# K-12 Mathematics Curriculum: 10-Week Online Course

## Module 1: Numbers and Operations
**Week 1: Foundations of Arithmetic**

1. Number Systems
   - Natural numbers, whole numbers, integers, rational numbers, and real numbers
   - Place value and number representation
   - Comparing and ordering numbers

2. Basic Operations
   - Addition and subtraction with whole numbers and integers
   - Multiplication and division with whole numbers and integers
   - Order of operations (PEMDAS/BODMAS)

3. Properties of Operations
   - Commutative property
   - Associative property
   - Distributive property

4. Mental Math Strategies
   - Rounding and estimation
   - Breaking numbers apart
   - Using compatible numbers

**Assessment:** Quiz on number systems, basic operations, and mental math strategies

## Module 2: Fractions, Decimals, and Percentages
**Week 2: Understanding Rational Numbers**

1. Fractions
   - Proper, improper, and mixed fractions
   - Equivalent fractions
   - Comparing and ordering fractions
   - Operations with fractions (addition, subtraction, multiplication, division)

2. Decimals
   - Place value with decimals
   - Converting between fractions and decimals
   - Operations with decimals

3. Percentages
   - Converting between fractions, decimals, and percentages
   - Calculating percentages
   - Percent increase and decrease

4. Applications
   - Word problems involving fractions, decimals, and percentages
   - Real-life scenarios (e.g., discounts, taxes, interest)

**Assessment:** Problem set involving conversions and calculations with fractions, decimals, and percentages

## Module 3: Algebra Foundations
**Week 3: Introduction to Algebraic Thinking**

1. Variables and Expressions
   - Understanding variables as placeholders
   - Writing and evaluating algebraic expressions
   - Simplifying expressions

2. Equations and Inequalities
   - Solving one-step and two-step equations
   - Solving one-step and two-step inequalities
   - Graphing solutions on a number line

3. Functions
   - Introduction to functions
   - Function notation
   - Graphing linear functions

4. Patterns and Sequences
   - Recognizing and extending patterns
   - Arithmetic and geometric sequences
   - Finding the nth term of a sequence

**Assessment:** Algebra quiz covering expressions, equations, and basic functions

## Module 4: Geometry Basics
**Week 4: Exploring Shapes and Space**

1. 2D Shapes
   - Properties of triangles, quadrilaterals, and circles
   - Angle relationships (complementary, supplementary, vertical)
   - Area and perimeter of 2D shapes

2. 3D Shapes
   - Properties of cubes, prisms, pyramids, cylinders, cones, and spheres
   - Surface area and volume of 3D shapes

3. Coordinate Geometry
   - The coordinate plane
   - Plotting points and shapes
   - Distance and midpoint formulas

4. Transformations
   - Translations, rotations, and reflections
   - Similarity and congruence

**Assessment:** Geometry project involving creating and analyzing 2D and 3D shapes

## Module 5: Data Analysis and Probability
**Week 5: Working with Data**

1. Data Collection and Representation
   - Types of data (categorical, numerical)
   - Data collection methods
   - Bar graphs, histograms, line graphs, and scatter plots

2. Measures of Central Tendency
   - Mean, median, and mode
   - When to use each measure

3. Measures of Spread
   - Range
   - Interquartile range
   - Standard deviation (introduction)

4. Probability
   - Basic probability concepts
   - Compound events
   - Tree diagrams and probability calculations

**Assessment:** Data analysis project using real-world data sets

## Module 6: Advanced Algebra
**Week 6: Expanding Algebraic Knowledge**

1. Polynomials
   - Adding, subtracting, and multiplying polynomials
   - Factoring polynomials
   - Solving quadratic equations

2. Rational Expressions
   - Simplifying rational expressions
   - Operations with rational expressions
   - Solving rational equations

3. Exponential and Logarithmic Functions
   - Properties of exponents
   - Exponential growth and decay
   - Logarithms and their properties

4. Systems of Equations
   - Solving systems of linear equations
   - Graphing systems of equations
   - Applications of systems of equations

**Assessment:** Comprehensive algebra test covering polynomials, rational expressions, and systems of equations

## Module 7: Trigonometry
**Week 7: Exploring Circular Functions**

1. Right Triangle Trigonometry
   - Sine, cosine, and tangent ratios
   - Solving right triangles
   - Applications of right triangle trigonometry

2. The Unit Circle
   - Radian measure
   - Special angles and their trigonometric values
   - Periodic functions

3. Trigonometric Functions and Graphs
   - Graphing sine, cosine, and tangent functions
   - Amplitude, period, and phase shift
   - Inverse trigonometric functions

4. Trigonometric Identities and Equations
   - Fundamental trigonometric identities
   - Solving basic trigonometric equations

**Assessment:** Trigonometry problem set and graphing project

## Module 8: Precalculus Concepts
**Week 8: Preparing for Calculus**

1. Complex Numbers
   - Definition and operations
   - Graphing complex numbers
   - Polar form of complex numbers

2. Conic Sections
   - Parabolas, ellipses, and hyperbolas
   - Graphing and analyzing conic sections

3. Vectors
   - Vector operations
   - Dot product and cross product
   - Applications of vectors

4. Limits and Continuity
   - Intuitive understanding of limits
   - Limit laws
   - Continuous functions

**Assessment:** Precalculus concept quiz and graphing assignment

## Module 9: Introduction to Calculus
**Week 9: Foundations of Calculus**

1. Derivatives
   - Definition of the derivative
   - Basic differentiation rules
   - Applications of derivatives (rates of change, optimization)

2. Integrals
   - Definite and indefinite integrals
   - Fundamental Theorem of Calculus
   - Basic integration techniques

3. Applications of Calculus
   - Area under a curve
   - Volume of revolution
   - Related rates problems

4. Calculus and Physics
   - Position, velocity, and acceleration
   - Work and energy

**Assessment:** Calculus problem set focusing on derivatives and basic integrals

## Module 10: Mathematical Problem Solving and Applications
**Week 10: Putting It All Together**

1. Problem-Solving Strategies
   - Understanding the problem
   - Devising a plan
   - Carrying out the plan
   - Looking back and reflecting

2. Modeling Real-World Situations
   - Creating mathematical models
   - Interpreting and validating models
   - Limitations of models

3. Interdisciplinary Applications
   - Mathematics in science
   - Mathematics in economics and finance
   - Mathematics in art and music

4. Technology in Mathematics
   - Graphing calculators and software
   - Computer algebra systems
   - Programming basics for mathematical computations

**Final Assessment:** Comprehensive project involving multiple areas of mathematics and real-world applications