Course Content
A. Number Sense Fundamentals
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A.01. Understand whole numbers and their properties.
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A.02. Identify prime and composite numbers.
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A.03. Find prime factorization of numbers.
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A.04. Apply divisibility rules.
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A.05. Determine greatest common factor (GCF).
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A.06. Determine least common multiple (LCM).
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A.07. Solve word problems involving GCF and LCM.
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A.08. Classify numbers (integers, rational, irrational).
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A.09. Explain the concept of a factor tree and its use in prime factorization.
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A.10. Explore the relationship between GCF, LCM, and prime factorization.
B. Integers and Absolute Value
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B.01. Represent integers on a number line.
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B.02. Understand opposite integers.
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B.03. Understand the concept of absolute value.
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B.04. Compare and order integers.
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B.05. Solve integer inequalities.
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B.06. Solve word problems involving integers and absolute value.
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B.07. Explain the significance of zero in the context of integers.
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B.08. Apply integers to real-world scenarios like temperature and elevation.
C. Operations with Integers
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C.01. Add integers using various methods (counters, number lines).
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C.02. Subtract integers using various methods (counters, number lines).
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C.03. Understand and apply integer addition and subtraction rules.
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C.04. Multiply integers and understand the rules.
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C.05. Divide integers and understand the rules.
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C.06. Evaluate numerical expressions involving integers.
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C.07. Solve multi-step problems involving integers.
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C.08. Apply integer operations to real-world scenarios.
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C.09. Explain the relationship between addition and subtraction, and multiplication and division of integers.
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C.10. Solve equations involving integer operations.
D. Decimals and Operations
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D.01. Understand decimal place value.
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D.02. Compare and order decimals.
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D.03. Round decimals to a given place value.
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D.04. Add and subtract decimals.
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D.05. Multiply decimals.
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D.06. Divide decimals.
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D.07. Evaluate numerical expressions involving decimals.
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D.08. Solve word problems involving decimal operations.
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D.09. Convert fractions to decimals and vice versa.
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D.10. Explain the concept of repeating and terminating decimals.
E. Fractions and Mixed Numbers
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E.01. Understand fractions and their representation.
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E.02. Find equivalent fractions.
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E.03. Simplify fractions to lowest terms.
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E.04. Compare and order fractions.
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E.05. Convert between mixed numbers and improper fractions.
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E.06. Add and subtract fractions with like denominators.
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E.07. Add and subtract fractions with unlike denominators.
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E.08. Add and subtract mixed numbers.
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E.09. Solve word problems involving fractions and mixed numbers.
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E.10. Apply fraction operations to real-world scenarios like baking or measurement.
F. Operations with Fractions
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F.01. Multiply fractions and whole numbers.
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F.02. Multiply fractions.
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F.03. Multiply mixed numbers.
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F.04. Divide whole numbers by unit fractions.
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F.05. Divide fractions.
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F.06. Divide mixed numbers.
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F.07. Solve word problems involving fraction multiplication and division.
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F.08. Explain the concept of reciprocal and its application in division.
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F.09. Apply fraction operations to solve complex equations.
G. Rational Numbers
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G.06. Evaluate numerical expressions involving rational numbers.
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G.07. Solve word problems involving rational numbers.
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G.08. Represent rational numbers on a number line.
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G.09. Explain the relationship between rational and irrational numbers.
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G.01. Identify rational numbers.
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G.02. Convert between decimals, fractions, and mixed numbers.
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G.03. Find the absolute value of rational numbers.
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G.04. Compare and order rational numbers.
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G.05. Add, subtract, multiply, and divide rational numbers.
H. Exponents and Square Roots
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H.01. Understand exponents and powers.
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H.02. Evaluate powers with positive integer exponents.
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H.03. Evaluate expressions involving exponents.
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H.04. Understand square roots of perfect squares.
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H.05. Estimate square roots of non-perfect squares.
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H.06. Solve equations with variable exponents.
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H.07. Explore powers with negative and fractional exponents (introductory).
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H.08. Explain the connection between exponents and repeated multiplication.
I. Ratios, Rates, and Proportions
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I.01. Understand ratios and rates.
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I.02. Identify equivalent ratios.
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I.03. Find unit rates.
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I.04. Compare ratios and rates.
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I.05. Solve proportions.
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I.06. Solve word problems involving ratios, rates, and proportions.
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I.07. Apply ratios and proportions to real-world scenarios (e.g., scaling recipes, map scales).
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I.08. Introduce the concept of proportional relationships.
J. Proportional Relationships
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J.01. Identify proportional relationships from tables and graphs.
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J.02. Find the constant of proportionality.
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J.03. Write equations for proportional relationships.
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J.04. Interpret graphs of proportional relationships.
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J.05. Solve problems using proportional relationships.
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J.06. Explain the meaning of the constant of proportionality in context.
K. Percentages
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K.01. Convert between percents, fractions, and decimals.
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K.02. Find percents of numbers.
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K.03. Solve percent equations.
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K.04. Solve word problems involving percentages (e.g., discounts, tax, tips).
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K.05. Explain the meaning of percent in different contexts.
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K.06. Apply percentage calculations to real-world scenarios like sales and interest.
L. Consumer Math
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L.01. Perform calculations involving money.
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L.02. Calculate unit prices.
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L.03. Calculate sales tax, discounts, and simple interest.
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L.04. Solve multi-step problems involving consumer math.
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L.05. Analyze and compare different deals and offers.
M. Problem Solving and Estimation
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M.01. Estimate answers to problems.
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M.02. Solve multi-step word problems.
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M.03. Use various problem-solving strategies (e.g., guess-and-check, diagrams).
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M.04. Solve problems involving elapsed time.
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M.05. Develop strategies for checking the reasonableness of answers.
N. Measurement
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N.01. Estimate metric measurements.
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N.02. Convert between metric units.
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N.03. Understand precision in measurement.
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N.04. Solve problems involving metric units.
O. Coordinate Plane
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O.01. Understand coordinates on a coordinate plane.
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O.02. Plot points on a coordinate plane.
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O.03. Find the distance between two points.
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O.04. Use the coordinate plane to represent real-world situations.
P. Sequences
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P.01. Identify arithmetic and geometric sequences.
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P.02. Find the nth term in a sequence.
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P.03. Write variable expressions for sequences.
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P.04. Extend patterns and analyze sequences.
Q. Algebraic Expressions and Properties
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Q.01. Write variable expressions.
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Q.02. Evaluate variable expressions.
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Q.03. Understand properties of addition and multiplication.
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Q.04. Use the distributive property.
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Q.05. Simplify algebraic expressions.
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Q.06. Identify equivalent expressions.
R. One-Variable Equations
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R.01. Solve one-step equations.
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R.02. Solve two-step equations.
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R.03. Solve equations with variables on both sides.
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R.04. Solve word problems using equations.
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R.05. Explain the process of solving equations.
S. One-Variable Inequalities
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S.01. Understand inequalities and their solutions.
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S.02. Graph inequalities on a number line.
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S.03. Solve one-step inequalities.
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S.04. Solve two-step inequalities.
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S.05. Solve word problems using inequalities.
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S.06. Explain the concept of inequality.
T. Two-Variable Equations
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T.01. Identify independent and dependent variables.
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T.02. Complete tables for two-variable relationships.
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T.03. Write equations for two-variable relationships.
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T.04. Graph two-variable equations.
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T.05. Solve word problems involving two-variable equations.
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T.06. Interpret graphs of two-variable equations.
U. Two-Dimensional Figures
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U.01. Identify and classify polygons.
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U.02. Classify triangles and quadrilaterals.
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U.03. Understand angles (complementary, supplementary, vertical, adjacent).
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U.04. Find missing angles in triangles.
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U.05. Understand parallel and perpendicular lines.
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U.06. Understand transversals and angle relationships.
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U.07. Explore different types of polygons.
V. Transformations
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V.01. Identify reflections, rotations, and translations.
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V.02. Graph transformations.
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V.03. Identify congruent figures.
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V.04. Identify similar figures.
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V.05. Understand dilations.
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V.06. Explain the properties of transformations.
W. Constructions
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W.01. Construct the midpoint or perpendicular bisector of a segment.
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W.02. Construct an angle bisector.
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W.03. Construct a congruent angle.
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W.04. Construct a perpendicular line.
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W.05. Construct parallel lines.
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W.06. Explain the steps involved in geometric constructions.
X. Three-Dimensional Figures
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X.01. Identify three-dimensional figures.
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X.02. Understand nets of three-dimensional figures.
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X.03. Find volume and surface area of three-dimensional figures.
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X.04. Explore different three-dimensional shapes and their properties.
Y. Geometric Measurement
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Y.01. Calculate perimeter and area of various shapes.
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Y.02. Calculate circumference and area of circles.
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Y.03. Calculate volume of prisms and cylinders.
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Y.04. Calculate surface area of prisms and cylinders.
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Y.05. Solve word problems involving geometric measurement.
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Y.06. Explain the relationship between perimeter, area, and volume.
Z. Data Analysis and Graphs
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Z.01. Interpret and create various types of graphs (line plots, bar graphs, histograms, circle graphs, line graphs).
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Z.02. Choose the best type of graph for given data.
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Z.03. Interpret data from tables.
AA. Statistics
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AA.01. Calculate mean, median, mode, and range.
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AA.02. Identify outliers.
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AA.03. Understand samples and populations.
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AA.04. Interpret data to draw conclusions.
BB. Probability
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BB.01. Understand probability of simple events.
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BB.02. Understand probability of compound events.
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BB.03. Make predictions based on probability.
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BB.04. Explain the concept of probability.
