# AGWCS Pre-Algebra Syllabus ## 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