Course Summary: Functions
This course provides middle school students with a comprehensive understanding of functions, a foundational concept in mathematics. Through hands-on activities, real-world applications, and engaging lessons, students will learn how functions are defined, explored, and applied in various contexts. From basic operations to advanced transformations, the course equips students with essential problem-solving skills and prepares them for future mathematical studies.
Course Units:
- Explore the concept of functions, their notation, domains, ranges, and how they are represented graphically.
- Learn about linear, quadratic, absolute value, and exponential functions, including their properties and graphs.
- Perform operations such as addition, subtraction, multiplication, and division on functions, and understand composition and inverses.
- Investigate how functions change through shifts, reflections, stretches, compressions, and combinations of transformations.
- Solve real-world problems using functions, explore piecewise and step functions, and apply optimization techniques.
This course lays the groundwork for understanding the powerful role functions play in mathematics and beyond.
This course provides a comprehensive exploration of probability, guiding students from foundational concepts to advanced applications in real-world scenarios. Students will learn how to calculate probabilities, analyze random events, and apply these concepts in diverse fields such as science, business, and decision-making. Through hands-on activities and practical examples, this course equips learners with the skills to understand and work with uncertainty effectively.
Course Units:
- Learn the basics of probability, including terminology, sample spaces, and different types of probability.
Basic Probability Rules and Operations
- Explore fundamental probability rules, including addition, multiplication, complementary events, and conditional probability.
- Dive into random variables, discrete and continuous distributions, and analyze real-world scenarios using probability distributions.
Permutations, Combinations, and Counting Principles
- Understand counting principles, permutations, and combinations, and use them to solve probability problems.
Advanced Applications of Probability
- Apply advanced concepts like the law of large numbers, Bayes’ theorem, and probability in decision-making and real-world systems.
This course is perfect for students aiming to master probability and its applications across various disciplines. It fosters critical thinking, analytical skills, and problem-solving abilities in an engaging and practical way.
This course introduces middle school students to the foundational concepts of congruence and similarity in geometry. Through engaging lessons and hands-on activities, students will explore how shapes relate to each other through transformations, proportional reasoning, and geometric criteria. By understanding congruence and similarity, students will develop critical problem-solving skills and learn to apply these concepts to real-world scenarios in design, architecture, and science.
Course Units:
- Understand the definition of congruence, identify congruent figures, and explore their properties.
- Learn triangle congruence criteria (SSS, SAS, ASA, RHS) and apply them to solve geometric problems.
- Define similarity, differentiate it from congruence, and explore the properties of similar shapes.
- Apply triangle similarity criteria (AA, SSS, SAS) and solve problems involving proportions in similar triangles.
Transformations and Relationships Between Congruence and Similarity
- Explore transformations like translation, rotation, reflection, and dilation, and understand their role in defining congruence and similarity.
This course equips students with a strong foundation in geometry, preparing them for advanced mathematical studies and practical applications in everyday life.
Mastering Linear Equations: From Basics to Real-World Applications
Course Summary:
This course is designed to provide a comprehensive understanding of linear equations, starting from foundational concepts and building up to advanced applications in real-world scenarios. Students will explore various methods of solving, graphing, and interpreting linear equations and systems of equations. Through engaging activities, practice problems, and assessments, learners will develop problem-solving skills and the ability to apply linear equations in diverse contexts.
Course Topics:
Unit 1: Introduction to Linear Equations
- What is a linear equation?
- Forms of linear equations: standard form and slope-intercept form
- Components of a linear equation: slope and y-intercept
- Visualizing linear equations on graphs
- Real-world applications of linear equations
Unit 2: Graphing Linear Equations
- Graphing using slope-intercept form
- Using tables of values to graph linear equations
- Graphing horizontal and vertical lines
- Understanding transformations of linear graphs
- Interpreting graphs to analyze relationships
Unit 3: Solving Linear Equations
- Solving one-step and two-step linear equations
- Solving multi-step equations
- Equations with variables on both sides
- Solving equations with fractions and decimals
- Writing and solving equations from real-world problems
Unit 4: Systems of Linear Equations
- Solving systems by graphing
- Solving systems using substitution
- Solving systems using elimination
- Applications of systems of equations in real-world scenarios
- Comparing and choosing the best methods for solving systems
Unit 5: Applications and Advanced Concepts
- Solving and graphing linear inequalities
- Exploring parallel and perpendicular lines
- Linear regression and best-fit lines for data analysis
- Modeling real-world problems using linear equations
- Capstone project: Integrating and applying linear equations
Learning Outcomes:
By the end of this course, students will:
- Understand the fundamental concepts of linear equations and their forms.
- Graph and interpret linear equations and systems effectively.
- Solve linear equations and systems using various methods.
- Apply linear equations to real-world scenarios and advanced mathematical problems.
- Develop critical thinking and analytical skills through collaborative projects and assessments.
This course is perfect for high school students seeking to master linear equations and their applications. Enroll now to unlock the power of linear relationships!
Introduction to Algebra: Building Foundational Skills
Course Summary:
This course introduces students to the fundamental concepts of algebra, focusing on understanding variables, solving equations, graphing, and applying algebra to real-world problems. Through five well-structured units, students will develop essential problem-solving skills and build a strong mathematical foundation for future topics.
Course Units:
Understanding Variables and Expressions
- Learn the basics of algebraic expressions, including variables, constants, and terms. Explore how to simplify and evaluate expressions.
Basic Equations and Problem Solving
- Develop the ability to solve one-step and two-step equations, write equations from word problems, and check solutions.
- Explore the coordinate plane, plot points, and graph simple linear equations. Understand the relationship between equations and their graphs.
- Understand and solve inequalities, graph solutions on a number line, and apply inequalities to real-world scenarios.
Real-Life Applications of Algebra
- Apply algebra to everyday problems, including geometry, patterns, and sequences. Solve multi-step word problems and complete a capstone project.
This course provides students with a clear and engaging pathway to mastering the fundamentals of algebra. Enroll now to start building your algebraic skills!
Math 8 topics include:
- Numbers
- Algebraic manipulation
- Solving systems of linear equations
- Exponents
- Solutions of simple quadratic equations
- Graphs of linear functions and relations
- Measurement
- Angles, triangles, polygons
- Congruence and similarity
- Pythagorean's theorem
- Data analysis
Math 9 topics include:
- Numbers
- Lines and linear relationships
- Quadratic relationships
- Fundamentals of probability
- Geometry
- Inverse Proportions
- Powers and polynomials
- Graphs of relations
- Functions
- Cosine and Sine rules
- Circular and radian measure
- Trigonometric functions
- Combinations
- Conditional probability and independence
This section is relevant to grades 8 and 9 and focusses on surface area and volume of
- cubes, prisms and cylinders
- pyramids and cones
- spheres and composite shapes