.03. Identify prime and composite numbers up to 20
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G.04. Identify prime and composite numbers up to 100
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G.05. Apply divisibility rules to determine factors
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G.06. Find the prime factorization of a number
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G.07. Find the highest common factor (HCF) of two numbers
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G.08. Find the lowest common multiple (LCM) of two numbers
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G.09. Solve word problems using divisibility rules
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G.10. Explore real-world applications of prime factorization
H. Fractions and Mixed Numbers
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H.01. Review basic fraction concepts (numerator, denominator)
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H.02. Identify fractions of a whole in word problems
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H.03. Identify fractions of a group in word problems
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H.04. Recognize and generate equivalent fractions
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H.05. Identify patterns of equivalent fractions
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H.06. Write fractions in their lowest terms (simplest form)
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H.07. Determine the lowest common denominator (LCD) of two fractions
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H.08. Understand the concept of mixed numbers
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H.09. Convert between improper fractions and mixed numbers
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H.10. Relate division and fractions
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H.11. Compare fractions and mixed numbers
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H.12. Graph and compare fractions on number lines
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H.13. Understand fractions as division: word problems
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H.14. Put fractions in order
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H.15. Round mixed numbers
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H.16. Identify reciprocals of fractions and whole numbers
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H.17. Fractions as division: decimal quotients
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H.18. Understand and apply arithmetic sequences with fractions
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H.19. Understand and apply geometric sequences with fractions
I. Decimals
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I.01. Recognize decimals represented visually
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I.02. Model decimals and fractions using diagrams
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I.03. Interpret decimals expressed in words
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I.04. Identify place values in decimal numbers
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I.05. Understand the relationship between decimal place values
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I.06. Convert decimals between standard and expanded form
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I.07. Recognize and generate equivalent decimals
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I.08. Round decimals to a specified place value
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I.09. Locate decimals on number lines
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I.10. Compare decimals on number lines
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I.11. Compare decimal numbers
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I.12. Put decimal numbers in order
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I.13. Convert fractions to decimals
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I.14. Convert mixed numbers to decimals
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I.15. Convert decimals to fractions
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I.16. Convert decimals to mixed numbers
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I.17. Convert decimals between standard and expanded form using fractions
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I.18. Compare decimals and fractions on number lines
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I.19. Compare decimals and fractions
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I.20. Put assorted decimals, fractions and mixed numbers in order
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I.21. Number sequences involving decimals
J. Adding and Subtracting Decimals
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J.01. Add decimal numbers using blocks
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J.02. Add decimal numbers
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J.03. Subtract decimal numbers
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J.04. Add and subtract decimal numbers
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J.05. Add and subtract decimals: word problems
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J.06. Choose decimals with a particular sum or difference
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J.07. Complete the decimal addition or subtraction sentence
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J.08. Inequalities with decimal addition and subtraction
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J.09. Estimate sums and differences of decimals
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J.10. Use properties to add three decimals
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J.11. Use compensation to add and subtract decimals
K. Multiplying Decimals
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K.01. Multiply a decimal by 10, 100 or 1,000
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K.02. Multiply by 0.1 or 0.01
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K.03. Estimate products of two-digit whole numbers and decimals
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K.04. Estimate products of decimals
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K.05. Multiply a decimal by a one-digit whole number using blocks
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K.06. Multiply a decimal by a one-digit whole number using the distributive property
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K.07. Multiply a decimal by a one-digit whole number
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K.08. Multiply a decimal by a two-digit whole number using area models
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K.09. Multiply a decimal by a two-digit whole number
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K.10. Multiply three or more numbers, one of which is a decimal
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K.11. Multiply by a power of ten with decimals: find the missing number
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K.12. Multiply a decimal by a one-digit whole number: word problems
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K.13. Multiply a decimal by a one- or two-digit whole number: word problems
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K.14. Inequalities with decimal multiplication
L. Dividing Decimals
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L.01. Divide a whole number by 10, 100 or 1,000: decimal quotients
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L.02. Divide a decimal by 10, 100 or 1,000
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L.03. Estimate decimal quotients
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L.04. Divide two whole numbers: decimal quotients
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L.05. Divide decimals using blocks: complete the equation
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L.06. Divide decimals using area models: complete the equation
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L.07. Divide decimals by one-digit whole numbers
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L.08. Division with decimal quotients and rounding
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L.09. Divide a decimal by a power of ten with decimals: find the missing number
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L.10. Decimal division patterns over increasing place values
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L.11. Division with decimal quotients: word problems
M. Adding and Subtracting Fractions
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M.01. Decompose fractions into multiple sums of fractions
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M.02. Add and subtract fractions with the same denominator using number lines
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M.03. Add and subtract fractions with the same denominator
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M.04. Add three or more fractions with the same denominator
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M.05. Add and subtract mixed numbers with the same denominator
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M.06. Add up to 4 fractions with denominators of 10 and 100
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M.07. Add fractions with different denominators using models
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M.08. Subtract fractions with different denominators using models
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M.09. Add fractions with different denominators
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M.10. Subtract fractions with different denominators
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M.11. Add and subtract fractions with different denominators
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M.12. Add three or more fractions with different denominators
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M.13. Add mixed numbers with different denominators
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M.14. Subtract mixed numbers with different denominators
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M.15. Add and subtract mixed numbers with different denominators
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M.16. Estimate sums and differences of mixed numbers
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M.17. Add and subtract fractions with the same denominator: word problems
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M.18. Add three or more fractions with the same denominator: word problems
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M.19. Add and subtract mixed numbers with the same denominator: word problems
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M.20. Add and subtract fractions with different denominators: word problems
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M.21. Add three or more fractions with different denominators: word problems
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M.22. Add and subtract mixed numbers with different denominators: word problems
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M.23. Complete addition and subtraction sentences with fractions
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M.24. Complete addition and subtraction sentences with mixed numbers
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M.25. Inequalities with addition and subtraction of fractions
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M.26. Inequalities with addition and subtraction of mixed numbers
N. Multiplying and Dividing Fractions
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N.01. Multiply unit fractions by whole numbers using number lines
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N.02. Multiply unit fractions by whole numbers using models
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N.03. Identify multiples of fractions
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N.04. Multiply unit fractions and whole numbers: sorting
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N.05. Multiply fractions by whole numbers using number lines
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N.06. Multiply fractions by whole numbers: choose the model
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N.07. Multiply fractions and whole numbers: sorting
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N.08. Multiply fractions by whole numbers
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N.09. Multiply two unit fractions using models
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N.10. Multiply two fractions using models
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N.11. Multiply two fractions
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N.12. Divide unit fractions by whole numbers using models
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N.13. Divide unit fractions by whole numbers using area models
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N.14. Divide unit fractions by whole numbers
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N.15. Divide fractions by whole numbers
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N.16. Fractions of a number
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N.17. Scaling whole numbers by fractions
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N.18. Multiply fractions by whole numbers: input/output tables
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N.19. Fractions of a number: word problems
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N.20. Scaling whole numbers by fractions: justify your answer
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N.21. Multiply fractions: word problems
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N.22. Complete the fraction multiplication sentence I
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N.23. Complete the fraction multiplication sentence II
O. Integers
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O.01. Understand the concept of integers and their signs
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O.02. Represent integers on number lines
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O.03. Graph integers on horizontal and vertical number lines
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O.04. Understand the concept of opposite integers
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O.05. Compare integers
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O.06. Put integers in order
P. Adding and Subtracting Integers
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P.01. Add integers using number lines
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P.02. Subtract integers using number lines
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P.03. Add and subtract integers using number lines
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P.04. Apply integer operations to real-world contexts
Q. Ratios and Rates
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Q.01. Write a ratio to compare two quantities
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Q.02. Express a ratio using a fraction
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Q.03. Solve word problems involving ratios
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Q.04. Identify equivalent ratios
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Q.05. Write an equivalent ratio
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Q.06. Use ratio tables to find equivalent ratios
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Q.07. Determine unit rates
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Q.08. Identify equivalent rates
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Q.09. Solve word problems involving ratios and rates
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Q.10. Determine if two ratios form a proportion
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Q.11. Solve proportions
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Q.12. Solve word problems involving scale drawings
R. Percents
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R.01. Identify the percentage represented in a visual model
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R.02. Understand percents using bar models
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R.03. Convert fractions to percents using grid models
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R.04. Convert between percents, fractions, and decimals
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R.05. Compare percents to each other and to fractions
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R.06. Calculate the percent of a number
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R.07. Convert between percents, fractions, and decimals: word problems
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R.08. Compare percents and fractions: word problems
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R.09. Compare percents of numbers
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R.10. Calculate percentage increase and decrease in simple scenarios
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R.11. Apply percentages to real-world situations like discounts and taxes
S. Time
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S.01. Convert between different units of time (seconds, minutes, hours, days)
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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 start and end times
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S.05. Convert between 12-hour and 24-hour time formats
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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 and extend time patterns
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S.11. Analyze and solve complex scheduling problems involving multiple time zones
T. Units of Measurement
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T.16. Convert between metric and imperial units
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T.17. Understand and apply the concept of precision in measurement
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T.18. Estimate measurements using appropriate units and tools
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T.01. Choose the more reasonable temperature in Celsius or Fahrenheit
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T.02. Calculate temperature differences
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T.03. Choose the appropriate metric unit of measure for a given situation
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T.04. Compare and convert metric units of length (mm, cm, m, km)
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T.05. Compare and convert metric units of mass (mg, g, kg)
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T.06. Compare and convert metric units of volume (mL, L)
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T.07. Convert metric mixed units (e.g., 1.5 kg to grams)
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T.08. Add and subtract metric mixed units
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T.09. Solve multi-step problems involving metric unit conversions
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T.10. Choose the appropriate imperial unit of measure for a given situation
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T.11. Compare and convert imperial units of length (in, ft, yd, mi)
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T.12. Compare and convert imperial units of weight (oz, lb, ton)
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T.13. Compare and convert imperial units of volume (fl oz, cup, pt, qt, gal)
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T.14. Work with imperial mixed units
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T.15. Convert between miles and kilometres
U. Two-Dimensional Figures
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U.01. Identify whether a given shape is a polygon
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U.02. Differentiate between regular and irregular polygons
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U.03. Identify the number of sides in different polygons
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U.04. Identify the types of angles found inside a polygon
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U.05. Sort polygons into Venn diagrams based on their properties
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U.06. Describe and apply properties of polygons (e.g., number of sides, angles)
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U.07. Define and differentiate between lines, line segments, and rays
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U.08. Identify parallel, perpendicular, and intersecting lines
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U.09. Identify and describe parts of a circle (radius, diameter, circumference)
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U.10. Investigate tessellations and patterns created by polygons
V. Angles
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V.01. Identify different types of angles (acute, obtuse, right, straight, reflex)
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V.02. Measure angles using a protractor
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V.03. Draw angles with a protractor
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V.04. Find a missing angle when given vertical angles
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V.05. Find a missing angle when given adjacent angles
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V.06. Find a missing angle when given supplementary angles
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V.07. Find a missing angle when given vertical, adjacent, and supplementary angles
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V.08. Find a missing angle when given complementary angles
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V.09. Find measures of complementary and supplementary angles
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V.10. Apply angle properties to solve geometric problems
W. Triangles and Quadrilaterals
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W.01. Classify triangles based on their sides and angles (e.g., equilateral, isosceles, scalene, acute, right, obtuse)
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W.02. Find missing angles in triangles using the angle sum property
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W.03. Identify parallel sides in quadrilaterals
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W.04. Describe the sides and angles of different quadrilaterals
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W.05. Identify parallelograms based on their properties
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W.06. Identify trapeziums based on their properties
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W.07. Identify rectangles based on their properties
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W.08. Identify rhombuses based on their properties
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W.09. Classify quadrilaterals based on their properties
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W.10. Pick all the names that apply to a given quadrilateral
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W.11. Draw quadrilaterals with specific properties
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W.12. Graph triangles and quadrilaterals on the coordinate plane
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W.13. Identify the relationships between different types of quadrilaterals
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W.14. Describe relationships among quadrilaterals using precise language
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W.15. Find missing angles in quadrilaterals using angle properties
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W.16. Explore the hierarchical relationships among different types of quadrilaterals
X. Symmetry and Transformations
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X.01. Identify lines of symmetry in two-dimensional figures
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X.02. Draw lines of symmetry in various shapes
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X.03. Count the number of lines of symmetry in a figure
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X.04. Determine if a figure has rotational symmetry
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X.05. Quantify the amount of rotation required for rotational symmetry
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X.06. Identify reflections, rotations, and translations
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X.07. Perform translations and graph the image on a coordinate plane
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X.08. Perform reflections and graph the image on a coordinate plane
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X.09. Recognize and describe combinations of reflections, rotations, and translations
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X.10. Identify congruent and similar figures
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X.11. Identify similar triangles and quadrilaterals
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X.12. Explore the properties that are preserved under different transformations
Y. Three-Dimensional Figures
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Y.01. Identify common three-dimensional figures (e.g., cube, sphere, cylinder, cone, pyramid, prism)
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Y.02. Count the number of vertices, edges, and faces on various 3D figures
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Y.03. Identify a 3D figure based on its description
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Y.04. Recognize and match nets to their corresponding 3D figures
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Y.05. Visualize and describe three-dimensional figures from different perspectives
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Y.06. Investigate and create different nets for the same 3D figure
Z. Geometric Measurement
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Z.01. Find the perimeter of rectangles using formulas
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Z.02. Calculate the perimeter of shapes with whole number side lengths
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Z.03. Calculate the perimeter of shapes with decimal side lengths
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Z.04. Calculate the area of squares and rectangles
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Z.05. Understand the concept of area of a parallelogram
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Z.06. Calculate the area of parallelograms
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Z.07. Understand the concept of area of a triangle
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Z.08. Calculate the area of right triangles
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Z.09. Calculate the area of triangles
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Z.10. Calculate the area of compound figures
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Z.11. Calculate the area between two rectangles
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Z.12. Determine area and perimeter of figures on grids
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Z.13. Solve word problems involving area and perimeter
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Z.14. Use area and perimeter calculations to determine cost
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Z.15. Explore the relationship between area and perimeter
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Z.16. Calculate the volume of figures made of unit cubes
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Z.17. Calculate the volume of cubes and cuboids
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Z.18. Apply the relationship between volume and the area of the base in word problems
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Z.19. Compare volumes and dimensions of cuboids in word problems
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Z.20. Investigate how changes in dimensions affect area and volume
AA. Data and Graphs
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AA.01. Extract information from a table
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AA.02. Interpret data presented in pictograms
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AA.03. Construct pictograms to represent given data
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AA.04. Interpret data presented in line graphs
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AA.05. Construct line graphs to represent given data
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AA.06. Interpret bar graphs for categorical data
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AA.07. Construct bar graphs for categorical data
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AA.08. Interpret double bar graphs for categorical data
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AA.09. Construct double bar graphs for categorical data
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AA.10. Interpret bar graphs for grouped data
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AA.11. Construct bar graphs for grouped data
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AA.12. Interpret data presented in line plots
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AA.13. Construct line plots to represent given data
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AA.14. Interpret frequency charts: one-step problems
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AA.15. Interpret frequency charts: multi-step problems
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AA.16. Create frequency charts
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AA.17. Interpret stem-and-leaf plots
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AA.18. Create stem-and-leaf plots
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AA.19. Interpret pie charts
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AA.20. Relate pie charts to central angles
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AA.21. Choose the best type of graph to represent a given data set
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AA.22. Identify potential biases or misinterpretations in graphical representations
BB. Probability and Statistics
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BB.01. Understand the basic concepts of probability
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BB.02. Calculate the probability of simple events
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BB.03. Express probability as a fraction
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BB.04. Determine experimental probability based on observed outcomes
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BB.05. Use collected data to find probabilities and make predictions
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BB.06. Make predictions based on probability calculations
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BB.07. Distinguish between statistical and non-statistical questions
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BB.08. Calculate the mode of a data set
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BB.09. Calculate the mean of a data set
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BB.10. Calculate the median of a data set
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BB.11. Calculate the range of a data set
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BB.12. Determine the missing number given the mode
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BB.13. Determine the missing number given the mean
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BB.14. Determine the missing number given the median
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BB.15. Determine the missing number given the range
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BB.16. Interpret charts to find mode
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BB.17. Interpret charts to find mean
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BB.18. Interpret charts to find median
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BB.19. Interpret charts to find range
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BB.20. Identify representative, random, and biased samples
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BB.21. Evaluate the validity of statistical claims and arguments
CC. Equations and Variables
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CC.01. Write variable expressions to represent real-world situations
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CC.02. Write variable expressions based on word problems
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CC.03. Evaluate variable expressions by substituting given values
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CC.04. Apply properties of addition with variables (commutative, associative)
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CC.05. Apply properties of multiplication with variables (commutative, associative)
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CC.06. Identify equivalent expressions using bar models
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CC.07. Translate a one-step equation from words into symbolic form
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CC.08. Model and solve one-step equations using algebra tiles
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CC.09. Write and solve one-step equations represented by diagrams
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CC.10. Solve one-step addition and subtraction equations with whole numbers
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CC.11. Solve one-step multiplication and division equations with whole numbers
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CC.12. Solve one-step equations involving whole numbers
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CC.13. Write one-step equations based on word problems
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CC.14. Solve one-step equations in the context of word problems
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CC.15. Determine if a given ordered pair (x, y) satisfies an equation
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CC.16. Find a missing value using two-variable equations
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CC.17. Complete a table for a two-variable relationship given an equation
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CC.18. Complete a table from a graph representing a two-variable relationship
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CC.19. Graph a two-variable relationship on the coordinate plane
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CC.20. Write a two-variable equation to represent a given relationship
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CC.21. Analyze and interpret the meaning of variables and constants in equations
DD. Problem Solving
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DD.01. Write numerical expressions to represent word problems
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DD.02. Solve multi-step addition and subtraction word problems
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DD.03. Solve general multi-step word problems
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DD.04. Solve multi-step word problems involving remainders
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DD.05. Identify reasonable answers in multi-step word problems
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DD.06. Solve word problems with extra or missing information
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DD.07. Apply the guess-and-check strategy to solve problems
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DD.08. Determine the correct order of steps in a problem
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DD.09. Use Venn diagrams to solve problems
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DD.10. Make the largest possible quotient by strategically arranging digits
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DD.11. Develop and apply problem-solving strategies to novel situations
EE. Financial Literacy
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EE.01. Identify advantages and disadvantages of different payment methods
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EE.02. Evaluate the suitability of different payment methods for various situations
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EE.03. Interpret information presented in financial records (e.g., bank statements, receipts)
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EE.04. Maintain accurate financial records
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EE.05. Create and balance a personal budget
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EE.06. Adjust a budget to accommodate changing circumstances
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EE.07. Analyze spending habits and identify areas for improvement
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EE.08. Make informed decisions about saving and investing