Course Content
A. Place Value and Number Sense
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A.01. Identify place value up to 100,000.
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A.02. Write numbers in expanded form up to 100,000.
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A.03. Write the word name for numbers up to 100,000.
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A.04. Spell the word names for numbers up to 100,000.
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A.05. Compare and order numbers up to 100,000.
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A.06. Identify place value up to 1,000,000.
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A.07. Write numbers in expanded form up to 1,000,000.
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A.08. Write the word name for numbers up to 1,000,000.
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A.09. Spell the word names for numbers up to 1,000,000.
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A.10. Compare and order numbers up to 1,000,000.
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A.11. Understand the relationship between place values.
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A.12. Convert between different place values.
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A.13. Represent whole numbers on number lines.
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A.14. Round whole numbers to a given place value.
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A.15. Identify even and odd numbers using arithmetic rules.
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A.16. Create and extend skip-counting sequences.
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A.17. Understand and use Roman numerals.
B. Addition and Subtraction
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B.01. Add and subtract whole numbers up to 100,000.
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B.02. Solve addition and subtraction word problems up to 100,000.
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B.03. Use properties of addition to simplify calculations.
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B.04. Use compensation strategies for addition and subtraction.
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B.05. Add and subtract whole numbers up to 1,000,000.
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B.06. Solve addition and subtraction word problems up to 1,000,000.
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B.07. Identify and correct mistakes in addition and subtraction problems.
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B.08. Complete addition and subtraction number sentences.
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B.09. Identify numbers with specific sums or differences.
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B.10. Recognize addition and subtraction patterns across place values.
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B.11. Write and solve inequalities involving addition and subtraction.
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B.12. Estimate sums and differences of whole numbers.
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B.13. Estimate sums and differences in word problems.
C. Multiplication
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C.01. Master multiplication facts to 10.
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C.02. Master multiplication facts to 12.
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C.03. Multiply by 1-digit numbers.
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C.04. Solve multiplication word problems with 1-digit multipliers.
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C.05. Multiply numbers ending in zeroes.
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C.06. Solve multiplication word problems involving numbers ending in zeroes.
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C.07. Understand and apply properties of multiplication.
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C.08. Use area models to multiply 2-digit numbers by 2-digit numbers.
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C.09. Multiply 2-digit numbers by 2-digit numbers using standard algorithm.
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C.10. Solve multiplication word problems with 2-digit multipliers.
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C.11. Multiply 3-digit numbers by 2-digit numbers.
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C.12. Solve multiplication word problems with 3-digit multipliers.
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C.13. Multiply three or four numbers.
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C.14. Solve multiplication word problems involving three or four numbers.
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C.15. Use alternative multiplication methods (box, lattice).
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C.16. Recognize multiplication patterns across place values.
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C.17. Write and solve inequalities involving multiplication.
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C.18. Estimate products of whole numbers.
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C.19. Estimate products in word problems.
D. Division
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D.01. Master division facts to 10.
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D.02. Solve division word problems with facts to 10.
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D.03. Master division facts to 12.
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D.04. Solve division word problems with facts to 12.
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D.05. Divide by 1-digit numbers.
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D.06. Solve division word problems with 1-digit divisors.
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D.07. Interpret remainders in division problems.
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D.08. Divide numbers ending in zeroes.
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D.09. Solve division word problems involving numbers ending in zeroes.
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D.10. Divide by 2-digit numbers using models and partial quotients.
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D.11. Divide 2-digit and 3-digit numbers by 2-digit numbers.
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D.12. Solve division word problems with 2-digit divisors.
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D.13. Divide 4-digit numbers by 2-digit numbers.
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D.14. Express remainders as decimals in division problems.
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D.15. Solve division word problems with 4-digit dividends and 2-digit divisors.
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D.16. Adjust quotients to find more accurate answers.
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D.17. Solve multi-step word problems involving multiplicative comparison.
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D.18. Relate multiplication and division concepts.
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D.19. Solve division problems with missing numbers.
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D.20. Recognize division patterns across place values.
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D.21. Estimate quotients.
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D.22. Estimate quotients in word problems.
E. Exponents
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E.01. Understand the concept of exponents.
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E.02. Write multiplication expressions using exponents.
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E.03. Evaluate powers of whole numbers.
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E.04. Write powers of ten using exponents.
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E.05. Multiply and divide whole numbers by powers of ten using exponents.
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E.06. Multiply and divide decimals by powers of ten using exponents.
F. Number Theory
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F.01. Identify prime and composite numbers.
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F.02. Find the prime factorization of a number.
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F.03. Apply divisibility rules to determine factors.
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F.04. Solve word problems using divisibility rules.
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F.05. Find the greatest common factor (GCF) of two numbers.
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F.06. Find the least common multiple (LCM) of two numbers.
G. Decimals to Hundredths
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G.01. Identify decimals represented by models.
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G.02. Relate decimals and fractions using models.
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G.03. Understand decimals expressed in words (to hundredths).
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G.04. Identify place values in decimals (to hundredths).
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G.05. Write decimals in expanded form (to hundredths).
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G.06. Identify equivalent decimals (to hundredths).
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G.07. Round decimals to the nearest whole number or tenth.
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G.08. Represent decimals on number lines.
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G.09. Compare decimals using models and number lines.
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G.10. Compare and order decimals (to hundredths).
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G.11. Convert between fractions and decimals (to hundredths).
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G.12. Convert between standard and expanded forms using fractions (to hundredths).
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G.13. Compare decimals and fractions on number lines.
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G.14. Compare and order decimals and fractions (to hundredths).
H. Decimals to Thousandths
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H.01. Understand decimals expressed in words (to thousandths).
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H.02. Identify place values in decimals (to thousandths).
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H.03. Understand the relationship between decimal place values.
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H.04. Write decimals in expanded form (to thousandths).
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H.05. Identify equivalent decimals (to thousandths).
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H.06. Round decimals to the nearest whole number, tenth, or hundredth.
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H.07. Compare and order decimals (to thousandths).
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H.08. Convert between fractions and decimals (to thousandths).
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H.09. Convert between standard and expanded forms using fractions (to thousandths).
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H.10. Compose and decompose decimals in multiple ways.
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H.11. Compare and order decimals and fractions (to thousandths).
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H.12. Solve word problems involving comparing, ordering, and rounding decimals.
I. Add and Subtract Decimals to Hundredths
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I.01. Add decimal numbers (to hundredths) using models.
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I.02. Add decimal numbers (to hundredths) using the standard algorithm.
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I.03. Subtract decimal numbers (to hundredths) using models.
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I.04. Subtract decimal numbers (to hundredths) using the standard algorithm.
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I.05. Add and subtract decimal numbers (to hundredths).
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I.06. Solve word problems involving adding and subtracting decimals (to hundredths).
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I.07. Choose decimals with a particular sum or difference (to hundredths).
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I.08. Complete addition and subtraction sentences with decimals (to hundredths).
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I.09. Write and solve inequalities involving decimal addition and subtraction (to hundredths).
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I.10. Estimate sums and differences of decimals using rounding and benchmarks (to hundredths).
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I.11. Apply properties of addition to add three decimals up to hundredths.
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I.12. Use compensation to add and subtract decimals up to hundredths.
J. Add and Subtract Decimals to Thousandths
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J.01. Add decimal numbers (to thousandths) using the standard algorithm.
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J.02. Subtract decimal numbers (to thousandths) using the standard algorithm.
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J.03. Add and subtract decimal numbers (to thousandths).
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J.04. Solve word problems involving adding and subtracting decimals (to thousandths).
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J.05. Choose decimals with a particular sum or difference (to thousandths).
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J.06. Complete addition and subtraction sentences with decimals (to thousandths).
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J.07. Write and solve inequalities involving decimal addition and subtraction (to thousandths).
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J.08. Estimate sums and differences of decimals using rounding (to thousandths).
K. Multiply Decimals
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K.01. Estimate products of decimals.
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K.02. Multiply a decimal by a power of ten.
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K.03. Multiply a whole number by 0.1 or 0.01.
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K.04. Multiply a decimal by a 1-digit whole number using models and distributive property.
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K.05. Multiply a decimal by a 1-digit whole number.
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K.06. Multiply a decimal by a 2-digit whole number using area models.
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K.07. Multiply a decimal by a 2-digit whole number.
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K.08. Solve word problems involving multiplying decimals and whole numbers.
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K.09. Multiply two decimals using grids and standard algorithm.
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K.10. Determine decimal placement in decimal multiplication.
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K.11. Write and solve inequalities involving decimal multiplication.
L. Divide Decimals
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L.01. Divide by powers of ten.
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L.02. Recognize decimal division patterns across place values.
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L.03. Divide decimals using models and area models.
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L.04. Divide decimals by whole numbers.
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L.05. Solve word problems involving dividing decimals by whole numbers.
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L.06. Divide decimals resulting in decimal quotients and rounding.
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L.07. Estimate decimal quotients.
M. Money
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M.01. Add and subtract money amounts.
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M.02. Solve word problems involving adding and subtracting money.
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M.03. Use price lists to solve addition and subtraction problems.
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M.04. Solve word problems involving multiplying and dividing money amounts.
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M.05. Multiply and divide money amounts with decimals.
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M.06. Solve word problems involving multiplying and dividing money with decimals.
N. Fractions and Mixed Numbers
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N.01. Represent fractions using models (fraction bars, area models).
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N.02. Identify fractions.
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N.03. Solve word problems involving fractions of a whole and fractions of a group.
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N.04. Represent fractions on number lines.
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N.05. Understand mixed numbers.
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N.06. Round mixed numbers.
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N.07. Relate division to fractions.
O. Equivalent Fractions
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O.01. Find equivalent fractions using area models and number lines.
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O.02. Identify equivalent fractions.
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O.03. Recognize patterns of equivalent fractions.
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O.04. Simplify fractions to lowest terms.
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O.05. Convert between improper fractions and mixed numbers.
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O.06. Find the least common denominator (LCD).
P. Compare and Order Fractions
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P.01. Compare fractions using number lines and benchmarks.
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P.02. Compare fractions with like denominators and like numerators.
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P.03. Compare fractions with unlike denominators.
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P.04. Compare fractions and mixed numbers.
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P.05. Order fractions with like denominators, like numerators, and unlike denominators.
Q. Add and Subtract Fractions with Like Denominators
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Q.01. Decompose fractions in multiple ways.
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Q.02. Add and subtract fractions with like denominators using models and number lines.
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Q.03. Add and subtract fractions with like denominators.
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Q.04. Solve word problems involving adding and subtracting fractions with like denominators.
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Q.05. Add three or more fractions with like denominators.
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Q.06. Solve word problems involving adding three or more fractions with like denominators.
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Q.07. Complete addition and subtraction sentences with fractions with like denominators.
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Q.08. Write and solve inequalities involving addition and subtraction of fractions with like denominators.
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Q.09. Estimate sums and differences of mixed numbers with like denominators.
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Q.10. Add and subtract mixed numbers with like denominators.
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Q.11. Solve word problems involving adding and subtracting mixed numbers with like denominators.
R. Add and Subtract Fractions with Unlike Denominators
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R.01. Add and subtract fractions with unlike denominators using models.
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R.02. Add and subtract fractions with unlike denominators.
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R.03. Add up to 4 fractions with denominators of 10 and 100.
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R.04. Identify fraction expressions with a particular sum (denominators of 10 and 100).
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R.05. Add and subtract fractions with denominators of 10 and 100.
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R.06. Add and subtract fractions with unlike denominators.
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R.07. Solve word problems involving adding and subtracting fractions with unlike denominators.
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R.08. Add three or more fractions with unlike denominators.
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R.09. Solve word problems involving adding three or more fractions with unlike denominators.
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R.10. Complete addition and subtraction sentences with fractions with unlike denominators.
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R.11. Write and solve inequalities involving addition and subtraction of fractions with unlike denominators.
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R.12. Add and subtract mixed numbers with unlike denominators.
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R.13. Solve word problems involving adding and subtracting mixed numbers with unlike denominators.
S. Multiply Fractions
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S.01. Multiply unit fractions by whole numbers using models and number lines.
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S.02. Multiply unit fractions by whole numbers.
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S.03. Solve word problems involving multiplying unit fractions by whole numbers.
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S.04. Multiply fractions by whole numbers using models and number lines.
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S.05. Multiply fractions by whole numbers.
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S.06. Solve word problems involving multiplying fractions by whole numbers.
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S.07. Use input/output tables to show multiplication of fractions and whole numbers.
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S.08. Find fractions of a number.
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S.09. Solve word problems involving fractions of a number.
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S.10. Scale whole numbers by fractions.
T. Divide Fractions
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T.01. Divide whole numbers by unit fractions using models and area models.
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T.02. Divide whole numbers by unit fractions.
U. Integers
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U.01. Understand the concept of integers.
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U.02. Represent integers on number lines.
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U.03. Understand opposite integers.
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U.04. Compare and order integers.
V. Mixed Operations
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V.01. Add, subtract, multiply, and divide whole numbers.
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V.02. Solve word problems involving mixed operations with whole numbers.
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V.03. Write numerical expressions.
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V.04. Evaluate numerical expressions, including those with parentheses.
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V.05. Identify and correct mistakes involving order of operations.
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V.06. Solve problems with missing operators.
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V.07. Add, subtract, multiply, and divide decimals.
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V.08. Solve word problems involving mixed operations with decimals.
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V.09. Add, subtract, multiply, and divide fractions.
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V.10. Solve word problems involving mixed operations with fractions.
W. Problem Solving
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W.07. Determine the order of events in word problems.
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W.08. Use Venn diagrams to solve problems.
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W.01. Solve problems to maximize quotients.
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W.02. Write numerical expressions for word problems.
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W.03. Solve multi-step word problems.
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W.04. Identify reasonable answers in word problems.
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W.05. Solve word problems with extra or missing information.
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W.06. Solve guess-and-check problems.
X. Ratios and Rates
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X.01. Write ratios using different notations (e.g., a:b, a/b).
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X.02. Write ratios from word problems.
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X.03. Identify equivalent ratios using models.
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X.04. Find equivalent ratios.
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X.05. Use ratio tables to solve problems.
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X.06. Calculate unit rates.
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X.07. Identify equivalent rates.
Y. Percents
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Y.01. Identify percents represented by models.
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Y.02. Understand percents using strip models.
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Y.03. Convert between fractions, decimals, and percents using models.
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Y.04. Convert between fractions, decimals, and percents.
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Y.05. Compare percents, fractions, and decimals.
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Y.06. Solve word problems involving comparing percents, fractions, and decimals.
Z. Patterns and Sequences
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Z.01. Identify and extend repeating patterns.
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Z.02. Create repeating patterns.
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Z.03. Identify and extend growing patterns of shapes.
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Z.04. Use rules to complete number sequences.
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Z.05. Compare number patterns.
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Z.06. Identify mistakes in number patterns.
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Z.07. Complete increasing and geometric number sequences.
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Z.08. Solve word problems involving number sequences.
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Z.09. Work with arithmetic and geometric sequences involving fractions.
AA. Coordinate Plane
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AA.01. Describe the coordinate plane.
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AA.02. Identify objects on a coordinate plane.
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AA.03. Graph points on a coordinate plane.
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AA.04. Graph points from a table.
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AA.05. Use rules to complete tables and graphs.
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AA.06. Analyze graphed relationships.
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AA.07. Use coordinate planes as maps.
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AA.08. Follow directions on a coordinate plane.
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AA.09. Work with coordinate planes involving all four quadrants.
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AA.10. Identify quadrants.
BB. Variable Expressions
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BB.01. Write variable expressions.
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BB.02. Write variable expressions from word problems.
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BB.03. Evaluate variable expressions.
CC. One-Variable Equations
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CC.01. Determine if a value satisfies an equation.
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CC.02. Find the value that makes an equation true.
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CC.03. Write an equation from words.
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CC.04. Model and solve equations using algebra tiles.
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CC.05. Write and solve equations that represent diagrams.
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CC.06. Solve addition and subtraction equations.
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CC.07. Solve multiplication and division equations.
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CC.08. Solve equations with whole numbers.
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CC.09. Write and solve one-step equations from word problems.
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CC.10. Match word problems to one-step equations.
DD. One-Variable Inequalities
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DD.01. Identify solutions to inequalities.
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DD.02. Graph inequalities on number lines.
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DD.03. Write inequalities from number lines.
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DD.04. Solve one-step inequalities.
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DD.05. Graph solutions to one-step inequalities.
EE. Two-Variable Equations
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EE.01. Find values using two-variable equations.
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EE.02. Complete tables for two-variable relationships.
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EE.03. Complete tables from graphs.
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EE.04. Graph patterns using rules.
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EE.05. Graph two-variable relationships.
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EE.06. Write two-variable equations.
FF. Data and Graphs
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FF.01. Read and interpret tables.
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FF.02. Interpret and create line graphs.
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FF.03. Interpret and create bar graphs.
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FF.04. Interpret and create double bar graphs.
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FF.05. Interpret and create pictographs.
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FF.06. Interpret and create line plots.
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FF.07. Interpret and create frequency charts.
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FF.08. Create relative frequency tables.
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FF.09. Interpret and create stem-and-leaf plots.
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FF.10. Interpret and create circle graphs.
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FF.11. Choose the best type of graph for given data.
GG. Probability and Statistics
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GG.01. Understand probability.
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GG.02. Find probability.
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GG.03. Make predictions based on probability.
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GG.04. Calculate experimental probability.
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GG.05. Calculate combinations.
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GG.06. Calculate mean, median, and mode.
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GG.07. Find missing values in mean, median, and mode problems.
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GG.08. Interpret charts and graphs to find mean, median, and mode.
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GG.09. Identify biased samples.
HH. Time
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HH.01. Convert between different units of time.
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HH.02. Add and subtract mixed time units.
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HH.03. Calculate elapsed time.
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HH.04. Find start and end times from word problems.
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HH.05. Convert between 12-hour and 24-hour time.
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HH.06. Work with time zones using 12-hour and 24-hour time.
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HH.07. Interpret schedules and timelines.
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HH.08. Identify time patterns.
II. Units of Measurement
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II.01. Choose appropriate metric units of length, mass, and capacity.
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II.02. Compare and convert metric units of length, mass, and capacity.
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II.03. Read and interpret temperatures on a thermometer.
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II.04. Choose the more reasonable temperature.
JJ. Two-Dimensional Figures
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JJ.01. Identify polygons.
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JJ.02. Count the sides of polygons.
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JJ.03. Identify regular and irregular polygons.
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JJ.04. Identify points, lines, line segments, rays, and angles.
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JJ.05. Identify parallel, perpendicular, and intersecting lines.
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JJ.06. Identify types of angles.
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JJ.07. Identify angles of 90, 180, 270, and 360 degrees.
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JJ.08. Measure and draw angles with a protractor.
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JJ.09. Sort polygons using Venn diagrams.
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JJ.10. Identify properties of polygons.
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JJ.11. Identify parts of a circle.
KK. Triangles and Quadrilaterals
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KK.01. Identify acute, obtuse, and right triangles.
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KK.02. Identify scalene, isosceles, and equilateral triangles.
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KK.03. Classify triangles.
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KK.04. Identify parallel sides in quadrilaterals.
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KK.05. Identify parallelograms, trapezoids, rectangles, and rhombuses.
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KK.06. Classify quadrilaterals.
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KK.07. Identify the relationships between quadrilaterals.
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KK.08. Describe relationships among quadrilaterals.
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KK.09. Draw quadrilaterals.
LL. Symmetry and Transformations
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LL.01. Identify lines of symmetry.
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LL.02. Identify rotational symmetry.
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LL.03. Identify reflections, rotations, and translations.
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LL.04. Identify combinations of transformations.
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LL.05. Perform transformations on the coordinate plane.
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LL.06. Identify congruent figures.
MM. Three-Dimensional Figures
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MM.01. Identify three-dimensional figures.
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MM.02. Count vertices, edges, and faces.
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MM.03. Identify faces of three-dimensional figures.
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MM.04. Identify nets of three-dimensional figures.
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MM.05. Identify three-dimensional figures from different perspectives.
NN. Geometric Measurement
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NN.01. Calculate perimeter with whole number and decimal side lengths.
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NN.02. Calculate perimeter of figures on grids.
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NN.03. Calculate area of squares and rectangles.
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NN.04. Understand and calculate the area of parallelograms and triangles.
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NN.05. Calculate area of figures on grids.
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NN.06. Solve word problems involving area and perimeter.
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NN.07. Use area and perimeter to determine cost.
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NN.08. Relate perimeter and area of rectangles.
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NN.09. Calculate volume of rectangular prisms and cubes.
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NN.10. Calculate volume of irregular figures made of unit cubes.
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NN.11. Calculate surface area.
OO. Financial Literacy
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OO.01. Identify advantages and disadvantages of payment methods.
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OO.02. Evaluate payment methods.
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OO.03. Understand debit and credit cards.
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OO.04. Read and interpret financial records.
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OO.05. Keep financial records.
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OO.06. Balance a budget.
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OO.07. Adjust a budget.
