Course Content
A. Whole Numbers
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A.01. Identify place value in whole numbers up to 100.
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A.02. Identify place value in whole numbers up to 1,000,000.
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A.03. Write whole numbers in word form.
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A.04. Write whole numbers from word form.
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A.05. Compare whole numbers using symbols (, =).
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A.06. Order whole numbers from least to greatest and greatest to least.
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A.07. Understand and apply the concept of Roman numerals.
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A.08. Convert between Roman numerals and standard numerals.
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A.09. Solve real-world problems involving place value and ordering of whole numbers.
B. Decimals
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B.01. Represent decimals using models (e.g., base-ten blocks).
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B.02. Identify place value in decimal numbers.
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B.03. Write decimals in word form.
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B.04. Write decimals from word form.
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B.05. Convert decimals between standard and expanded form.
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B.06. Round decimals to the nearest whole number, tenth, and hundredth.
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B.07. Compare decimals using models and number lines.
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B.08. Compare decimals using symbols (, =).
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B.09. Order decimals from least to greatest and greatest to least.
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B.10. Solve real-world problems involving comparing and ordering decimals.
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B.11. Understand and apply the concept of equivalent decimals.
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B.12. Compose and decompose decimals in multiple ways.
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B.13. Solve word problems involving rounding and comparing decimals.
C. Integers
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C.01. Understand the concept of integers and their representation on a number line.
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C.02. Plot integers on horizontal and vertical number lines.
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C.03. Compare and order integers using symbols (, =).
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C.04. Understand absolute value and its application.
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C.05. Solve real-world problems involving integers.
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C.06. Compare and contrast integers and whole numbers.
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C.07. Work with integers in various contexts (e.g., temperature, elevation).
D. Addition and Subtraction
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D.01. Add and subtract whole numbers fluently.
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D.02. Add and subtract whole numbers in word problems.
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D.03. Estimate sums and differences of whole numbers.
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D.04. Add and subtract decimal numbers fluently.
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D.05. Add and subtract decimals in word problems.
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D.06. Estimate sums and differences of decimals.
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D.07. Solve multi-step word problems involving addition and subtraction of whole numbers and decimals.
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D.08. Apply addition and subtraction to solve problems involving maps and distances.
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D.09. Use properties of addition (commutative, associative) to simplify calculations.
E. Multiplication
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E.01. Multiply whole numbers fluently.
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E.02. Multiply whole numbers in word problems.
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E.03. Estimate products of whole numbers.
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E.04. Multiply numbers ending in zeroes.
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E.05. Multiply three or more numbers.
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E.06. Understand and apply the distributive property of multiplication.
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E.07. Solve multi-step word problems involving multiplication.
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E.08. Use multiplication to solve area problems.
F. Division
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F.01. Understand divisibility rules for common numbers.
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F.02. Divide whole numbers by two-digit numbers.
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F.03. Divide whole numbers in word problems.
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F.04. Estimate quotients of whole numbers.
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F.05. Divide numbers ending in zeroes.
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F.06. Understand and apply the relationship between multiplication and division.
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F.07. Solve multi-step word problems involving division.
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F.08. Interpret remainders in division problems.
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F.09. Use long division to solve division problems efficiently.
G. Multiply and Divide Decimals
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G.01. Multiply and divide decimals by powers of ten.
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G.02. Multiply decimals by whole numbers using various methods (e.g., blocks, distributive property).
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G.03. Multiply decimals by decimals.
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G.04. Divide decimals by whole numbers using various methods (e.g., blocks, area models).
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G.05. Divide decimals by decimals.
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G.06. Estimate products and quotients of decimals.
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G.07. Solve word problems involving multiplication and division of decimals.
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G.08. Understand and apply the concept of decimal place value in multiplication and division.
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G.09. Solve real-world problems involving multiplication and division of decimals.
H. Exponents
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H.01. Write multiplication expressions using exponents.
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H.02. Evaluate powers with whole number bases.
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H.03. Evaluate powers with decimal bases.
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H.04. Understand the order of operations involving exponents.
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H.05. Solve equations involving exponents.
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H.06. Relate exponents to repeated multiplication.
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H.07. Explore the properties of exponents (e.g., power of a power).
I. Number Theory
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I.01. Identify prime and composite numbers.
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I.02. Identify factors of a number.
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I.03. Find the prime factorization of a number.
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I.04. Find the greatest common factor (GCF).
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I.05. Find the least common multiple (LCM).
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I.06. Solve real-world problems involving GCF and LCM.
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I.07. Understand and apply the fundamental theorem of arithmetic.
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I.08. Explore relationships between prime numbers and other number concepts.
J. Fractions and Mixed Numbers
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J.10. Apply the concept of least common denominator.
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J.01. Understand and represent fractions.
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J.02. Identify equivalent fractions.
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J.03. Simplify fractions to lowest terms.
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J.04. Convert between improper fractions and mixed numbers.
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J.05. Compare and order fractions using benchmarks (e.g., 0, ½, 1).
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J.06. Compare and order fractions using common denominators.
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J.07. Convert between fractions and decimals.
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J.08. Represent fractions on a number line.
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J.09. Solve real-world problems involving fractions and mixed numbers.
K. Add and Subtract Fractions
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K.01. Add and subtract fractions with like denominators.
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K.02. Add and subtract fractions with unlike denominators.
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K.03. Add and subtract mixed numbers with like denominators.
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K.04. Add and subtract mixed numbers with unlike denominators.
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K.05. Estimate sums and differences of fractions and mixed numbers.
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K.06. Solve word problems involving addition and subtraction of fractions and mixed numbers.
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K.07. Apply addition and subtraction of fractions to solve problems involving measurement.
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K.08. Use visual models to understand addition and subtraction of fractions.
L. Multiply and Divide Fractions
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L.01. Multiply fractions by whole numbers.
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L.02. Multiply fractions by fractions.
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L.03. Multiply mixed numbers by whole numbers and fractions.
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L.04. Divide whole numbers by unit fractions.
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L.05. Divide unit fractions by whole numbers.
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L.06. Divide fractions by fractions.
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L.07. Solve word problems involving multiplication and division of fractions and mixed numbers.
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L.08. Apply multiplication and division of fractions to solve real-world problems.
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L.09. Use visual models to understand multiplication and division of fractions.
M. Mixed Operations
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M.01. Add, subtract, multiply, or divide two whole numbers.
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M.02. Evaluate numerical expressions involving whole numbers and order of operations.
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M.03. Add, subtract, multiply, or divide decimals.
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M.04. Evaluate numerical expressions involving decimals and order of operations.
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M.05. Add, subtract, multiply, or divide fractions and mixed numbers.
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M.06. Evaluate numerical expressions involving fractions, mixed numbers, and order of operations.
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M.07. Solve multi-step word problems involving mixed operations.
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M.08. Apply problem-solving strategies to complex mixed operations problems.
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M.09. Apply the order of operations consistently in various contexts.
N. Rational Numbers
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N.01. Define rational numbers and provide examples.
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N.02. Compare and order rational numbers using a number line.
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N.03. Compare and order rational numbers using symbols (, =).
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N.04. Represent rational numbers in different forms (fractions, decimals, percentages).
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N.05. Apply rational numbers to solve real-world problems.
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N.06. Understand the relationship between rational numbers and their decimal representation.
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N.07. Identify and classify different types of rational numbers (integers, fractions, etc.)
O. Problem Solving and Estimation
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O.01. Estimate to solve word problems.
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O.02. Solve multi-step word problems.
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O.03. Identify extra or missing information in word problems.
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O.04. Use guess-and-check strategies to solve problems.
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O.05. Use logical reasoning to solve problems.
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O.06. Develop and apply problem-solving strategies to diverse problem types.
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O.07. Determine appropriate estimation strategies based on the problem context.
P. Ratios and Rates
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P.01. Understand the concept of a ratio.
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P.02. Write ratios in different forms (e.g., a:b, a/b).
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P.03. Identify equivalent ratios.
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P.04. Use ratio tables to find equivalent ratios.
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P.05. Understand the concept of a rate.
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P.06. Calculate unit rates.
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P.07. Solve problems involving ratios and rates.
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P.08. Use ratios and rates to solve real-world problems.
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P.09. Solve problems involving proportions.
Q. Percents
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Q.01. Understand the concept of percent.
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Q.02. Convert between fractions, decimals, and percents.
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Q.03. Find the percent of a number.
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Q.04. Find what percent one number is of another.
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Q.05. Find the whole given a part and a percent.
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Q.06. Solve real-world problems involving percents.
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Q.07. Apply percents to solve problems involving discounts, taxes, and tips.
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Q.08. Use visual models to understand percents.
R. Units of Measurement
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R.01. Estimate metric measurements.
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R.02. Convert between metric units.
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R.03. Solve problems involving metric unit conversions.
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R.04. Understand and use customary units of measurement.
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R.05. Convert between customary units of measurement.
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R.06. Solve problems involving customary unit conversions.
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R.07. Compare and contrast metric and customary systems.
S. Money
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S.01. Add, subtract, multiply, and divide money amounts.
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S.02. Solve real-world problems involving money.
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S.03. Understand and apply concepts related to budgeting and saving.
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S.04. Solve problems involving different types of coins and bills.
T. Consumer Math
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T.01. Calculate sale prices using discounts.
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T.02. Compare unit prices to determine the best buy.
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T.03. Calculate sales tax.
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T.04. Calculate simple interest.
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T.05. Solve real-world problems involving consumer math.
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T.06. Make informed consumer decisions based on calculations.
U. Time
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U.01. Understand units of time.
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U.02. Convert between units of time.
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U.03. Calculate elapsed time.
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U.04. Solve problems involving time.
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U.05. Convert between 12-hour and 24-hour time formats.
V. Coordinate Plane
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V.01. Identify and plot points on a coordinate plane (positive numbers only).
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V.02. Identify and plot points on a coordinate plane (positive and negative numbers).
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V.03. Understand the concept of quadrants.
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V.04. Use coordinate planes to represent real-world situations.
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V.05. Determine distances between points on a coordinate plane.
W. Expressions and Properties
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W.01. Write variable expressions.
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W.02. Evaluate variable expressions.
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W.03. Understand and apply properties of addition (commutative, associative, identity, inverse).
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W.04. Understand and apply properties of multiplication (commutative, associative, identity, inverse, distributive).
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W.05. Simplify expressions using properties.
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W.06. Identify equivalent expressions.
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W.07. Use algebraic reasoning to solve problems.
X. One-Variable Equations
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X.01. Understand the concept of an equation.
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X.02. Solve one-step equations.
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X.03. Solve two-step equations.
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X.04. Solve equations involving like terms.
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X.05. Solve word problems involving one-variable equations.
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X.06. Use different methods to solve equations (e.g., algebra tiles, balancing).
Y. One-Variable Inequalities
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Y.01. Understand the concept of an inequality.
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Y.02. Solve one-step inequalities.
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Y.03. Solve two-step inequalities.
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Y.04. Graph solutions to inequalities on a number line.
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Y.05. Solve word problems involving one-variable inequalities.
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Y.06. Compare and contrast equations and inequalities.
Z. Two-Variable Equations
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Z.01. Understand the concept of a two-variable equation.
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Z.02. Identify independent and dependent variables.
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Z.03. Complete a table of values for a two-variable equation.
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Z.04. Graph a two-variable equation on a coordinate plane.
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Z.05. Solve word problems involving two-variable equations.
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Z.06. Identify linear relationships from tables and graphs.
AA. Two-Dimensional Figures
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AA.01. Identify and classify polygons (triangles, quadrilaterals, etc.).
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AA.02. Measure angles using a protractor.
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AA.03. Classify angles (acute, obtuse, right, straight).
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AA.04. Understand and apply properties of triangles and quadrilaterals.
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AA.05. Find missing angles in triangles and quadrilaterals.
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AA.06. Understand and apply concepts of congruence and similarity.
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AA.07. Use geometric reasoning to solve problems.
BB. Symmetry and Transformations
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BB.01. Identify lines of symmetry.
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BB.02. Perform and identify reflections, rotations, and translations.
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BB.03. Describe transformations using coordinates.
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BB.04. Understand and apply the concept of composition of transformations.
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BB.05. Identify similar and congruent figures.
CC. Three-Dimensional Figures
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CC.01. Identify polyhedra (prisms, pyramids).
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CC.02. Identify nets of three-dimensional figures.
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CC.03. Draw front, side, and top views of three-dimensional figures.
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CC.04. Count vertices, edges, and faces of polyhedra.
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CC.05. Understand and apply Euler’s formula for polyhedra.
DD. Geometric Measurement
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DD.01. Calculate perimeter of various shapes.
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DD.02. Calculate area of squares, rectangles, parallelograms, triangles, trapezoids, and compound figures.
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DD.03. Calculate surface area of cubes and rectangular prisms.
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DD.04. Calculate volume of cubes and rectangular prisms.
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DD.05. Solve real-world problems involving geometric measurement.
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DD.06. Relate area and perimeter to real-world situations.
EE. Data and Graphs
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EE.01. Interpret and create pictographs, bar graphs, line plots, and line graphs.
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EE.02. Interpret and create stem-and-leaf plots and histograms.
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EE.03. Interpret and create circle graphs (pie charts).
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EE.04. Choose appropriate graphs to represent data.
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EE.05. Analyze data presented in various graphical formats.
FF. Statistics
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FF.01. Calculate mean, median, mode, and range of data sets.
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FF.02. Interpret data using measures of central tendency.
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FF.03. Identify representative and biased samples.
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FF.04. Identify discrete and continuous data.
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FF.05. Use statistical reasoning to interpret data.
GG. Probability
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GG.01. Understand the concept of probability.
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GG.02. Calculate probability of simple events.
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GG.03. Calculate probability of compound events.
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GG.04. Make predictions based on probability.
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GG.05. Understand and apply the concepts of theoretical and experimental probability.
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GG.06. Distinguish between independent and dependent events.
HH. Financial Literacy
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HH.01. Understand vocabulary related to financial institutions.
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HH.02. Identify advantages and disadvantages of different payment methods.
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HH.03. Compare savings options.
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HH.04. Balance a budget.
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HH.05. Adjust a budget to meet financial goals.
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HH.06. Make informed financial decisions.
II. Patterns and Sequences
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II.01. Identify and describe number patterns.
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II.02. Extend number patterns.
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II.03. Identify arithmetic and geometric sequences.
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II.04. Use rules to generate number sequences.
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II.05. Solve problems involving patterns and sequences.
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II.06. Recognize patterns in various contexts (e.g., shapes, numbers).
