1. The problem is to understand the number system for 6th grade students. 2. The number system includes different types of numbers: natural numbers, whole numbers, integers, rational numbers, and irrational numbers. 3. Natural numbers are counting numbers starting from 1, 2, 3, and so on. 4. Whole numbers include all natural numbers plus zero. 5. Integers include whole numbers and their negative counterparts. 6. Rational numbers are numbers that can be expressed as a fraction $\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$. 7. Irrational numbers cannot be expressed as a simple fraction; their decimal expansions are non-repeating and non-terminating, like $\sqrt{2}$ or $\pi$. 8. Understanding these categories helps in classifying any given number. 9. For example, the number $-3$ is an integer but not a natural number. 10. The number $\frac{1}{2}$ is a rational number but not an integer. 11. The number $\pi$ is irrational. 12. Practice problems: Classify the following numbers: 5, 0, -7, $\frac{3}{4}$, $\sqrt{5}$. Final answers: 5 is natural, whole, integer, rational; 0 is whole, integer, rational; -7 is integer, rational; $\frac{3}{4}$ is rational; $\sqrt{5}$ is irrational.