Skip to content

Addition and Subtraction

Definition

Addition and subtraction are fundamental arithmetic operations. Addition combines quantities to find a total (sum), while subtraction takes away or finds the difference between quantities.

Prerequisites

To understand addition and subtraction, you should have mastered:

  1. Number Recognition & Counting
  2. Greater Than/Less Than

Learning Objectives

After mastering addition and subtraction, you should be able to:

  1. Add single-digit numbers fluently
  2. Subtract single-digit numbers fluently
  3. Understand the relationship between addition and subtraction
  4. Use various strategies (counting on, making tens, etc.)
  5. Solve simple word problems
  6. Apply the commutative property of addition
  7. Recognize addition and subtraction patterns

Key Concepts

Addition Concepts

  • Combining quantities
  • Counting on
  • Making tens
  • Commutative property (a + b = b + a)

Subtraction Concepts

  • Taking away
  • Finding the difference
  • Comparison
  • Missing addend problems

Properties and Relationships

  • Addition and subtraction as inverse operations
  • Zero property
  • Fact families

Examples

Example 1: Basic Addition (K)

Problem: 3 + 2 = ?

Solution: 1. Start with 3 objects: ⚪⚪⚪ 2. Add 2 more: ⚪⚪ 3. Count total: ⚪⚪⚪⚪⚪ 4. Answer: 3 + 2 = 5

Example 2: Basic Subtraction (K)

Problem: 7 - 4 = ?

Solution: 1. Start with 7: ⚪⚪⚪⚪⚪⚪⚪ 2. Take away 4: ⚪⚪⚪⚪ 3. Count remaining: ⚪⚪⚪ 4. Answer: 7 - 4 = 3

Example 3: Word Problem (Grade 1)

Problem: Tom has 8 marbles. He gives 3 to his friend. How many does he have now?

Solution: 1. Starting amount: 8 2. Amount given away: 3 3. Operation needed: subtraction 4. 8 - 3 = 5 5. Answer: Tom has 5 marbles now

Common Misconceptions

  1. Thinking subtraction is commutative like addition
  2. Counting incorrectly when adding or subtracting
  3. Not understanding the relationship between addition and subtraction
  4. Confusing when to add vs. subtract in word problems

Progression Path

This skill leads to:

  1. Multiplication & Division
  2. Basic Equation Solving
  3. Variables & Expressions

Practice Activities

  1. Basic: Add numbers 1-5
  2. Intermediate: Subtract from numbers up to 10
  3. Advanced: Solve simple word problems
  4. Challenge: Complete fact family triangles