Prealgebra

Prealgebra serves as a bridge to connect arithmetic and algebra. As its name suggests, Prealgebra is a course to prepare students for algebra, the unifying thread of almost all mathematics.

In my Prealgebra course, I cover the following topics.

• Integers; Powers with integer exponents
• Basics of number theory: Divisibility, Prime factorization, LCM and GCD/GCF
• Fractions; Rational numbers
• Decimal numbers; Scientific notation
• Variables; Expressions; Equations; Inequalities
• Ratios; Proportions; Percents; Rates
• Square Roots; Irrational numbers; Real numbers
• Counting; Probability
• Data; Statistics
• Basics of Euclidean geometry: Common shapes; Perimeter; Area
• Basics of analytical geometry: Cartesian coordinates; Graphs of equations

I write my own notes for these topics using the AoPS Prealgebra book as the main reference. I choose practice problems from various sources and also make my own problems to include diverse problems with the gradient from fundamental to challenging levels. The objectives of my teaching are

• to deepen students’ understanding of mathematical concepts and ideas,
• to inspire students’ curiosity and interest in math,
• to sharpen students’ problem-solving skills.

How should Prealgebra be taught? Different instructors may have different takes, but I believe most agree that Prealgebra should be taught differently from math courses at higher levels because Prealgebra students are generally at very young ages with less attention span. Below are my two cents about the course design.

Instead of giving a full-class lecture, I split each class into the following phases

• Delivery phase: I deliver the the main topic for the class in a story-telling style with clear instructions. In this phase, the combination of algebraic concepts and geometric figures is always sought to help students understand.
• Practice phase: Students solve problems related to the current topic. The starting problems are fundamental problems. They help students get familiar with new ingredients and formulas. The other problems are about application of the fundamentals. They are more challenging and require critical thinking and problem-solving skills.
• Discussion and explanation phase: Students are encouraged to talk about their understanding of the fundamentals and their thoughts about problem solving, while I act as a moderator and commentator. After each problem is discussed, I give and explain the problem solving strategy and process.
• Summary phase: I make a summary of the fundamentals and problem-solving skills that are covered in the class.

After-class practice is essential to reinforce in-class learning. In addition, repetition is necessary to help young kids to comprehend and memorize what they have learned. I therefore deign homework to include:

• Problems that are tightly related to the corresponding class. These problems have the diversity and gradient from fundamental to challenging levels.
• Review problems that are challenging problems taken from past homework assignments.