Creating a tangible learning model (TLM) for understanding square roots using color paper and cardboard can be a great visual aid for learning this mathematical concept.

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

**Materials Needed:**

- Cardboard sheet
- Color papers (representing squares and square roots)
- 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 Squares and Square Roots**

- Use different color papers to represent squares and square roots:
**Red paper:**Representing squares**Yellow paper:**Representing square roots

**Step 3: Create Square Tiles**

- Cut the red colored paper into circle tiles, making sure each tile represents a perfect square. Write down examples of perfect squares on the tiles.
- For example:
**Red Tiles (Perfect Squares):**- Tile 1: “1” (1^2)
- Tile 2: “4” (2^2)
- Tile 3: “9” (3^2)
- Tile 4: “16” (4^2)
- …

- For example:

**Step 4: Create Square Root Tiles**

- Cut the blue colored paper into square root tiles. Write down examples of square roots on these tiles.
- For example:
**Blue Tiles (Square Roots):**- Tile 1: “√1” = “1”
- Tile 2: “√4” = “2”
- Tile 3: “√9” = “3”
- Tile 4: “√16” = “4”
- …

- For example:

**Step 5: Arrange Tiles**

- Place the square tiles (red) on the cardboard base, forming a grid-like pattern. Leave space between the tiles for the square root tiles (blue) to be placed.

**Step 6: Label and Explain**

- Use a marker to label each square tile with the corresponding perfect square value (e.g., “1”, “4”, “9”, etc.).

**Square Root Working Model Explanation:**

**Understanding Squares:**- Show how each square tile represents a perfect square. For example, “4” on a tile represents 2^2, and “9” represents 3^2.

**Introducing Square Roots:**- Introduce the concept of square roots using the blue tiles. Explain that the square root of a number “x” (√x) is the value that, when multiplied by itself, gives “x”.

**Matching Squares with Square Roots:**- Have students match the square tiles with their corresponding square root tiles. For example, match the tile with “4” to the tile with “√4” (which is “2”).

**Examples and Practice:**- Provide additional examples and let students practice matching other perfect squares with their respective square roots.

**Examples:**

- Match “9” (perfect square) with “√9” (square root), which is “3”.
- Match “16” (perfect square) with “√16” (square root), which is “4”.

By creating this TLM, students can visually and interactively learn about squares, square roots, and the relationship between them. It provides a hands-on experience that reinforces the concept and helps in understanding the mathematical operations involved.