Course Content
A. Whole Numbers and Place Value
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A.01. Understand place value up to one million.
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A.02. Convert between standard and expanded forms.
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A.03. Write numbers in words and spell word names for numbers.
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A.04. Understand the relationship between place values.
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A.05. Work with Roman numerals (I, V, X, L, C, D, M).
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A.06. Apply place value understanding to solve real-world problems.
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A.07. Compare and order large numbers using place value.
B. Addition and Subtraction of Whole Numbers
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B.01. Estimate sums and differences of whole numbers.
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B.02. Add and subtract whole numbers up to billions.
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B.03. Solve addition and subtraction word problems.
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B.04. Understand and apply the properties of addition (commutative, associative, identity).
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B.05. Solve multi-step addition and subtraction problems.
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B.06. Use mental math strategies for addition and subtraction.
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B.07. Identify and correct errors in addition and subtraction calculations.
C. Powers of Ten
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C.01. Understand the concept of powers of ten.
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C.02. Evaluate powers of ten.
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C.03. Write powers of ten using exponents.
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C.04. Apply powers of ten to solve problems involving large and small numbers.
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C.05. Explain the relationship between powers of ten and place value.
D. Multiplication of Whole Numbers
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D.01. Understand multiplication patterns over increasing place values.
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D.02. Multiply numbers ending in zeros.
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D.03. Multiply a whole number by a power of ten.
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D.04. Estimate products.
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D.05. Multiply by 1-digit and 2-digit numbers.
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D.06. Multiply by 3-digit numbers and larger numbers.
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D.07. Solve multiplication word problems.
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D.08. Understand and apply the properties of multiplication (commutative, associative, distributive, identity).
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D.09. Use different methods for multiplication (e.g., partial products, lattice multiplication).
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D.10. Compare products of whole numbers.
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D.11. Solve real-world problems involving multiplication.
E. Division of Whole Numbers
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E.01. Understand division patterns over increasing place values.
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E.02. Divide numbers ending in zeros.
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E.03. Estimate quotients.
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E.04. Divide multi-digit numbers by 1-digit numbers.
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E.05. Interpret remainders in division problems.
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E.06. Divide by 2-digit numbers using different methods (partial quotients, long division).
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E.07. Solve division word problems.
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E.08. Relate multiplication and division.
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E.09. Solve multi-step problems involving division.
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E.10. Understand and use the relationship between dividend, divisor, quotient, and remainder.
F. Factors, Multiples, and Divisibility
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F.01. Identify factors of a number.
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F.02. Identify prime and composite numbers.
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F.03. Find the prime factorization of a number.
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F.04. Apply divisibility rules.
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F.05. Find all factor pairs of a number.
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F.06. Determine the least common multiple (LCM) of two numbers.
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F.07. Solve real-world problems involving factors, multiples, and divisibility.
G. Mixed Operations with Whole Numbers
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G.01. Add, subtract, multiply, and divide whole numbers.
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G.02. Solve word problems involving mixed operations.
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G.03. Apply the order of operations (PEMDAS).
H. Numerical Expressions
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H.01. Write numerical expressions with one and two operations.
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H.02. Evaluate numerical expressions.
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H.03. Evaluate numerical expressions with parentheses and brackets.
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H.04. Identify and correct errors in order of operations.
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H.05. Compare numerical expressions.
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H.06. Evaluate numerical expressions involving fractions (new).
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H.07. Create numerical expressions to represent real-world situations.
I. Multi-Step Word Problems
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I.01. Write numerical expressions for word problems.
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I.02. Solve multi-step word problems.
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I.03. Solve word problems involving remainders.
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I.04. Identify reasonable answers to word problems.
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I.05. Solve multi-step word problems involving multiplicative comparison.
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I.06. Analyze word problems to identify the necessary operations.
J. Fractions and Mixed Numbers
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J.01. Review the concept of fractions.
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J.02. Identify equivalent fractions.
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J.03. Write fractions in lowest terms.
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J.04. Convert between improper fractions and mixed numbers.
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J.05. Find the least common denominator (LCD).
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J.06. Round mixed numbers.
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J.07. Determine reciprocals.
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J.08. Understand fractions as parts of a whole and parts of a set.
K. Comparing Fractions
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K.01. Graph and compare fractions on number lines.
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K.02. Compare fractions using benchmarks (0, 1/2, 1).
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K.03. Compare fractions and mixed numbers.
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K.04. Order fractions.
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K.05. Use different methods to compare fractions (e.g., common denominator, cross-multiplication).
L. Adding and Subtracting Fractions
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L.01. Estimate sums and differences of fractions using benchmarks.
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L.02. Add and subtract fractions with like denominators.
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L.03. Add and subtract fractions with unlike denominators using models.
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L.04. Add and subtract fractions with unlike denominators.
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L.05. Solve addition and subtraction word problems with fractions.
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L.06. Add 3 or more fractions with unlike denominators.
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L.07. Compare sums and differences of fractions.
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L.08. Apply addition and subtraction of fractions to real-world scenarios.
M. Adding and Subtracting Mixed Numbers
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M.01. Estimate sums and differences of mixed numbers.
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M.02. Add and subtract mixed numbers with like denominators.
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M.03. Add and subtract mixed numbers with unlike denominators (with and without regrouping).
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M.04. Solve addition and subtraction word problems with mixed numbers.
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M.05. Compare sums and differences of mixed numbers.
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M.06. Apply addition and subtraction of mixed numbers to real-world scenarios.
N. Understanding Fraction Multiplication
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N.01. Multiply fractions by whole numbers using models and equations.
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N.02. Multiply two unit fractions using models.
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N.03. Multiply two fractions using models.
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N.04. Understand fraction multiplication as repeated addition.
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N.05. Interpret fraction multiplication in real-world contexts.
O. Multiplying Fractions and Whole Numbers
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O.01. Multiply fractions by whole numbers.
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O.02. Solve word problems involving multiplying fractions and whole numbers.
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O.03. Understand fractions of a number.
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O.04. Apply fraction multiplication to real-world situations.
P. Multiplying Fractions
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P.01. Multiply two fractions.
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P.02. Solve word problems involving multiplying two fractions.
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P.03. Multiply three fractions and whole numbers.
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P.04. Understand fraction multiplication and area.
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P.05. Apply multiplication of fractions to real-world situations.
Q. Understanding Multiplication with Mixed Numbers
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Q.01. Multiply a mixed number by a whole number using models.
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Q.02. Use area models to multiply mixed numbers.
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Q.03. Explain the process of multiplying mixed numbers.
R. Multiplying Mixed Numbers
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R.01. Estimate products of mixed numbers.
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R.02. Multiply a mixed number by a whole number and by a fraction.
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R.03. Multiply two mixed numbers.
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R.04. Multiply mixed numbers, fractions, and whole numbers.
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R.05. Solve word problems involving multiplying mixed numbers.
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R.06. Apply multiplication of mixed numbers to real-world scenarios.
S. Scaling by Fractions
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S.01. Scale whole numbers and fractions by fractions.
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S.02. Scale mixed numbers by fractions.
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S.03. Solve problems involving scaling by fractions.
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S.04. Apply scaling to real-world scenarios.
T. Understanding Fraction Division
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T.01. Relate division and fractions.
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T.02. Understand fractions as division.
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T.03. Divide unit fractions by whole numbers using models.
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T.04. Divide whole numbers by unit fractions using models.
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T.05. Divide unit fractions and whole numbers using models and number lines.
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T.06. Explain the process of dividing fractions.
U. Dividing Unit Fractions and Whole Numbers
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U.01. Divide unit fractions by whole numbers.
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U.02. Divide whole numbers by unit fractions.
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U.03. Divide unit fractions and whole numbers.
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U.04. Solve word problems involving dividing unit fractions and whole numbers.
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U.05. Apply division of unit fractions and whole numbers to real-world situations.
V. Mixed Operations: Fractions
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V.01. Add, subtract, multiply, and divide fractions and mixed numbers.
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V.02. Solve word problems involving mixed operations with fractions and mixed numbers.
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V.03. Solve multi-step word problems with fractions and mixed numbers (new).
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V.04. Apply mixed operations with fractions to real-world scenarios.
W. Decimal Place Value
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W.01. Understand decimal place value.
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W.02. Convert between standard and expanded forms.
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W.03. Understand decimals expressed in words.
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W.04. Round decimals.
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W.05. Use models to represent decimals.
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W.06. Compare and order decimals.
X. Comparing Decimals
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X.01. Identify equivalent decimals.
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X.02. Compare decimals using grids and number lines.
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X.03. Compare and order decimal numbers.
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X.04. Solve word problems involving comparing and ordering decimals.
Y. Converting Between Decimals and Fractions
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Y.01. Model decimals and fractions.
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Y.02. Convert between fractions and decimals.
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Y.03. Convert between mixed numbers and decimals.
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Y.04. Use different methods to convert between fractions and decimals.
Z. Comparing Decimals and Fractions
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Z.01. Compare decimals and fractions on number lines.
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Z.02. Compare decimals and fractions.
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Z.03. Order a mix of decimals and fractions.
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Z.04. Order a mix of decimals, fractions, and mixed numbers.
AA. Adding and Subtracting Decimals
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AA.01. Add and subtract decimals using models and algorithms.
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AA.02. Solve word problems involving adding and subtracting decimals.
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AA.03. Use properties of addition to add three or more decimals (new).
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AA.04. Use compensation to add and subtract decimals (new).
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AA.05. Estimate sums and differences of decimals.
BB. Multiplying Decimals by Powers of Ten
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BB.01. Multiply a decimal by a power of ten.
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BB.02. Multiply a decimal by 0.1 or 0.01.
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BB.03. Understand the pattern of multiplying decimals by powers of ten.
CC. Multiplying Decimals by Whole Numbers
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CC.01. Estimate products of whole numbers and decimals.
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CC.02. Multiply a decimal by a one-digit and multi-digit whole number.
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CC.03. Solve word problems involving multiplying decimals by whole numbers.
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CC.04. Use different methods for multiplication (e.g., area models, distributive property).
DD. Multiplying Decimals
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DD.01. Estimate products of decimals.
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DD.02. Multiply two decimals using grids and area models.
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DD.03. Understand the placement of the decimal point in decimal multiplication.
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DD.04. Solve real-world problems involving multiplying decimals.
EE. Dividing Decimals by Powers of Ten
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EE.01. Divide decimals by powers of ten.
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EE.02. Divide by 0.1 or 0.01.
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EE.03. Understand the pattern of dividing decimals by powers of ten.
FF. Dividing Decimals
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FF.05. Solve word problems involving dividing decimals.
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FF.06. Round decimal quotients.
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FF.01. Estimate decimal quotients.
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FF.02. Divide decimals using models and algorithms.
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FF.03. Divide decimals by whole numbers using place value (new).
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FF.04. Divide by decimals using place value (new).
GG. Mixed Operations: Decimals
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GG.01. Add, subtract, multiply, and divide decimals.
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GG.02. Solve word problems involving mixed operations with decimals.
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GG.03. Evaluate equations with mixed operations.
HH. Money and Time
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HH.01. Add, subtract, multiply, and divide money amounts.
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HH.02. Solve word problems involving money.
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HH.03. Convert time units.
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HH.04. Solve real-world problems involving money and time.
II. Customary Units of Measurement
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II.01. Compare and convert customary units of length, weight, and volume.
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II.02. Solve problems involving customary unit conversions.
JJ. Metric Units of Measurement
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JJ.01. Compare and convert metric units of length, mass, and volume.
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JJ.02. Solve problems involving metric unit conversions.
KK. Number Patterns
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KK.01. Identify and extend number patterns.
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KK.02. Solve word problems involving number patterns.
LL. Coordinate Plane
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LL.01. Describe the coordinate plane.
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LL.02. Graph points on a coordinate plane.
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LL.03. Graph shapes on a coordinate plane.
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LL.04. Use coordinate planes to represent real-world situations.
MM. Variable Expressions
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MM.01. Write variable expressions.
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MM.02. Evaluate variable expressions.
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MM.03. Write and solve simple equations with one variable.
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MM.04. Understand and use variables in mathematical expressions.
NN. Data and Graphs
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NN.01. Interpret and create line plots, line graphs, bar graphs, frequency charts, stem-and-leaf plots, and scatter plots.
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NN.02. Analyze data presented in different types of graphs.
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NN.03. Make predictions and draw conclusions based on data.
OO. Statistics
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OO.01. Find the mean, median, mode, and range of a data set.
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OO.02. Interpret data to find measures of central tendency.
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OO.03. Understand the meaning and applications of different statistical measures.
PP. Triangles
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PP.01. Classify triangles by angles (acute, obtuse, right) and by sides (scalene, isosceles, equilateral).
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PP.02. Understand the properties of different types of triangles.
QQ. Quadrilaterals
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QQ.01. Identify and classify quadrilaterals (parallelograms, trapezoids, rectangles, rhombuses, squares).
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QQ.02. Understand the relationships between different types of quadrilaterals.
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QQ.03. Pick all the names for a quadrilateral (new).
RR. Polygons
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RR.01. Identify polygons and classify them by the number of sides.
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RR.02. Understand properties of regular and irregular polygons.
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RR.03. Sort polygons using Venn diagrams.
SS. Perimeter
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SS.01. Calculate perimeter of shapes with whole number, decimal, and fractional side lengths.
TT. Area
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TT.01. Calculate the area of squares, rectangles, and compound figures.
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TT.02. Solve problems involving area.
UU. Volume
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UU.01. Calculate the volume of cubes and rectangular prisms.
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UU.02. Solve problems involving volume.
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UU.03. Compare volumes of rectangular prisms.
VV. Financial Literacy
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VV.01. Understand income, payroll taxes, sales taxes, and property taxes.
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VV.02. Calculate gross and net income.
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VV.03. Evaluate payment methods.
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VV.04. Manage and budget personal finances.
