Creating a tangible learning model (TLM) for the real number system using cardboard and color paper can be a fun and effective way to understand this mathematical concept.

Here’s a step-by-step guide to making the TLM:

**Materials Needed:**

- Cardboard sheet
- Color papers (representing different categories of numbers)
- Scissors
- Glue
- Marker
- Ruler

**Procedure:**

**Step 1: Prepare the Base**

- Take a piece of cardboard and cut it into a rectangular base. This will serve as the foundation for your TLM.

**Step 2: Define Categories of Numbers**

- Use different color papers to represent various categories of numbers:
**Orange paper:**Representing natural numbers**Blue paper:**Representing whole numbers**Yellow paper:**Representing integers**Pink paper:**Representing rational numbers

**Step 3: Create Number Tiles**

- Cut the colored papers into square tiles, making sure each color represents its respective category of numbers. Write down examples of numbers from each category on the corresponding colored tiles.
- For example:
**Orange Tiles (Natural Numbers):**- Tile 1: “1”
- Tile 2: “2”
- Tile 3: “3”
- …

**Blue Tiles (Whole Numbers):**- Tile 1: “0”
- Tile 2: “1”
- Tile 3: “2”
- …

**Yellow Tiles (Integers):**- Tile 1: “-3”
- Tile 2: “-2”
- Tile 3: “-1”
- …

**Pink Tiles (Rational Numbers):**- Tile 1: “1/2”
- Tile 2: “0.75”
- Tile 3: “-3/4”
- ..

- For example:

**Step 4: Arrange Tiles**

- Place the tiles on the cardboard base in an organized manner, forming a visual representation of the real number system.

**Definition and Examples:**

**Real Numbers (R):**The set of all rational and irrational numbers. This includes numbers like fractions, decimals, square roots, and more.- Examples: √2, -3/4, 0.5, π, -√3, etc.

**Rational Numbers (Q):**Numbers that can be expressed as the quotient or fraction of two integers.- Examples: 1/2, -3/5, 0.75, 2, -7, etc.

**Irrational Numbers (I):**Numbers that cannot be expressed as a fraction of two integers. They have non-repeating, non-terminating decimal expansions.- Examples: √2, π, e, etc.

**Integers (Z):**The set of positive whole numbers, negative whole numbers, and zero.- Examples: -3, -2, -1, 0, 1, 2, 3, etc.

**Whole Numbers (W):**The set of positive whole numbers and zero.- Examples: 0, 1, 2, 3, 4, 5, etc.

**Natural Numbers (N):**The set of positive counting numbers.- Examples: 1, 2, 3, 4, 5, 6, etc.

By creating this real number systems math’s working model or TLM,

students can visually see the relationships between different categories of numbers and gain a better understanding of the real number system.