Course Content
A. Numbers and Counting
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A.01. Identify place values in whole numbers up to five digits.
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A.02. Read and write word names for numbers up to five digits.
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A.03. Convert between place values within a five-digit number.
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A.04. Use ordinal numbers up to 100th to represent position.
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A.05. Compare numbers up to five digits using comparison symbols.
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A.06. Identify Roman numerals and convert them to corresponding Arabic numerals.
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A.07. Determine if a number is even or odd using arithmetic rules.
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A.08. Round numbers to the nearest ten, hundred, or thousand.
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A.09. Identify prime and composite numbers.
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A.10. Represent inequalities on a number line.
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A.11. Apply place value understanding to solve real-world problems.
B. Addition
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B.01. Identify and apply properties of addition (commutative, associative, identity).
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B.02. Add numbers up to five digits without regrouping.
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B.03. Add numbers up to five digits with regrouping.
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B.04. Add three or more numbers up to five digits each.
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B.05. Identify addition patterns over increasing place values.
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B.06. Fill in missing digits in addition problems.
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B.07. Estimate sums of numbers up to five digits.
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B.08. Solve addition word problems involving numbers up to five digits.
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B.09. Choose numbers that yield a particular sum.
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B.10. Solve multi-step word problems involving addition.
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B.11. Estimate sums in word problems.
C. Subtraction
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C.01. Subtract numbers up to five digits without regrouping.
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C.02. Subtract numbers up to five digits with regrouping.
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C.03. Fill in missing digits in subtraction problems.
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C.04. Identify subtraction patterns over increasing place values.
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C.05. Estimate differences of numbers up to five digits.
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C.06. Solve subtraction word problems involving numbers up to five digits.
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C.07. Choose numbers that yield a particular difference.
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C.08. Solve multi-step word problems involving subtraction.
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C.09. Estimate differences in word problems.
D. Multiplication
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D.01. Recall multiplication facts up to 10 x 10 fluently.
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D.02. Choose the multiples of a given number up to 12.
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D.03. Identify and apply properties of multiplication (commutative, associative, distributive, identity, zero).
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D.04. Multiply 1-digit numbers by 2-digit numbers using various methods.
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D.05. Multiply 1-digit numbers by 3-digit or 4-digit numbers.
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D.06. Identify multiplication patterns over increasing place values.
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D.07. Multiply a two-digit number by a two-digit number.
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D.08. Multiply a two-digit number by a two-digit number, completing missing steps.
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D.09. Multiply numbers ending in zeroes.
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D.10. Estimate products when multiplying by 1-digit numbers.
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D.11. Estimate products when multiplying by larger numbers.
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D.12. Multiply three numbers.
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D.13. Compare numbers using multiplication.
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D.14. Use the box or lattice method for multiplication.
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D.15. Choose numbers that yield a particular product.
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D.16. Solve inequalities involving multiplication.
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D.17. Solve word problems involving multiplication of up to three numbers.
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D.18. Solve word problems involving multiplication of numbers ending in zeroes.
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D.19. Estimate products in word problems.
E. Division
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E.01. Recall division facts up to 100 ÷ 10 fluently.
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E.02. Interpret remainders in division problems.
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E.03. Identify and apply properties of division.
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E.04. Divide larger numbers by 1-digit divisors.
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E.05. Complete division tables.
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E.06. Divide numbers ending in zeroes by 1-digit divisors.
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E.07. Estimate quotients in division problems.
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E.08. State the divisibility rules for 2, 3, 5, and 10.
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E.09. Recognize division patterns over increasing place values.
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E.10. Divide numbers ending in zeroes by multi-digit divisors.
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E.11. Divide two-digit numbers by multiples of 10.
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E.12. Divide by two-digit numbers.
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E.13. Choose numbers that yield a particular quotient.
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E.14. Solve inequalities involving division.
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E.15. Solve word problems involving division.
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E.16. Solve word problems involving division with remainders.
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E.17. Solve word problems involving the divisibility rules.
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E.18. Solve word problems involving division of numbers ending in zeroes.
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E.19. Estimate quotients in word problems.
F. Fractions
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F.07. Identify patterns of equivalent fractions.
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F.08. Write fractions in lowest terms (simplify).
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F.09. Graph fractions on number lines.
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F.10. Compare fractions using number lines.
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F.11. Compare fractions with like numerators or denominators.
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F.12. Compare fractions with unlike numerators or denominators.
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F.13. Order fractions with like numerators or denominators.
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F.14. Order fractions with unlike numerators or denominators.
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F.15. Identify smaller or larger fractions from a set.
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F.16. Calculate fractions of a number.
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F.17. Solve word problems involving fractions of a number.
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F.18. Define and recognize mixed numbers.
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F.19. Convert between improper fractions and mixed numbers.
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F.01. Recognize fractions as parts of a whole.
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F.02. Solve word problems involving fractions of a whole.
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F.03. Solve word problems involving fractions of a group.
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F.04. Identify equivalent fractions using area models.
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F.05. Identify equivalent fractions using number lines.
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F.06. Generate equivalent fractions.
G. Decimals
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G.01. Model decimals and fractions using visual aids.
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G.02. Read and write decimals expressed in words.
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G.03. Identify place values in decimal numbers.
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G.04. Identify equivalent decimals.
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G.05. Graph decimals on number lines.
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G.06. Graph fractions as decimals on number lines.
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G.07. Convert fractions and mixed numbers to decimals.
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G.08. Convert decimals to fractions and mixed numbers.
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G.09. Convert decimals between standard and expanded form using fractions.
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G.10. Round decimals to the nearest whole number or tenth.
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G.11. Compare decimals using number lines.
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G.12. Compare decimal numbers.
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G.13. Order decimal numbers from least to greatest.
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G.14. Compare decimals and fractions on number lines.
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G.15. Compare decimals and fractions.
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G.16. Identify number sequences involving decimals.
H. Add and Subtract Fractions
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H.01. Decompose fractions in multiple ways.
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H.02. Add and subtract fractions with like denominators using number lines.
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H.03. Add and subtract fractions with like denominators.
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H.04. Complete addition and subtraction sentences with fractions
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H.05. Add and subtract mixed numbers with like denominators.
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H.06. Add up to 4 fractions with denominators of 10 and 100.
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H.07. Add three or more fractions with like denominators.
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H.08. Solve word problems involving addition and subtraction of fractions with like denominators.
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H.09. Solve word problems involving addition and subtraction of mixed numbers with like denominators.
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H.10. Solve word problems involving the addition of three or more fractions with like denominators.
I. Multiply Fractions
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I.01. Multiply unit fractions by whole numbers using number lines.
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I.02. Multiply unit fractions by whole numbers using models.
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I.03. Find multiples of fractions.
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I.04. Multiply unit fractions by whole numbers.
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I.05. Multiply fractions by whole numbers using number lines.
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I.06. Multiply fractions by whole numbers using models.
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I.07. Multiply fractions by whole numbers.
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I.08. Distinguish between multiplying unit fractions and multiplying fractions by whole numbers.
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I.09. Solve word problems involving multiplication of unit fractions by whole numbers.
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I.10. Solve word problems involving multiplication of fractions by whole numbers.
J. Add and Subtract Decimals
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J.01. Add decimal numbers to the hundredths place.
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J.02. Subtract decimal numbers to the hundredths place.
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J.03. Add three or more decimal numbers.
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J.04. Choose decimal numbers that yield a particular sum or difference.
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J.05. Estimate sums and differences of decimals.
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J.06. Solve inequalities with addition and subtraction of decimals.
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J.07. Complete the addition or subtraction sentence involving decimals
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J.08. Solve decimal problems using diagrams.
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J.09. Solve word problems involving addition and subtraction of decimals.
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J.10. Solve word problems involving the addition of three or more decimals.
K. Multiply and Divide 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 decimal by a one-digit whole number.
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K.04. Divide decimals by powers of ten.
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K.05. Identify decimal division patterns over increasing place values.
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K.06. Perform division with decimal quotients.
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K.07. Perform division with decimal quotients and rounding.
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K.08. Solve word problems involving multiplication of decimals and whole numbers.
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K.09. Solve word problems involving multiplication of money amounts.
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K.10. Solve word problems involving division with decimal quotients.
L. Mixed Operations
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L.01. Add, subtract, multiply, and divide whole numbers.
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L.02. Mentally add and subtract numbers ending in zeroes.
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L.03. Choose numbers with a particular sum, difference, product, or quotient.
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L.04. Solve inequalities involving addition, subtraction, multiplication, and division.
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L.05. Estimate sums, differences, products, and quotients in word problems.
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L.06. Solve multi-step word problems involving mixed operations.
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L.07. Solve word problems with extra or missing information.
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L.08. Solve word problems using guess-and-check.
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L.09. Create and solve real-world problems involving mixed operations.
M. Variable Expressions
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M.01. Write variable expressions to represent mathematical phrases.
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M.02. Evaluate variable expressions by substituting given values.
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M.03. Write variable equations to represent word problems.
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M.04. Solve simple variable equations involving one operation.
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M.05. Write variable expressions to represent real-world scenarios.
N. Functions
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N.01. Complete input/output tables with addition, subtraction, multiplication, and division.
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N.02. Complete a table for a two-variable relationship.
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N.03. Write a two-variable equation based on a table.
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N.04. Graph a two-variable relationship on a coordinate plane.
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N.05. Analyze and interpret functional relationships in real-world contexts.
O. Logical Reasoning
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O.01. Find two numbers based on their sum and difference.
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O.02. Find two numbers based on their sum, difference, product, and quotient.
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O.03. Determine the correct order of events or objects based on given clues.
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O.04. Solve logic puzzles involving numerical relationships.
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O.05. Apply deductive reasoning to solve mathematical problems.
P. Data and Graphs
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P.01. Read and interpret data presented in a table.
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P.02. Interpret data presented in line graphs.
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P.03. Create line graphs from given data.
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P.04. Interpret data presented in bar graphs.
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P.05. Create bar graphs from given data.
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P.06. Interpret data presented in line plots.
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P.07. Create line plots from given data.
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P.08. Create and interpret frequency charts.
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P.09. Interpret data presented in stem-and-leaf plots.
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P.10. Create stem-and-leaf plots from given data.
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P.11. Read and interpret data presented in pie charts.
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P.12. Choose the best type of graph to represent a given set of data.
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P.13. Draw conclusions and make inferences based on data displays.
Q. Probability and Statistics
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Q.01. Understand the basic concepts of probability.
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Q.02. Calculate the probability of simple events.
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Q.03. Make predictions based on probability.
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Q.04. Calculate the mean (average) of a data set.
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Q.05. Determine the mode of a data set.
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Q.06. Interpret charts to find the mean and mode.
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Q.07. Determine possible combinations from a set of items.
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Q.08. Apply probability and statistics to solve real-world problems.
R. Patterns and Sequences
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R.01. Identify the next shape in a repeating pattern.
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R.02. Complete a repeating pattern of shapes or numbers.
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R.03. Create a repeating pattern of shapes or numbers.
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R.04. Identify the next row in a growing pattern of shapes.
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R.05. Complete an increasing number pattern.
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R.06. Complete a geometric number pattern.
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R.07. Solve word problems involving number patterns.
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R.08. Identify and extend numerical patterns with mixed operations.
S. Money
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S.01. Compare different money amounts using comparison symbols.
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S.02. Round money amounts to the nearest dollar or cent.
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S.03. Add and subtract money amounts.
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S.04. Add, subtract, multiply, and divide money amounts.
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S.05. Calculate making change from a purchase.
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S.06. Interpret information from price lists.
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S.07. Calculate costs using price lists with multiplication.
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S.08. Determine unit prices for given items.
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S.09. Solve multi-step word problems involving money.
T. Units of Measurement
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T.01. Choose the appropriate metric unit of measure for length, mass, and volume.
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T.02. Compare and convert metric units of length (mm, cm, m, km).
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T.03. Compare and convert metric units of mass (g, kg).
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T.04. Compare and convert metric units of volume (mL, L).
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T.05. Solve problems involving metric mixed units.
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T.06. Select the correct tools for measurements.
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T.07. Estimate measurements in metric units.
U. Time
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U.01. Convert between different units of time (seconds, minutes, hours, days, weeks, months, years).
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U.02. Add and subtract mixed time units.
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U.03. Calculate fractions of time units.
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U.04. Calculate elapsed time between two given times.
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U.05. Determine start and end times in multi-step word problems.
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U.06. Interpret transportation schedules (e.g., bus, train).
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U.07. Identify and extend time patterns.
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U.08. Relate time to daily life events.
V. Geometry
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V.01. Identify and describe two-dimensional figures (squares, circles, triangles, rectangles, etc.).
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V.02. Identify three-dimensional figures (cubes, spheres, cones, cylinders, pyramids, etc.).
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V.03. Count vertices, edges, and faces of three-dimensional figures.
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V.04. Identify faces of three-dimensional figures.
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V.05. Describe three-dimensional figures based on their properties.
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V.06. Identify nets of three-dimensional figures.
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V.07. Determine if a shape is a polygon.
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V.08. Identify the number of sides in polygons.
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V.09. Recognize parallel, perpendicular, and intersecting lines.
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V.10. Identify acute, right, obtuse, and straight angles.
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V.11. Classify different types of triangles (acute, right, obtuse, equilateral, isosceles, scalene).
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V.12. Identify parallel sides in quadrilaterals.
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V.13. Identify parallelograms, trapeziums, rectangles, and rhombuses.
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V.14. Classify quadrilaterals based on their properties.
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V.15. Recognize congruent figures.
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V.16. Identify lines of symmetry in two-dimensional figures.
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V.17. Determine if a figure has rotational symmetry.
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V.18. Apply geometric concepts to real-world scenarios.
W. Geometric Measurement
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W.01. Calculate the perimeter of rectangles.
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W.02. Calculate the perimeter of polygons.
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W.03. Calculate the perimeter of rectilinear shapes.
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W.04. Determine a missing side length given the perimeter of a polygon.
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W.05. Use perimeter to determine the cost of fencing or bordering.
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W.06. Find the area of figures made of unit squares.
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W.07. Select figures with a given area.
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W.08. Select two figures with the same area.
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W.09. Create figures with a given area using unit squares.
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W.10. Find the area of a rectangle using its length and width.
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W.11. Determine the missing side length of a rectangle given its area and one side.
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W.12. Solve word problems involving area and perimeter.
