AGWCS Pre-Algebra Syllabus
Fall Term
Week 1: Number System:
1.1 Real number: rational number: integers, fractions, decimals
Irrational number: Definition
Imaginary number
Challenge: why a number is rational if it can be presented as a fraction.
1.2 Number and Number Lines
Negation – Introduce negative numbers and Number line
Addition/subtraction
Week 2: Signed Multiplication / Division
Reciprocal
Signed multiplication/division
Review: Orders of operations:
Week 3: Exponents I
Definition: How to read
Show example of square, cube of positive number, negative number
Exponents Operation, derive
Week 4: Exponents II
Negative exponent
Zeroth exponent
One to the n th power
Review order of operation, PEMDAS

Week 5: Factors and Multiples I
Prime numbers and composite numbers
Multiples and LCM
Week 6: Factors and Multiples II
Factors-Prime factors,
Divisible by 2, 4, 5, 9, 3. Students need to know how to deduct.
GCD
Week 7: Review, Midterm
Review exponents, factors and multiples,
Week 8: Fractions I
Proper fraction, improper fraction, mixed number, equivalent fractions.
Week 9: Fractions II
Compare two fractions: same denominator, same numerator, greater than 1 or half
Compare: (1) a-b>0, then a>b;
(2) a>0, b>0, If a/b > 1, then a>b
Fraction addition, subtraction. – Same denominator, different denominator, mixed number
Fraction multiplication, division – mixed number, equivalent fractions
Week 10: Decimals I
Introduce decimal
Express decimal as 10 -n , shift decimal to multiply 10 or divided by 10
Compare decimal numbers
Exponent of a decimal number

Week 11: Decimal II
Rounding
Decimal and Fraction: conversion
Conversion to fraction of a repeating decimal
Students need to know how to derive, what if two digits or three digits repeat?
Rational number with infinitely repeating digits, to express it in fraction form, for example,
Week 12: Linear Equation with one variable I
Conception: expression and Equation
Solve for one variable equation, one-step,
Word problems
Week 13: Linear Equation with one variable II
Solve for one variable equation, two-step,
Word problems
Week 14: Final