Creating a rotating model that visually represents different types of basic mathematical functions can be a great hands-on teaching and learning material (TLM).

Here’s a step-by-step guide to help you build a graphing model inspired by a merry-go-round concept:

### Materials Needed:

**Cardboard**– For creating the base, graph, and function representations.**Slow-running motor**– To rotate the model.**Battery pack and wires**– To power the motor.**LED lights (optional)**– To highlight specific parts of the model.**Hot glue gun or strong adhesive**– For assembly.**Markers and paints**– For labeling and decorating.**Scissors or craft knife**– For cutting cardboard.**Ruler and compass**– For accurate measurements.**Stand**– To hold the motor and the rotating platform.**Plastic or foam balls**– To represent points on the graph.**Small dowels or sticks**– To represent the function curves.

### Step-by-Step Instructions:

#### Step 1: Create the Base Structure

**Cut the Base:**- Cut a large circular piece of cardboard to serve as the rotating platform (merry-go-round base).
- Divide the circle into equal sections, with each section representing a different basic function (linear, quadratic, cubic, sine, etc.).

**Mount the Motor:**- Securely attach the motor to the center of the base. Ensure it can rotate the platform smoothly.

#### Step 2: Prepare the Graphs

**Draw Axes:**- Draw X and Y axes on each section of the circular platform using a ruler and markers. Ensure they intersect at the center of the platform.

**Label the Axes:**- Label the X and Y axes appropriately for each function type. For example, X could range from -10 to 10 and Y could range from -10 to 10.

#### Step 3: Represent the Functions

**Create Function Curves:**- For each section, draw the graph of a basic function:
**Linear:**y=mx+by = mx + by=mx+b**Quadratic:**y=ax2+bx+cy = ax^2 + bx + cy=ax2+bx+c**Cubic:**y=ax3+bx2+cx+dy = ax^3 + bx^2 + cx + dy=ax3+bx2+cx+d**Sine:**y=asin(bx+c)+dy = a \sin(bx + c) + dy=asin(bx+c)+d

- Use markers to draw these graphs on the respective sections.

- For each section, draw the graph of a basic function:
**Add 3D Elements (optional):**- Attach small dowels or sticks along the function curves and place small plastic or foam balls at intervals to represent points on the graph.

#### Step 4: Assemble the Rotating Model

**Attach the Platform:**- Attach the circular platform to the motor shaft securely using a hot glue gun or strong adhesive.

**Install LED Lights (optional):**- If using LED lights, attach them around the edge of the platform or along the function curves to highlight specific parts when the model is rotating.

**Create the Stand:**- Build or use a stand to hold the motor and the rotating platform. Ensure the stand is stable and the platform can rotate freely.

#### Step 5: Wiring the Motor

**Connect the Motor:**- Connect the wires from the motor to the battery pack, incorporating a switch to easily turn the motor on and off.
- Secure all connections and insulate any exposed wires.

#### Step 6: Testing and Final Adjustments

**Test the Rotation:**- Turn on the motor and observe the rotation of the platform. Ensure the movement is smooth and stable.
- Make any necessary adjustments to the alignment of the graphs or the stability of the stand.

### Summary:

This rotating model will demonstrate different basic mathematical functions in a visually engaging way. As the platform rotates, students can observe and compare the various function graphs, enhancing their understanding of mathematical concepts. The merry-go-round concept adds an interactive and dynamic element to the learning experience.