What Arithmetic is
Arithmetic is the foundation of mathematics. It teaches students how to work with numbers using the basic operations of addition, subtraction, multiplication, and division to build accuracy, number sense, and calculation skills. Think of arithmetic as the starting ground for all higher math: it develops confidence with numbers, patterns, and simple problem-solving so students are prepared for more advanced topics later.
Key Goals of Arithmetic:
- Learn to work confidently with numbers, fractions, decimals, and negative numbers
- Understand ratios, proportions, and percentages
- Explore exponents, radicals, and scientific notation
- Introduce variables, expressions, and equations
- Solve word problems using logical reasoning
- Begin graphing and understanding patterns
Why Arithmetic Matters:
Arithmetic Course Syllabus
Unit 1 — Numbers & Operations
- Lesson 1:Â Â Numbers and Negative Numbers
- Lesson 2:Â Â Number Sets
- Lesson 3:Â Â Identity Numbers
- Lesson 4:Â Â Opposite of a Number
- Lesson 5:Â Â Adding and Subtracting Signed Numbers
- Lesson 6:Â Â Multiplying Signed Numbers
- Lesson 7:Â Â Dividing Signed Numbers
- Lesson 8:Â Â Absolute Value
Unit 2 — Factors and Multiples
- Lesson 9:Â Â Divisibility
- Lesson 10:Â Â Multiples
- Lesson 11:Â Â Prime and Composite Numbers
- Lesson 12:Â Â Prime Factorization
- Lesson 13:Â Â Least Common Multiple
- Lesson 14:Â Â Greatest Common Factor
Unit 3 — Fractions
- Lesson 15:Â Â Reducing Fractions and Cancellation
- Lesson 16:Â Â Equivalent Fractions
- Lesson 17:Â Â Division by Zero
- Lesson 18:Â Â Adding and Subtracting Fractions
- Lesson 19:Â Â Multiplying and Dividing Fractions
- Lesson 20:Â Â Signs of Fractions
- Lesson 21:Â Â Reciprocals
Unit 4 — Mixed Numbers
- Lesson 22:Â Â Mixed Numbers and Improper Fractions
- Lesson 23:Â Â Adding and Subtracting Mixed Numbers
- Lesson 24:Â Â Multiplying and Dividing Mixed Numbers
- Lesson 25:Â Â Relationships of Numbers
- Lesson 26:Â Â Adding Mixed Measures
Unit 5 — Decimals
- Lesson 27:Â Â Place Value
- Lesson 28:Â Â Decimal Arithmetic
- Lesson 29:Â Â Repeating Decimals
- Lesson 30:Â Â Rounding
Unit 6 — Ratios, Proportions & Percents
- Lesson 31:Â Â Ratio and Proportion
- Lesson 32:Â Â Unit Price
- Lesson 33:Â Â Unit Multipliers
- Lesson 34:Â Â Percent and Percentage Problems
- Lesson 35:Â Â Percent Increase and Decrease
- Lesson 36:Â Â Simple Interest and Real-Life Applications
Unit 7 — Exponents & Radicals
- Lesson 37:Â Â Exponents
- Lesson 38:Â Â Rules of Exponents
- Lesson 39:Â Â Power Rule
- Lesson 40:Â Â Quotient Rule
- Lesson 41:Â Â Adding & Subtracting Radicals
- Lesson 42:Â Â Multiplying Radicals
- Lesson 43:Â Â Dividing Radicals
- Lesson 44:Â Â Radical Expressions
Unit 8 — Scientific Notation
- Lesson 45:Â Â Powers of 10
- Lesson 46:Â Â Scientific Notation
- Lesson 47:Â Â Multiplying Scientific Notation
- Lesson 48:Â Â Dividing Scientific Notation
- Lesson 49:Â Â Multiplying & Dividing Scientific Notation
- Lesson 50:Â Â Estimating with Scientific Notation
Unit 9 — Variables & Expressions
- Lesson 51:Â Â Introduction to Variables
- Lesson 52:Â Â Writing Expressions from Words
- Lesson 53:Â Â Combining Like Terms
- Lesson 54:Â Â Evaluating Expressions
Unit 10 — Equations & Inequalities
- Lesson 55:Â Â One-Step Equations
- Lesson 56:Â Â Two-Step Equations
- Lesson 57:Â Â Equations with Fractions
- Lesson 58:Â Â Solving Inequalities
- Lesson 59:Â Â Graphing Inequalities
Unit 11 — Order of Operations
- Lesson 60:Â Â PEMDAS with Whole Numbers
- Lesson 61:Â Â PEMDAS with Negative Numbers
- Lesson 62:Â Â PEMDAS with Fractions & Decimals
- Lesson 63:Â Â Nested Parentheses
Unit 12 — Coordinate Plane & Patterns
- Lesson 64:Â Â Plotting Points
- Lesson 65:Â Â Quadrants and Coordinates
- Lesson 66:Â Â Simple Linear Patterns
Unit 13 — Word Problems & Problem Solving
- Lesson 67:Â Â Multi-Step Word Problems
- Lesson 68:Â Â Word Problems Combining Fractions, Decimals, Percents
- Lesson 69:Â Â Word Problems Using Variables and Equations
Unit 14 — Basic Geometry (Optional, Helpful)
- Lesson 70:Â Â Perimeter and Area Formulas
- Lesson 71:Â Â Volume Formulas
- Lesson 72:Â Â Using Variables in Geometry Formulas
- Lesson 73:Â Â Introduction to Coordinate Geometry