Course Content
A. Numbers and Counting
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A.01. Classify numbers as prime or composite
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A.02. Identify factors and multiples of a given number
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A.03. Find the prime factorization of a number
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A.04. Determine the highest common factor (HCF) of two or more numbers
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A.05. Determine the lowest common multiple (LCM) of two or more numbers
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A.06. Apply HCF and LCM to solve real-world word problems
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A.07. Develop strategies for solving complex problems involving HCF and LCM
B. Integers and Number Lines
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B.01. Represent integers on a number line
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B.02. Graph integers on horizontal and vertical number lines
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B.03. Compare and order integers using a number line
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B.04. Apply the concept of absolute value to determine the distance of an integer from zero
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B.05. Solve problems involving comparing and ordering integers in real-world contexts
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B.06. Explore number lines with varying scales and their impact on representing integers
C. Operations with Integers
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C.01. Add and subtract integers using number lines
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C.02. Add and subtract integers using counters or other visual aids
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C.03. State and apply integer addition and subtraction rules
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C.04. Perform addition and subtraction of integers
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C.05. Complete addition and subtraction sentences with integers
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C.06. Add and subtract three or more integers efficiently
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C.07. Understand multiplying by a negative integer using a number line
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C.08. State and apply integer multiplication and division rules
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C.09. Perform multiplication and division of integers
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C.10. Complete multiplication and division sentences with integers
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C.11. Evaluate numerical expressions involving integers using order of operations
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C.12. Translate and solve word problems involving integer operations
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C.13. Investigate the properties of integer operations (commutative, associative, distributive)
D. Rational Numbers: Representation and Ordering
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D.01. Convert between decimals and fractions or mixed numbers
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D.02. Represent rational numbers on number lines
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D.03. Compare and order rational numbers using number lines
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D.04. Compare rational numbers without using number lines
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D.05. Put rational numbers in ascending or descending order
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D.06. Identify and differentiate between rational and irrational numbers
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D.07. Apply rational number comparisons to solve word problems
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D.08. Explore the density property of rational numbers
E. Operations with Rational Numbers
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E.02. Add and subtract positive and negative fractions
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E.03. Add and subtract rational numbers
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E.04. Multiply and divide positive and negative decimals
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E.05. Multiply and divide positive and negative fractions
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E.06. Multiply and divide rational numbers
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E.07. Apply addition and subtraction rules for rational numbers in multi-step problems
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E.08. Apply multiplication and division rules for rational numbers in multi-step problems
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E.09. Apply addition, subtraction, multiplication and division rules in combined operations with rational numbers
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E.10. Evaluate numerical expressions involving rational numbers
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E.11. Solve word problems involving operations with positive rational numbers
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E.12. Create and solve real-world problems involving rational number operations
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E.13. Examine the closure property of rational numbers under different operations
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E.01. Add and subtract positive and negative decimals
F. Indices and Roots
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F.01. Understand the concept of indices (exponents) and their notation
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F.02. Evaluate simple indices (e.g., 2^3, 5^2)
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F.03. Evaluate indices with decimal and fractional bases
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F.04. Evaluate indices with negative bases
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F.05. Understand negative indices and their relationship to reciprocals
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F.06. Evaluate negative indices
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F.07. Solve equations with variable indices by trial and error
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F.08. Express numbers as powers of ten
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F.09. Square roots of perfect squares
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F.10. Positive and negative square roots
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F.11. Estimate positive and negative square roots
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F.12. Cube roots of perfect cubes
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F.13. Estimate cube roots
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F.14. Identify equivalent expressions involving indices
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F.15. Apply the multiplication rule for indices (a^m a^n = a^(m+n))
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F.16. Apply the division rule for indices (a^m / a^n = a^(m-n))
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F.17. Apply the power rule for indices ((a^m)^n = a^(mn))
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F.18. Simplify expressions using combined index laws
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F.19. Solve equations involving squares and square roots
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F.20. Explain the relationship between squares and square roots
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F.21. Evaluate expressions using properties of indices, including negative and fractional exponents
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F.22. Investigate and apply more advanced index laws and their applications
G. Ratios, Rates and Proportions
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G.01. Identify equivalent ratios
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G.02. Write an equivalent ratio for a given ratio
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G.03. Find unit rates from given ratios
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G.04. Determine equivalent rates
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G.05. Determine if two ratios form a proportion
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G.06. Solve proportions using cross-multiplication
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G.07. Apply ratio and rate concepts to solve word problems
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G.08. Apply proportional reasoning to solve word problems
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G.09. Interpret and create scale drawings
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G.10. Apply scale factor in word problems involving scale drawings
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G.11. Solve complex problems involving ratios, rates, and proportions, including multi-step conversions
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G.12. Compare ratios in word problems
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G.13. Compare rates in word problems
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G.14. Apply proportions to real-world situations and problem-solving
H. Direct and Inverse Proportions
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H.01. Identify proportional relationships from tables
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H.02. Identify proportional relationships by graphing
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H.03. Write equations for proportional relationships from tables
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H.04. Write equations for proportional relationships from graphs
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H.05. Find the constant of proportionality from a table
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H.06. Find the constant of proportionality from a graph
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H.07. Complete a table and graph a proportional relationship
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H.08. Graph proportional relationships
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H.09. Interpret graphs of proportional relationships
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H.10. Write and solve equations for proportional relationships
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H.11. Identify proportional relationships from graphs and equations
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H.12. Identify direct variation and inverse variation
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H.13. Write inverse variation equations
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H.14. Write and solve inverse variation equations
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H.15. Solve real-world problems involving direct and inverse proportion
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H.16. Explore the graphical representation of inverse proportion
I. Standard Form
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I.01. Convert between ordinary numbers and standard form (scientific notation)
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I.02. Use standard form on calculators
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I.03. Compare numbers written in standard form
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I.04. Perform calculations (addition, subtraction, multiplication, division) with numbers in standard form
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I.05. Apply standard form to solve real-world problems involving very large or very small numbers
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I.06. Understand the significance of significant figures in standard form
J. Percents
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J.01. Convert between percents, fractions, and decimals
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J.02. Compare percents to fractions and decimals
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J.03. Estimate percents of numbers
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J.04. Find percents of numbers and money amounts
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J.05. Find what percent one number is of another
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J.06. Solve percent equations
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J.07. Apply percentages to solve word problems
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J.08. Find the total given a part and a percent
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J.09. Calculate percent of change (increase or decrease)
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J.10. Apply percent of change to solve word problems
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J.11. Solve percent of change problems where you need to find the original amount
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J.12. Solve word problems related to discounts, sales tax, and other real-world applications of percentages
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J.13. Analyze and solve complex problems involving multiple percentage calculations
K. Consumer Maths
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K.01. Interpret and use price lists to calculate costs
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K.02. Calculate unit prices to compare values
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K.03. Use unit prices to find the total price of multiple items
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K.04. Calculate the percent of a number for VAT (Value Added Tax), discount, and mark-up
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K.05. Calculate the percent for discount and mark-up
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K.06. Determine the original price given the sale price and discount percentage
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K.07. Solve multi-step problems involving percentages in consumer contexts
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K.08. Estimate tips based on percentages
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K.09. Calculate simple interest
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K.10. Calculate compound interest
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K.11. Evaluate different consumer scenarios to make informed financial decisions
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K.12. Differentiate between simple and compound interest and their implications over time
L. Units of Measurement
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L.01. Convert rates and measurements: metric units
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L.02. Convert between square metres and hectares
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L.03. Convert square and cubic units of length
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L.04. Convert between cubic metres and litres
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L.05. Convert rates and measurements: imperial units
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L.06. Convert between metric and imperial units
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L.07. Multi-step problems with metric unit conversions
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L.08. Metric mixed units
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L.09. Imperial mixed units
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L.10. Precision
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L.11. Greatest possible error
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L.12. Minimum and maximum area and volume
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L.13. Percent error
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L.14. Percent error: area and volume
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L.15. Apply unit conversions to solve real-world problems involving length, area, volume, and mass
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L.16. Evaluate the impact of measurement precision on calculations
M. Expressions and Properties
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M.01. Write variable expressions
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M.02. Write variable expressions from diagrams
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M.03. Evaluate one-variable expressions
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M.04. Identify terms and coefficients
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M.05. Add and subtract like terms
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M.06. Evaluate multi-variable expressions
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M.07. Evaluate radical expressions
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M.08. Evaluate rational expressions
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M.09. Properties of addition and multiplication
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M.10. Multiply using the distributive property: area models
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M.11. Multiply using the distributive property
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M.12. Factors of linear expressions
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M.13. Sort factors of expressions
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M.14. Write equivalent expressions using properties
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M.15. Simplify linear expressions
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M.16. Identify equivalent linear expressions
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M.17. Identify equivalent linear expressions: word problems
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M.18. Apply algebraic properties to justify simplification steps
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M.19. Formulate and solve real-world problems using algebraic expressions
N. One-Variable Equations
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N.01. Determine which value satisfies an equation
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N.02. Write an equation from words
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N.03. Write and solve equations that represent diagrams
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N.04. Properties of equality
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N.05. Solve two-step equations
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N.06. Solve equations involving like terms
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N.07. Solve multi-step equations
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N.08. Solve equations with variables on both sides
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N.09. Solve equations: mixed review
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N.10. Solve equations: complete the solution
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N.11. Solve two-step equations: word problems
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N.12. Solve multi-step equations with fractional coefficients
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N.13. Model and solve equations using algebra tiles
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N.14. Rearrange multi-variable equations
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N.15. Construct and solve equations to model real-world scenarios
O. One-Variable Inequalities
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O.01. Solutions to inequalities
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O.02. Graph inequalities on number lines
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O.03. Write inequalities from number lines
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O.04. Solve one-step inequalities
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O.05. Solve two-step linear inequalities
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O.06. Solve multi-step inequalities
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O.07. Graph solutions to one-step inequalities
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O.08. Graph solutions to two-step inequalities
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O.09. Graph solutions to multi-step inequalities
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O.10. Write and graph inequalities: word problems
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O.11. One-step inequalities: word problems
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O.12. Represent and solve real-world problems using inequalities
P. Problem Solving
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P.01. Multi-step word problems
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P.02. Guess-and-check word problems
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P.03. Use Venn diagrams to solve problems
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P.04. Multi-step word problems: identify reasonable answers
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P.05. Develop and apply problem-solving strategies in various mathematical contexts
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P.06. Analyze the reasonableness of solutions in word problems
Q. Functions
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Q.01. Identify functions
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Q.02. Identify independent and dependent variables
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Q.03. Evaluate a linear function: word problems
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Q.04. Rate of change
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Q.05. Constant rate of change
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Q.06. Find values using function graphs
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Q.07. Complete a table for a function graph
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Q.08. Identify linear and nonlinear functions
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Q.09. Determine whether a relation is a function given different representations (graph, table, mapping)
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Q.10. Explore and describe the characteristics of different types of functions
R. Linear Functions
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R.01. Does (x, y) satisfy the linear equation?
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R.02. Complete a table for a linear equation
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R.03. Find the gradient of a graph
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R.04. Find the gradient from two points
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R.05. Find the gradient and y-intercept of a linear equation
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R.06. Graph a line using gradient
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R.07. Complete a table and graph a linear equation
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R.08. Find a missing coordinate using gradient
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R.09. Graph an equation in y=mx+c form
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R.10. Write an equation in y=mx+c form from a gradient and y-intercept
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R.11. Write an equation in y=mx+c form from a graph
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R.12. Write an equation in y=mx+c form from a gradient and a point
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R.13. Write an equation in y=mx+c form from two points
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R.14. Interpret points on the graph of a line: word problems
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R.15. Write a linear equation from a table
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R.16. Write a linear equation: word problems
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R.17. Compare linear functions: graphs, tables and equations
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R.18. Equations of horizontal and vertical lines
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R.19. Graph a horizontal or vertical line
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R.20. Linear equations: solve for y
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R.21. Analyze the relationship between slope, y-intercept, and the equation of a line
S. Monomials and Polynomials
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S.01. Identify monomials
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S.02. Add and subtract polynomials
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S.03. Multiply monomials
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S.04. Divide monomials
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S.05. Multiply and divide monomials
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S.06. Powers of monomials
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S.07. Square and cube roots of monomials
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S.08. Add and subtract polynomials using algebra tiles
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S.09. Model polynomials with algebra tiles
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S.10. Multiply a polynomial by a monomial
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S.11. Multiply polynomials using algebra tiles
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S.12. Multiply two binomials
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S.13. Multiply two binomials: special cases
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S.14. Multiply polynomials
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S.15. Add polynomials to find perimeter
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S.16. Multiply polynomials to find area
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S.17. Apply polynomial operations to solve geometric and algebraic problems
T. Number Sequences
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T.01. Identify arithmetic and geometric sequences
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T.02. Arithmetic sequences
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T.03. Geometric sequences
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T.04. Evaluate variable expressions for arithmetic sequences
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T.05. Evaluate variable expressions for geometric sequences
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T.06. Write variable expressions for arithmetic sequences
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T.07. Number sequences: mixed review
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T.08. Number sequences: word problems
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T.09. Generate terms of a sequence given a specific rule or formula
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T.10. Determine the nth term of an arithmetic sequence
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T.11. Determine the nth term of a geometric sequence
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T.12. Investigate patterns in sequences and their applications
U. Coordinate Plane
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U.01. Coordinate plane review
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U.02. Quadrants and axes
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U.03. Follow directions on a coordinate plane
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U.04. Find the distance between two points
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U.05. Apply coordinate plane concepts to represent and solve real-world problems
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U.06. Explore transformations and their effects on coordinates
V. Data and Graphs
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V.11. Create bar graphs for grouped data
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V.12. Create frequency charts
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V.13. Interpret pie charts
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V.14. Pie charts and central angles
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V.15. Choose the best type of graph
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V.16. Critically evaluate the effectiveness of different types of graphs in representing data
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V.01. Interpret tables
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V.02. Interpret bar graphs for categorical data
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V.03. Create bar graphs for categorical data
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V.04. Interpret line graphs
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V.05. Create line graphs
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V.06. Interpret line plots
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V.07. Create line plots
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V.08. Interpret stem-and-leaf plots
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V.09. Create stem-and-leaf plots
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V.10. Interpret bar graphs for grouped data
W. Statistics
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W.01. Calculate mean, median, mode and range
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W.02. Interpret charts to find mean, median, mode and range
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W.03. Changes in mean, median, mode and range
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W.04. Identify an outlier
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W.05. Mean, median, mode and range: find the missing number
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W.06. Describe distributions in line plots
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W.07. Identify an outlier and describe the effect of removing it
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W.08. Identify representative, random and biased samples
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W.09. Create scatter plots
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W.10. Identify trends with scatter plots
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W.11. Make predictions with scatter plots
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W.12. Outliers in scatter plots
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W.13. Analyze the impact of outliers on measures of central tendency
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W.14. Evaluate the validity of statistical claims based on sample data
X. Probability
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X.01. Probability of simple events
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X.02. Probability of simple events and opposite events
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X.03. Experimental probability
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X.04. Make predictions using theoretical probability
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X.05. Make predictions using experimental probability
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X.06. Compound events: find the number of outcomes
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X.07. Probability of compound events
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X.08. Find the number of outcomes: word problems
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X.09. Probability of mutually exclusive events and overlapping events
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X.10. Find probabilities using two-way frequency tables
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X.11. Apply probability concepts to real-world scenarios and decision-making
Y. Two-Dimensional Figures
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Y.01. Identify complementary, supplementary, vertical, adjacent and congruent angles
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Y.02. Find measures of complementary, supplementary, vertical and adjacent angles
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Y.03. Identify alternate interior and alternate exterior angles
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Y.04. Transversals of parallel lines: name angle pairs
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Y.05. Find missing angles in triangles and quadrilaterals
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Y.06. Transversals of parallel lines: find angle measures
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Y.07. Find lengths and measures of bisected line segments and angles
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Y.08. Parts of a circle
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Y.09. Triangle inequality
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Y.10. Exterior Angle Theorem
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Y.11. Interior angles of polygons
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Y.12. Apply geometric principles to solve angle-related problems
Z. Geometric Measurement
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Z.01. Area of triangles and quadrilaterals
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Z.02. Circumference of circles
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Z.03. Area of circles
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Z.04. Area and perimeter of squares and rectangles: word problems
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Z.05. Area of compound figures with triangles
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Z.06. Semicircles: calculate area, perimeter, radius and diameter
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Z.07. Quarter circles: calculate area, perimeter and radius
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Z.08. Circles: word problems
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Z.09. Area of compound figures with triangles, semicircles and quarter circles
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Z.10. Area between two shapes
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Z.11. Apply area and perimeter formulas to solve geometric problems
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Z.12. Volume of prisms and cylinders
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Z.13. Surface area of prisms and cylinders
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Z.14. Volume of compound figures
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Z.15. Relate surface area and volume to real-world applications
AA. Three-Dimensional Figures
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AA.01. Parts of three-dimensional figures
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AA.02. Nets of three-dimensional figures
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AA.03. Front, side and top view
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AA.04. Base plans
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AA.05. Visualize and represent three-dimensional objects using nets and different views
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AA.06. Identify and classify different types of three-dimensional figures
BB. Quadratic functions
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BB.01. Complete a function table: quadratic functions
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BB.02. Does (x, y) satisfy the quadratic equation?
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BB.03. Characteristics of quadratic functions: graphs
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BB.04. Characteristics of quadratic functions: equations
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BB.05. Match quadratic functions and graphs
CC. Transformations
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CC.01. Identify reflections, rotations and translations
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CC.02. Translations: graph the image
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CC.03. Reflections: graph the image
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CC.04. Rotations: graph the image
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CC.05. Translations: find the coordinates
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CC.06. Reflections: find the coordinates
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CC.07. Rotations: find the coordinates
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CC.08. Translations: write the rule
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CC.09. Reflections and rotations: write the rule
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CC.10. Dilations: graph the image
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CC.11. Dilations: find the coordinates
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CC.12. Reflections, rotations and translations: graph the image
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CC.13. Reflections, rotations and translations: find the coordinates
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CC.14. Dilations: scale factor and classification
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CC.15. Describe the properties preserved and changed under different transformations
DD. Congruence and Similarity
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DD.01. Identify congruent figures
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DD.02. Identify similar figures
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DD.03. Ratios in similar figures
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DD.04. Congruence statements and corresponding parts
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DD.05. Similarity statements
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DD.06. Side lengths and angle measures of congruent figures
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DD.07. Side lengths and angle measures of similar figures
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DD.08. Congruent triangles: SSS, SAS and ASA
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DD.09. Similar figures and indirect measurement
EE. Triangles and Trigonometry
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EE.01. Pythagoras’ theorem: find the length of the hypotenuse
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EE.02. Pythagoras’ theorem: find the missing leg length
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EE.03. Pythagoras’ theorem: find the missing leg or hypotenuse length
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EE.04. Pythagoras’ theorem: find the perimeter
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EE.05. Converse of Pythagoras’ theorem: is it a right triangle?
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EE.06. Trigonometric ratios: sin, cos and tan
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EE.07. Find trigonometric functions using a calculator
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EE.08. Pythagoras’ theorem: word problems
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EE.09. Find trigonometric functions of special angles: sin, cos and tan
FF. Constructions
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FF.01. Construct the midpoint or perpendicular bisector of a segment
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FF.02. Construct an angle bisector
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FF.03. Construct a perpendicular line
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FF.04. Construct parallel lines
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FF.05. Construct an equilateral triangle or regular hexagon
