Course Content
A. Understanding Integers
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A.01. Define integers and identify them on a number line.
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A.02. Determine the absolute value of an integer.
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A.03. Find the opposite of an integer.
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A.04. Compare and order integers using number lines and inequalities.
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A.05. Graph integers on horizontal and vertical number lines.
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A.06. Apply integers to real-world contexts, such as temperature and altitude.
B. Number and Counting
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B.01. Identify prime and composite numbers.
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B.02. Determine the prime factorization of a number.
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B.03. Find the multiplicative inverse of a number.
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B.04. Apply divisibility rules for common numbers (e.g., 2, 3, 5, 10).
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B.05. Calculate the highest common factor (HCF) of two or more numbers.
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B.06. Calculate the lowest common multiple (LCM) of two or more numbers.
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B.07. Solve word problems involving HCF and LCM.
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B.08. Express numbers in scientific notation.
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B.09. Compare numbers written in scientific notation.
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B.10. Classify numbers as natural, whole, integer, rational, or irrational.
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B.11. Identify perfect squares and perfect cubes.
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B.12. Estimate square roots and cube roots.
C. Operations with Integers
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C.01. State and apply the rules for adding and subtracting integers.
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C.02. Add and subtract integers using visual aids like counters and number lines.
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C.03. Complete addition and subtraction sentences with integers.
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C.04. Solve word problems involving addition and subtraction of integers.
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C.05. State and apply the rules for multiplying and dividing integers.
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C.06. Multiply and divide integers.
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C.07. Complete multiplication and division sentences with integers.
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C.08. Evaluate numerical expressions involving integers, using the order of operations.
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C.09. Use the distributive property with integer operations.
D. Understanding Fractions
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D.01. Solve word problems to understand fractions as parts of a whole.
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D.02. Identify and generate equivalent fractions.
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D.03. Write fractions in their lowest terms (simplest form).
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D.04. Interpret fractions from graphs and tables in word problems.
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D.05. Determine the lowest common denominator (LCD) for a set of fractions.
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D.06. Compare and order fractions.
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D.07. Solve word problems involving the comparison of fractions.
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D.08. Convert between mixed numbers and improper fractions.
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D.09. Compare mixed numbers and improper fractions.
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D.10. Round mixed numbers to the nearest whole number or specified decimal place.
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D.11. Model fractions and mixed numbers using diagrams.
E. Understanding Decimals
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E.01. Review place value and representation of decimal numbers.
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E.02. Plot decimals on a number line.
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E.03. Compare and order decimals.
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E.04. Round decimals to a specified place value.
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E.05. Convert between decimals and fractions.
F. Operations with Decimals
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F.01. Add and subtract decimals.
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F.02. Solve word problems involving addition and subtraction of decimals.
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F.03. Multiply decimals.
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F.04. Solve word problems involving the multiplication of decimals and whole numbers.
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F.05. Divide decimals.
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F.06. Solve word problems involving the division of decimals by whole numbers.
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F.07. Estimate sums, differences, products, and quotients of decimals.
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F.08. Solve multi-step word problems involving decimals.
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F.09. Evaluate numerical expressions involving decimals.
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F.10. Apply operations with decimals to solve problems involving maps with decimal distances.
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F.11. Solve inequalities involving decimals.
G. Operations with Fractions
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G.01. Add and subtract fractions with like denominators.
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G.02. Add and subtract fractions with unlike denominators.
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G.03. Solve word problems involving the addition and subtraction of fractions.
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G.04. Add and subtract mixed numbers with like denominators.
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G.05. Add and subtract mixed numbers with unlike denominators.
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G.06. Solve word problems involving the addition and subtraction of mixed numbers.
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G.07. Estimate sums and differences of mixed numbers.
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G.08. Multiply fractions and whole numbers.
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G.09. Multiply two fractions using models.
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G.10. Multiply fractions.
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G.11. Multiply mixed numbers.
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G.12. Solve word problems involving the multiplication of fractions and mixed numbers.
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G.13. Divide whole numbers and unit fractions.
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G.14. Divide fractions.
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G.15. Divide mixed numbers.
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G.16. Solve word problems involving the division of fractions and mixed numbers.
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G.17. Estimate products and quotients of fractions and mixed numbers.
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G.18. Evaluate numerical expressions involving fractions using order of operations.
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G.19. Solve inequalities involving addition and subtraction of fractions and mixed numbers.
H. Rational Numbers
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H.01. Define and identify rational numbers.
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H.02. Convert between decimals and fractions or mixed numbers.
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H.03. Compare rational numbers.
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H.04. Order rational numbers from least to greatest or greatest to least.
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H.05. Add and subtract rational numbers.
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H.06. Apply addition and subtraction rules for rational numbers in various contexts.
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H.07. Multiply and divide rational numbers.
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H.08. Apply multiplication and division rules for rational numbers in various contexts.
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H.09. Solve real-world problems involving operations with rational numbers.
I. Ratios, Rates, and Proportions
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I.01. Define and understand the concept of a ratio.
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I.02. Identify equivalent ratios.
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I.03. Write an equivalent ratio.
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I.04. Solve word problems involving equivalent ratios.
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I.05. Determine unit rates.
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I.06. Solve word problems comparing ratios.
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I.07. Apply ratios to scale drawings in word problems.
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I.08. Determine if two ratios form a proportion.
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I.09. Solve word problems to determine if ratios form a proportion.
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I.10. Solve proportions.
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I.11. Solve word problems involving proportions.
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I.12. Estimate population size using proportions.
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I.13. Determine the rate of change.
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I.14. Identify constant rate of change.
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I.15. Use proportions to convert between different units of measurement.
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I.16. Calculate and compare different rates of change.
J. Percents
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J.01. Identify the percentage illustrated in a visual representation.
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J.02. Convert between percents, fractions, and decimals.
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J.03. Compare percents to fractions and decimals.
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J.04. Estimate percents of numbers.
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J.05. Calculate percentages of numbers and money amounts.
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J.06. Solve word problems involving percentages of numbers.
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J.07. Solve percent equations.
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J.08. Solve percent equations in word problems.
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J.09. Calculate percentage increase and decrease.
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J.10. Apply percentages to solve problems involving discounts and sales tax.
K. Exponents
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K.05. Evaluate powers with decimal and fractional bases.
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K.06. Evaluate numerical expressions involving exponents using order of operations.
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K.07. Express repeated multiplication using exponents.
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K.08. Apply the rules of exponents (product, quotient, power of a power) for simplification.
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K.01. Understand the concept of exponents and their notation.
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K.02. Evaluate powers.
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K.03. Solve equations with variable exponents.
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K.04. Evaluate powers with negative bases.
L. Expressions and Properties
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L.01. Write variable expressions to represent mathematical relationships.
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L.02. Translate word problems into variable expressions.
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L.03. Evaluate linear expressions by substituting given values.
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L.04. Evaluate multi-variable expressions.
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L.05. Evaluate absolute value expressions.
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L.06. Evaluate nonlinear expressions.
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L.07. Identify terms and coefficients in algebraic expressions.
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L.08. Sort factors of expressions.
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L.09. Identify and apply properties of addition and multiplication (commutative, associative, distributive, identity, inverse).
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L.10. Multiply using the distributive property.
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L.11. Solve equations using algebraic properties.
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L.12. Write equivalent expressions using algebraic properties.
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L.13. Add and subtract like terms.
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L.14. Add, subtract, and multiply linear expressions.
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L.15. Factor linear expressions.
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L.16. Identify equivalent linear expressions.
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L.17. Simplify algebraic expressions by combining like terms and using the distributive property.
M. One-Variable Equations
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M.01. Determine which value of x satisfies a given equation.
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M.02. Translate verbal statements into algebraic equations.
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M.03. Model and solve equations using algebra tiles.
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M.04. Write and solve equations that represent diagrams.
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M.05. Solve one-step equations using inverse operations.
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M.06. Solve two-step equations.
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M.07. Solve multi-step equations.
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M.08. Solve equations in word problems.
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M.09. Solve equations involving like terms.
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M.10. Solve equations, completing the solution steps.
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M.11. Verify solutions to equations by substitution.
N. Consumer Maths
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N.01. Solve word problems involving addition, subtraction, multiplication, and division of money amounts.
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N.02. Interpret and use price lists to calculate costs.
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N.03. Determine unit prices.
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N.04. Use unit prices to find the total price.
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N.05. Calculate percent of a number, discount, and more.
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N.06. Find the percent of discount and mark-up.
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N.07. Calculate sale prices, finding the original price.
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N.08. Solve multi-step problems with percents related to consumer situations.
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N.09. Estimate tips.
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N.10. Calculate simple interest.
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N.11. Compare prices and make informed purchasing decisions.
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N.12. Calculate sales tax and total cost of items.
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. Solve word problems using the guess-and-check strategy.
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O.04. Use Venn diagrams to solve problems involving sets.
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O.05. Find the number of each type of coin in a given situation.
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O.06. Solve elapsed time word problems.
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O.07. Apply logical reasoning to solve mathematical puzzles.
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O.08. Develop and use problem-solving plans.
P. Number Sequences
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P.01. Identify arithmetic and geometric sequences.
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P.02. Determine the common difference in arithmetic sequences.
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P.03. Generate terms in arithmetic sequences.
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P.04. Determine the common ratio in geometric sequences.
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P.05. Generate terms in geometric sequences.
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P.06. Solve word problems involving arithmetic and geometric sequences.
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P.07. Evaluate variable expressions for number sequences.
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P.08. Write variable expressions for arithmetic sequences.
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P.09. Identify patterns in number sequences and extend them.
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P.10. Find a specific term in a number sequence using a formula.
Q. Units of Measurement
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Q.01. Estimate metric measurements.
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Q.02. Compare and convert metric units.
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Q.03. Work with metric mixed units.
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Q.04. Convert square and cubic units of length.
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Q.05. Convert between cubic metres and litres.
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Q.06. Determine the precision of measurements.
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Q.07. Convert between different units of measurement within the same system (e.g., inches to feet).
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Q.08. Apply unit conversions to solve real-world problems.
R. Two-Dimensional Figures
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R.01. Identify and classify polygons based on their properties.
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R.02. Name, measure, and classify angles (acute, obtuse, right, straight).
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R.03. Classify triangles by their sides and angles (e.g., equilateral, isosceles, scalene, acute, right, obtuse).
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R.04. Identify trapeziums.
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R.05. Classify quadrilaterals (e.g., square, rectangle, parallelogram, rhombus).
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R.06. Graph triangles and quadrilaterals on the coordinate plane.
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R.07. Apply the triangle angle-sum property to find missing angles.
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R.08. Use the exterior angle property of triangles to find missing angles.
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R.09. Find missing angles in triangles and quadrilaterals.
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R.10. Calculate interior angles of polygons.
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R.11. Define lines, line segments, and rays.
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R.12. Identify parallel, perpendicular, and intersecting lines.
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R.13. Identify complementary, supplementary, vertical, adjacent, and congruent angles.
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R.14. Find measures of complementary, supplementary, vertical, and adjacent angles.
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R.15. Analyze transversals of parallel lines and their resulting angle relationships.
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R.16. Find lengths and measures of bisected line segments and angles.
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R.17. Identify parts of a circle (e.g., radius, diameter, chord, circumference).
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R.18. Identify lines and rotational symmetry in two-dimensional figures.
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R.19. Calculate perimeter and area of basic polygons.
S. Congruence and Similarity
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S.01. Differentiate between similar and congruent figures.
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S.02. Determine corresponding side lengths and angle measures of congruent figures.
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S.03. Write congruence statements and identify corresponding parts.
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S.04. Determine corresponding side lengths and angle measures of similar figures.
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S.05. Use similar figures and indirect measurement to solve problems.
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S.06. Apply scale factors to find missing side lengths in similar figures.
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S.07. Determine if two figures are congruent or similar based on given information.
T. Constructions
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T.01. Construct the midpoint or perpendicular bisector of a segment using geometric tools.
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T.02. Construct an angle bisector using geometric tools.
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T.03. Construct a perpendicular line to a given line through a given point using geometric tools.
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T.04. Construct parallel lines using geometric tools.
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T.05. Construct an equilateral triangle or regular hexagon using geometric tools.
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T.06. Construct various polygons using compass and straightedge.
U. Pythagoras’ Theorem
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U.01. State Pythagoras’ theorem and apply it to find the length of the hypotenuse in a right-angled triangle.
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U.02. Apply Pythagoras’ theorem to find the missing leg length in a right-angled triangle.
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U.03. Solve word problems involving Pythagoras’ theorem.
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U.04. Apply the converse of Pythagoras’ theorem to determine if a triangle is a right triangle.
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U.05. Use Pythagoras’ theorem to solve problems involving distances in coordinate geometry.
V. Three-Dimensional Figures
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V.01. Identify the bases of three-dimensional figures (e.g., prisms, pyramids, cylinders, cones).
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V.02. Recognize and draw nets of three-dimensional figures.
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V.03. Draw and interpret front, side, and top views of three-dimensional figures.
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V.04. Classify different types of three-dimensional figures.
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V.05. Calculate the surface area and volume of basic three-dimensional figures.
W. Geometric Measurement
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W.11. Determine the effect of changes in scale on perimeter, area, and volume.
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W.12. Calculate the surface area of three-dimensional figures.
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W.13. Calculate the volume of three-dimensional figures.
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W.01. Calculate the perimeter of various two-dimensional shapes.
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W.02. Calculate the area of rectangles and parallelograms.
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W.03. Calculate the area of triangles.
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W.04. Solve word problems involving area and perimeter.
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W.05. Calculate area, circumference, radius, and diameter of circles.
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W.06. Solve word problems involving circles.
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W.07. Calculate area, perimeter, radius, and diameter of semicircles.
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W.08. Calculate area, perimeter, and radius of quarter circles.
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W.09. Calculate the area of compound figures with triangles, semicircles, and quarter circles.
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W.10. Calculate the area between two shapes.
X. Data and Graphs
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X.01. Interpret data presented in tables.
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X.02. Interpret data presented in line plots.
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X.03. Create line plots from given data.
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X.04. Interpret stem-and-leaf plots.
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X.05. Create stem-and-leaf plots from given data.
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X.06. Interpret bar graphs.
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X.07. Create bar graphs from given data.
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X.08. Interpret histograms.
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X.09. Create histograms from given data.
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X.10. Create frequency charts.
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X.11. Interpret line graphs.
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X.12. Create line graphs from given data.
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X.13. Choose the appropriate type of graph to represent a given dataset.
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X.14. Identify trends and patterns in data displayed in graphs.
Y. Statistics
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Y.01. Calculate the mean, median, mode, and range of a dataset.
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Y.02. Interpret charts to find the mean, median, mode, and range.
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Y.03. Find the missing number in a dataset given the mean, median, mode, or range.
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Y.04. Analyze the effects of changes in data on the mean, median, mode, and range.
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Y.05. Identify outliers in a dataset and their impact on statistical measures.
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Y.06. Compare and contrast different measures of central tendency and dispersion.
Z. Probability
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Z.01. Calculate the probability of simple events.
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Z.02. Determine the probability of opposite, mutually exclusive, and overlapping events.
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Z.03. Calculate experimental probability based on observed outcomes.
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Z.04. Make predictions based on probability.
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Z.05. Determine the number of outcomes in compound events.
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Z.06. Apply the counting principle to calculate the number of possible outcomes.
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Z.07. Use tree diagrams and other visual aids to represent and analyze probabilities.
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Z.08. Calculate conditional probabilities.
