PreAlgebra
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This course is designed to be the critical bridge between elementary arithmetic and high-school Algebra I. It provides a comprehensive review of fundamental arithmetic operations with real numbers and introduces the basic algebraic language, concepts, and problem-solving techniques essential for all future mathematics courses. Emphasis is placed on solidifying skills with fractions, decimals, percentages, and introducing variables, expressions, and linear equations.
Upon successful completion of this course, students will be able to:
Perform all four operations fluently with integers, fractions, and decimals.
Apply the Order of Operations (PEMDAS) consistently and correctly.
Understand and apply concepts of ratios, proportions, and percentages to solve real-world problems.
Define, write, and evaluate algebraic expressions.
Solve one-step linear equations and simple inequalities.
Use basic geometric formulas for perimeter, area, and volume.
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1
The Real Number System & Order of OperationsClassification of numbers (rational, irrational, integers). PEMDAS. Introduction to absolute value and opposites.
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2
Operations with Integers
Rules for adding, subtracting, multiplying, and dividing positive and negative numbers. Using number lines.
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3
Properties & Exponents
Commutative, Associative, and Distributive Properties. Inverse and Identity Properties. Introduction to Exponents (bases and powers).
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4
Assessment: Quiz 1 (Order of Operations & Integers)
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5
Fractions and Mixed Numbers
Fractions and Mixed Numbers
Converting between types. Finding the Least Common Denominator (LCD). Simplifying and comparing fractions.
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6
Operations with Fractions
Addition and subtraction of fractions. Multiplication and division (using reciprocals). Solving multi-step fraction problems.
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7
Decimals and Scientific Notation
Operations with decimals. Converting fractions $leftrightarrow$ decimals. Introduction to Scientific Notation. Rounding and estimation.
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8
Assessment: Unit Test 2 (Fractions and Decimals)
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9
Ratios and Rates
Ratios and Rates
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10
Proportions
Setting up and solving proportions using cross-multiplication. Applications: Scale drawings and similar figures.
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11
Percentages
Converting between percent, decimal, and fraction forms. Solving the three types of percent problems: finding the part, the whole, and the percent. Applications: Tax, Tip, Discount, Percent Change.
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12
Assessment: Quiz 3 (Ratios, Rates, and Percentages)
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13
Variables and Writing Expressions
Variables and Writing Expressions
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14
Evaluating Expressions
Substituting given values for variables and using PEMDAS to simplify numerical results.
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15
Simplifying Expressions
Identifying and combining like terms. Applying the Distributive Property to remove parentheses and simplify.
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16
Assessment: Unit Test 2 (Algebraic Expressions)
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17
Solving One-Step Equations
Understanding equality and inverse operations. Solving equations using addition/subtraction. Solving equations using multiplication/division. Checking solutions.
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18
Introduction to Inequalities
Graphing inequalities on a number line. Solving one-step inequalities (including the rule for multiplying/dividing by a negative).
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19
Assessment: Quiz 3 (Equations and Inequalities)
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20
Measurement and Geometry
Calculating Perimeter and Area of 2D shapes (rectangles, triangles, circles).
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21
Volume
Calculating the Volume of rectangular prisms and cylinders
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22
Data Basics
Introduction to basic data: mean, median, mode, and range.
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23
Introduction to the coordinate plane (plotting points).
Introduction to the coordinate plane (plotting points).
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24
Unit 6 Assessment