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Greater Than/Less Than

Definition

Greater than and less than are fundamental comparison concepts in mathematics that allow us to determine the relative size or value of numbers and quantities. These relationships are represented by the symbols > (greater than) and < (less than).

Prerequisites

To understand greater than and less than concepts, you should have mastered:

  1. Number Recognition & Counting

Learning Objectives

After mastering greater than and less than concepts, you should be able to:

  1. Compare two numbers using greater than and less than symbols
  2. Order multiple numbers from least to greatest and greatest to least
  3. Identify which symbol (> or <) belongs between two numbers
  4. Compare quantities of objects without counting (up to 5)
  5. Use equality (=) appropriately with numbers
  6. Apply comparison concepts to real-world situations
  7. Understand that numbers further right on a number line are greater

Key Concepts

Comparison Symbols

  • Greater than (>)
  • Less than (<)
  • Equal to (=)
  • Number line representation

Visual Comparisons

  • The "alligator mouth" always points to the smaller number
  • The open side of the symbol faces the larger number
  • The point faces the smaller number

Examples

Example 1: Basic Comparison (PreK)

Problem: Which group has more dots? ⚪⚪⚪ or ⚪⚪⚪⚪

Solution: ⚪⚪⚪ < ⚪⚪⚪⚪ 3 < 4 (3 is less than 4)

Example 2: Number Line Comparison (Early K)

Problem: Fill in the correct symbol (< or >): 5 ___ 3

Solution: - Locate 5 and 3 on the number line - 5 is further right than 3 - Therefore: 5 > 3

Example 3: Real World Application (K)

Problem: Sam has 6 cookies and Jane has 4 cookies. Who has more?

Solution: 1. Compare the numbers: 6 and 4 2. 6 > 4 3. Therefore, Sam has more cookies

Common Misconceptions

  1. Confusing the direction of > and < symbols
  2. Thinking equal amounts are "greater than"
  3. Not understanding that numbers further right on a number line are greater
  4. Mixing up "greater than" with "greater than or equal to"

Progression Path

This skill leads to:

  1. Addition & Subtraction
  2. Basic Statistics
  3. Linear Inequalities (much later)

Practice Activities

  1. Basic: Compare numbers 1-5 using > and <
  2. Intermediate: Order three numbers from least to greatest
  3. Advanced: Compare quantities in different arrangements
  4. Challenge: Fill in missing numbers to make comparisons true (2 < ___ < 5)