This prealgebra course is a comprehensive introduction to basic algebraic concepts and skills, essential for further study in mathematics. It is structured into eleven chapters, each focusing on fundamental areas of prealgebra.
Chapter 1: Whole Numbers
This chapter introduces whole numbers, covering basic operations like addition, subtraction, multiplication, and division. It lays the foundation for understanding number operations.
Chapter 2: The Language of Algebra
Here, students learn algebra's language, including how to evaluate, simplify, and translate expressions. It also covers solving equations using properties of equality, finding multiples and factors, prime factorization, and the least common multiple.
Chapter 3: Integers
Focusing on integers, this chapter teaches adding, subtracting, multiplying, and dividing integers. It also explores solving equations using integers and the division property of equality.
Chapter 4: Fractions
This chapter deals with understanding and operating with fractions, including visualizing, multiplying, dividing, adding, and subtracting fractions and mixed numbers. It also covers solving equations involving fractions.
Chapter 5: Decimals
Students learn about decimals, including operations involving decimals, converting between decimals and fractions, solving equations with decimals, and understanding averages, probability, ratios, rates, and square roots.
Chapter 6: Percents
This chapter covers understanding and calculating percent, including applications in sales tax, commission, discount, simple interest, and proportions.
Chapter 7: The Properties of Real Numbers
It introduces rational and irrational numbers and explores essential properties like commutative, associative, distributive, identity, inverses, and zero. It also touches on systems of measurement.
Chapter 8: Solving Linear Equations
Focusing on linear equations, this chapter teaches solving equations using various properties of equality, handling variables and constants, and dealing with fractions or decimal coefficients.
Chapter 9: Math Models and Geometry
This chapter applies prealgebra concepts to solve real-world problems, including money applications and geometry problems involving angles, triangles, the Pythagorean theorem, and properties of various shapes. It also covers volume and surface area calculations.
Chapter 10: Polynomials
Students learn about polynomials, including adding, subtracting, multiplying, dividing, understanding integer exponents, scientific notation, and an introduction to factoring polynomials.
Chapter 11: Graphs
The final chapter introduces the rectangular coordinate system, graphing linear equations, understanding intercepts, and the slope of a line.
Overall, this course provides a thorough grounding in prealgebra, equipping students with the necessary skills and understanding for more advanced mathematical studies.
