Complete Middle School Mathematics Mastery Program

📚 Topics Covered

• Understanding place value system
• Reading and writing large numbers (up to billions)
• Expanded form and word form
• Comparing and ordering whole numbers
• Number line representation
• Rounding to nearest 10, 100, 1000
• Roman numerals basics
• Introduction to negative numbers
• Integer concepts and number line
• Absolute value understanding

• Real-world contexts for negative numbers
• Temperature, elevation, and financial contexts

📚 Topics Covered

• Multi-digit addition with regrouping
• Addition properties: commutative, associative, identity
• Mental math strategies for addition
• Multi-digit subtraction with borrowing
• Subtraction as inverse of addition
• Estimation strategies for sums and differences
• Adding and subtracting integers
• Using number lines for integer operations
• Word problems with addition and subtraction
• Multi-step problem solving

• Checking answers using inverse operations
• Real-world applications: budgets, distances

📚 Topics Covered

• Multiplication as repeated addition
• Times tables mastery (up to 12×12)
• Multiplication properties: commutative, associative, distributive
• Multi-digit multiplication algorithms
• Lattice multiplication method
• Area model for multiplication
• Multiplying by powers of 10
• Estimation in multiplication
• Mental math tricks for multiplication
• Multiplying integers and sign rules

• Word problems involving multiplication
• Real-world applications: area, arrays, scaling

📚 Topics Covered

• Division as inverse of multiplication
• Long division algorithm step-by-step
• Division with remainders
• Interpreting remainders in context
• Divisibility rules (2, 3, 4, 5, 6, 9, 10)
• Factors and multiples
• Prime and composite numbers
• Prime factorization
• Greatest Common Factor (GCF)
• Least Common Multiple (LCM)

• Division of integers and sign rules
• Word problems with division

📚 Topics Covered

• Introduction to order of operations
• Parentheses/Brackets in expressions
• Exponents and powers basics
• Multiplication and Division (left to right)
• Addition and Subtraction (left to right)
• Complex expressions with multiple operations
• Nested parentheses
• Common mistakes and misconceptions
• Using calculators correctly
• Writing expressions from word problems

• Evaluating expressions with variables
• Creating equivalent expressions

📚 Topics Covered

• Understanding the problem: what's being asked?
• Identifying relevant information
• Drawing diagrams and models
• Making organized lists
• Looking for patterns
• Working backwards strategy
• Guess and check method
• Using simpler numbers first
• Breaking complex problems into steps
• Checking reasonableness of answers

• Multiple solution methods
• Mathematical communication and explanation

📚 Topics Covered

• Number systems comprehensive review
• Operations mastery check
• Order of operations practice
• Problem-solving strategy application
• Common errors and corrections
• Speed and accuracy building

📚 Topics Covered

• Fraction concepts: parts of a whole
• Numerator and denominator meaning
• Proper fractions, improper fractions, mixed numbers
• Converting between improper fractions and mixed numbers
• Fractions on a number line
• Equivalent fractions using models
• Simplifying fractions to lowest terms
• Finding equivalent fractions algebraically
• Comparing fractions with like denominators
• Comparing fractions with unlike denominators

• Cross multiplication for comparison
• Ordering fractions from least to greatest

📚 Topics Covered

• Adding fractions with like denominators
• Adding fractions with unlike denominators
• Finding common denominators
• Adding mixed numbers with regrouping
• Subtracting fractions and mixed numbers
• Borrowing in mixed number subtraction
• Multiplying fractions by whole numbers
• Multiplying fractions by fractions
• Understanding fraction multiplication visually
• Dividing fractions: keep-change-flip

• Dividing mixed numbers
• Word problems with fraction operations

📚 Topics Covered

• Decimal place value: tenths, hundredths, thousandths
• Reading and writing decimals
• Decimals on number lines
• Comparing and ordering decimals
• Rounding decimals to various places
• Converting fractions to decimals
• Converting decimals to fractions
• Terminating vs repeating decimals
• Adding and subtracting decimals
• Lining up decimal points

• Estimation with decimals
• Real-world decimal applications: money, measurements

📚 Topics Covered

• Multiplying decimals by whole numbers
• Multiplying decimals by decimals
• Counting decimal places in products
• Multiplying by powers of 10
• Dividing decimals by whole numbers
• Dividing by decimals: moving decimal points
• Dividing decimals by powers of 10
• Scientific notation introduction
• Estimation strategies for decimal operations
• Calculator use and interpretation

• Word problems with decimal operations
• Unit pricing and comparison shopping

📚 Topics Covered

• Understanding percent as per hundred
• Converting between fractions, decimals, and percents
• Finding percentages of numbers
• Mental math with percentages (10%, 25%, 50%)
• Finding what percent one number is of another
• Finding the whole given a part and percent
• Percent increase and decrease
• Simple interest calculations
• Sales tax and discount problems
• Tips and commission calculations

• Percent error in measurements
• Data representation with percentages

📚 Topics Covered

• Ratio concepts and notation
• Part-to-part vs part-to-whole ratios
• Equivalent ratios
• Simplifying ratios
• Ratios with three quantities
• Rates and unit rates
• Finding unit prices
• Speed, distance, and time relationships
• Comparing rates
• Best buy problems

• Ratio tables and their uses
• Graphing ratios on coordinate plane

📚 Topics Covered

• Understanding proportions
• Setting up proportions from word problems
• Cross multiplication to solve proportions
• Checking proportion solutions
• Direct variation
• Inverse variation introduction
• Scale drawings and maps
• Finding actual distances from maps
• Creating scale drawings
• Similar figures and proportions

• Scale factor
• Proportional relationships in data

📚 Topics Covered

• Currency exchange rates
• Unit conversions using proportions
• Mixture problems
• Work rate problems
• Population density calculations
• Fuel efficiency comparisons
• Nutritional information analysis
• Sports statistics and ratios
• Business applications: profit margins
• Scientific applications: concentrations

• Engineering: gear ratios
• Cooking and baking proportions

📚 Topics Covered

• Circle graphs (pie charts) with percentages
• Bar graphs with fractional values
• Line graphs with decimal scales
• Converting between data representations
• Misleading graphs and statistics
• Surveys and sampling basics
• Calculating averages with decimals
• Finding median and mode with fractions
• Data interpretation questions
• Creating data displays

• Spreadsheet basics for calculations
• Technology tools for data analysis

📚 Topics Covered

• Comprehensive fraction review
• Decimal operations mastery
• Percentage problem solving
• Ratio and proportion applications
• Mixed problem sets
• Speed and accuracy challenges

📚 Topics Covered

• Introduction to variables as unknowns
• Variables as varying quantities
• Writing algebraic expressions
• Translating words to algebra
• Evaluating expressions with substitution
• Terms, coefficients, and constants
• Like terms and unlike terms
• Combining like terms
• Distributive property with variables
• Factoring out common factors

• Expanding expressions
• Simplifying algebraic expressions

📚 Topics Covered

• Understanding equations vs expressions
• Solution concept and checking
• Solving using addition/subtraction
• Solving using multiplication/division
• Inverse operations review
• Equations with negative numbers
• Equations with fractions
• Equations with decimals
• Writing equations from word problems
• Checking solutions by substitution

• Special cases: no solution, infinite solutions
• Real-world equation modeling

📚 Topics Covered

• Two-step equations strategy
• Order of operations in reverse
• Equations with parentheses
• Distributive property in equations
• Combining like terms before solving
• Variables on both sides
• Equations with fractions: clearing denominators
• Decimal equations: clearing decimals
• Word problems requiring multi-step equations
• Consecutive integer problems

• Perimeter and area equations
• Mixture and motion problems basics

📚 Topics Covered

• Understanding inequality symbols
• Graphing inequalities on number lines
• Writing inequalities from situations
• Solving one-step inequalities
• Solving two-step inequalities
• Multiplying/dividing by negatives: flipping the sign
• Compound inequalities (AND, OR)
• Graphing compound inequalities
• Inequality word problems
• Systems of inequalities introduction

• Real-world constraints and inequalities
• Checking inequality solutions

📚 Topics Covered

• Input-output relationships
• Function machines concept
• Function notation: f(x)
• Function tables
• Finding patterns in functions
• Linear functions basics
• Graphing functions on coordinate plane
• Domain and range introduction
• Vertical line test
• Real-world functions: temperature conversion

• Function composition basics
• Inverse operations and functions

📚 Topics Covered

• Cartesian coordinate system
• x-axis and y-axis
• Quadrants I, II, III, IV
• Plotting points (x, y)
• Finding coordinates of points
• Distance between points (horizontal/vertical)
• Midpoint of a line segment
• Reflections across axes
• Translations on coordinate plane
• Rotations (90°, 180°)

• Creating designs with coordinates
• Coordinate plane applications

📚 Topics Covered

• Understanding slope as rate of change
• Calculating slope from two points
• Positive, negative, zero, undefined slopes
• Slope-intercept form: y = mx + b
• Finding y-intercept
• Graphing using slope-intercept form
• Point-slope form introduction
• Writing equations from graphs
• Writing equations from two points
• Parallel and perpendicular lines

• Systems of linear equations (graphing method)
• Real-world linear relationships

📚 Topics Covered

• Number patterns recognition
• Arithmetic sequences
• Finding common difference
• nth term of arithmetic sequence
• Geometric sequences introduction
• Finding common ratio
• Extending patterns
• Visual patterns and growth
• Fibonacci sequence exploration
• Recursive patterns

• Creating pattern rules
• Patterns in nature and art

📚 Topics Covered

• Monomials, binomials, trinomials
• Degree of polynomials
• Adding polynomials
• Subtracting polynomials
• Multiplying monomials
• Multiplying polynomials by monomials
• FOIL method for binomials
• Special products: (a+b)², (a-b)²
• Factoring out GCF from polynomials
• Factoring simple trinomials

• Zero product property
• Polynomial applications

📚 Topics Covered

• Algebraic expressions and equations review
• Inequality solving and graphing
• Function concepts and graphing
• Coordinate geometry mastery
• Linear relationships
• Patterns and sequences
• Polynomial operations

📚 Topics Covered

• Points, lines, and planes
• Line segments and rays
• Parallel and perpendicular lines
• Angles: acute, right, obtuse, straight
• Measuring angles with protractor
• Angle relationships: complementary, supplementary
• Vertical angles and linear pairs
• Angles formed by transversals
• Corresponding angles
• Alternate interior and exterior angles

• Triangle angle sum theorem
• Exterior angles of triangles

📚 Topics Covered

• Types of triangles by sides: equilateral, isosceles, scalene
• Types of triangles by angles: acute, right, obtuse
• Triangle inequality theorem
• Congruent triangles: SSS, SAS, ASA
• Similar triangles and proportions
• Pythagorean theorem
• Pythagorean theorem applications
• Special right triangles: 45-45-90, 30-60-90
• Quadrilaterals: parallelograms, rectangles, squares
• Rhombus and trapezoid properties

• Diagonals of quadrilaterals
• Polygon angle sum formulas

📚 Topics Covered

• Circle vocabulary: center, radius, diameter
• Circumference formula: C = 2πr
• Area of circles: A = πr²
• Arc length
• Sector area
• Chords and secants
• Tangent lines to circles
• Inscribed angles
• Central angles
• Circle word problems

• Composite figures with circles
• Real-world circle applications

📚 Topics Covered

• Perimeter of polygons
• Area of rectangles and squares
• Area of parallelograms
• Area of triangles: ½bh
• Area of trapezoids
• Area of regular polygons
• Area of composite figures
• Perimeter of composite figures
• Area and perimeter word problems
• Optimization problems: maximum area

• Surface area introduction
• Real-world applications: flooring, fencing

📚 Topics Covered

• 3D shapes: prisms, pyramids, cylinders, cones, spheres
• Faces, edges, and vertices
• Nets of 3D shapes
• Volume of rectangular prisms
• Volume of triangular prisms
• Volume of cylinders
• Volume of pyramids and cones
• Volume of spheres
• Surface area of prisms
• Surface area of cylinders

• Composite 3D figures
• Volume and capacity conversions

📚 Topics Covered

• Types of data: categorical vs numerical
• Data collection methods
• Surveys and sampling techniques
• Bias in data collection
• Frequency tables
• Bar graphs and histograms
• Line graphs and time series
• Circle graphs (pie charts)
• Stem-and-leaf plots
• Box-and-whisker plots

• Scatter plots introduction
• Choosing appropriate graphs

📚 Topics Covered

• Mean (average) calculation
• Weighted averages
• Median finding
• Mode identification
• Comparing mean, median, mode
• Effects of outliers
• Range as measure of spread
• Quartiles and interquartile range
• Mean absolute deviation
• Standard deviation introduction

• Interpreting data spread
• Using measures to compare data sets

📚 Topics Covered

• Probability as likelihood
• Probability scale: 0 to 1
• Experimental vs theoretical probability
• Sample space and outcomes
• Simple probability calculations
• Complement of an event
• Probability of compound events
• Independent vs dependent events
• Tree diagrams
• Fundamental counting principle

• Permutations introduction
• Combinations introduction

📚 Topics Covered

• Correlation vs causation
• Positive and negative correlation
• Line of best fit basics
• Making predictions from data
• Margin of error concept
• Confidence intervals introduction
• Misleading statistics
• Statistical significance basics
• Comparing populations
• Data-driven decision making

• Technology tools for statistics
• Spreadsheet data analysis

📚 Topics Covered

• Multi-step problems combining algebra and geometry
• Rate, ratio, and proportion in geometry
• Statistical problems with percentages
• Probability with fractions and decimals
• Optimization problems
• Logic puzzles and reasoning
• Mathematical modeling
• Estimation and approximation
• Working with constraints
• Breaking down complex problems

• Checking solutions for reasonableness

📚 Topics Covered

• Modular arithmetic basics
• Number patterns and sequences
• Pascal's triangle
• Binary numbers introduction
• Different base systems
• Cryptography basics
• Mathematical proofs introduction
• Logic and truth tables
• Set theory basics
• Venn diagrams with three sets

• Infinity concepts

📚 Topics Covered

• Mathematics in science
• Mathematics in technology
• Mathematics in art and music
• Golden ratio and Fibonacci
• Fractals introduction
• Tessellations and symmetry
• Mathematical modeling in real life
• Financial mathematics
• Sports analytics
• Game theory basics

• Mathematics in nature

📚 Topics Covered

• Problem-solving strategies review
• Competition problem types
• Speed and accuracy techniques
• Mental math advanced strategies
• Olympiad-style problems
• Logic and reasoning puzzles
• Number theory problems
• Geometry competition problems
• Combinatorics basics
• Proof techniques

• Time management in tests

📚 Topics Covered

• Standardized test formats
• Multiple choice strategies
• Grid-in question techniques
• Extended response writing
• Time management during tests
• Test anxiety management
• Common test mistakes
• Calculator vs non-calculator sections
• Checking work efficiently
• Practice test analysis

• Study planning and organization

📚 Topics Covered

• Number systems and operations review
• Fractions, decimals, percentages mastery
• Algebraic concepts consolidation
• Geometry theorems and applications
• Statistics and probability review
• Problem-solving strategies compilation
• Cross-curricular connections
• Real-world applications synthesis
• Mathematical communication skills
• Technology integration review

• Portfolio organization
• Self-assessment and reflection

📚 Topics Covered

• Project planning and design
• Research and investigation
• Data collection and analysis
• Mathematical modeling
• Presentation preparation
• Peer collaboration
• Project documentation
• Technology integration
• Creative mathematical expression
• Real-world problem solving

• Community application

📚 Topics Covered

• Comprehensive final examination
• Portfolio presentation and defense
• Peer evaluations
• Self-reflection essays
• Goal setting for high school
• Advanced course recommendations
• Summer enrichment opportunities
• Mathematics career exploration
• Celebration of achievements
• Awards and recognition

• Parent conferences
• Transition planning