Creating a working model to demonstrate the concept of finding the Highest Common Factor (HCF) using syringes and cardboard can be an interesting and interactive project.

Here’s a simple and easy DIY (Do It Yourself) project for understanding HCF and LCM (Lowest Common Multiple):

**Materials Needed:**

- Cardboard
- Syringes (2 or more)
- Plastic tubing (cut into equal lengths)
- Water or colored liquid (for visibility)
- Funnel
- Markers
- Ruler
- Scissors
- Glue or tape
- Labels or index cards

**Steps to Create the HCF Working Model:**

**Step 1: Prepare the Base:**

- Cut a large piece of cardboard to use as the base for your working model.

**Step 2: Syringe Setup:**

- Attach plastic tubing to the nozzles of each syringe. The tubing should be long enough to reach a common point on the cardboard.

**Step 3: Mark the Syringes:**

- Use markers to label each syringe with a number representing a factor. For example, if you are finding the HCF of 45 and 60, label one syringe with ’45’ and the other with ’60.’

**Step 4: Fill the Syringes:**

- Fill each syringe with water using a funnel. The water level should represent the corresponding number on the syringe.

**Step 5: Display on Cardboard:**

- Attach the syringes to the cardboard, placing them side by side. Make sure the tubing reaches a common point.

**Step 6: Find the HCF:**

- Gradually press the plunger of each syringe until the water reaches its lowest level.
- Observe where all the water levels align at the same point. This point represents the HCF.

**Step 7: Optional – Label the HCF:**

- Use labels or index cards to label the common point as the Highest Common Factor.

**Explanation:**

- Explain that the water levels in the syringes represent the factors of the given numbers.
- Demonstrate how by adjusting the water levels, you can find the HCF where all the levels align.

**Extension – LCM:**

- If you want to demonstrate LCM as well, you can add more syringes and tubes for additional numbers.
- Show how the LCM is the value when all syringes reach their maximum levels simultaneously.

This DIY working model provides a hands-on way for students to understand the concept of HCF and LCM using syringes and water levels. It offers a visual and interactive representation, making it an effective Teaching-Learning Material (TLM) for mathematical concepts.