Goal
The goal of this course is to provide students with a strong foundation in mathematics that will enable them to succeed in their academic and professional pursuits. Through five comprehensive lessons, students will have a better understanding of mathematical concepts, and have the tools to apply these concepts in real-world situations.
Learning Aims
By the end of this course, students will be able to:
- Understand fundamental mathematical concepts
- Apply mathematical reasoning when solving problems
- Accurately interpret and create mathematical models
- Use mathematical language to express themselves precisely
- Develop a problem-solving mindset
Lesson 1: Numbers and Basic Arithmetic
Module 1: Understanding Numbers
- Introduction to real numbers
- Operations with real numbers
- Properties of real numbers
Module 2: Arithmetic Operations
- Understanding addition, subtraction, multiplication and division
- Mental Math techniques
- Order of operations
Module 3: Fractions, Decimals, and Percentages
- Conversion between fractions, decimals, and percentages
- Applications in real-world problems
- Comparing and ordering fractions and decimals
Lesson 2: Algebraic Expressions and Equations
Module 1: Basic Algebraic Expressions
- Variables, coefficients and terms
- Combining like terms
- Distributive property
Module 2: Solving Linear Equations
- Definition of an equation
- Solving simple linear equations
- Solving multi-step linear equations
Module 3: Applications of Equations
- Function notation
- Applications of linear equations
- Formulating equations from real-life situations
Lesson 3: Geometry
Module 1: Introduction to Geometry
- Points, Lines and Planes
- Angles and their types
- Parallel Lines and transversals
Module 2: Triangles and polygons
- Types of triangles
- Congruence and similarity
- Exterior and interior angles of polygons
Module 3: Circles
- Circumference, radius, and diameter
- Tangent lines
- Chords, secants, and angles in circles
Lesson 4: Data Analysis and Probability
Module 1: Collecting and Representing Data
- Types of data
- Data collection methods
- Frequency tables and graphs
Module 2: Measures of Central Tendency and Variability
- Mean, Median, and Mode
- Range, Variance, and Standard Deviation
- Interquartile range
Module 3: Probability
- Basics of probability
- Combinations and Permutations
- Conditional probability
Lesson 5: Advanced Topics in Mathematics
Module 1: Trigonometry
- Trigonometric identities
- Solving basic trigonometric equations
- Angles of elevation and depression
Module 2: Complex Numbers
- Introduction to complex numbers
- Basic operations with complex numbers
- Application of complex numbers
Module 3: Calculus
- Basic concepts of calculus
- Derivatives and Integrals
- Applications of Calculus
Conclusion
By completing this course, students will have a solid foundation in mathematics, equipping them to tackle more complex problems and analysis in the future. They will have mastered fundamental concepts, practiced critical thinking and reasoning, and honed their problem-solving skills, all while having fun!