Creating a **real numbers working model with LED lights** in a **tree format** is a fantastic way to visually represent the different sets of real numbers (natural numbers, whole numbers, integers, rational numbers, and irrational numbers) using an LED-powered structure.

The tree format will allow you to organize and categorize these numbers with branches, and LEDs can be used to highlight or activate different sets.

### Materials Needed:

**Cardboard or foam board**(for the tree structure)**LED lights**(multicolored to represent different sets)**Battery pack**or**power supply****Wires**(to connect LEDs to power)**Switches or buttons**(to activate specific LED sections)**Resistors**(to limit current to the LEDs)**Soldering iron**(optional, for connecting wires and LEDs)**Glue gun or strong adhesive**(to attach components)**Markers or paint**(to label branches and sections)**Scissors/cutter**(to shape the tree)**Labels or markers**(to explain number sets)

### Concept of the Model:

The model will be designed in the shape of a **tree**, with different branches representing the various subsets of real numbers:

**Root**: Represents the set of**real numbers**.**Main branches**: Divide into**rational numbers**and**irrational numbers**.**Sub-branches**: Under rational numbers, divide further into**integers**,**whole numbers**, and**natural numbers**. Each category or subset of numbers will be represented by a different color LED, and pressing buttons or switches will light up specific branches of the tree to show the number classification.

### Video Steps to Build the Model:

#### 1. **Create the Tree Structure**

**Cut the Shape**: Using cardboard or foam board, cut out a tree shape with multiple branches. The trunk of the tree will represent the real numbers, while the branches will represent subsets like natural numbers, whole numbers, integers, rational numbers, and irrational numbers.**Label the Tree**: Clearly mark and label each section of the tree:**Root (Real Numbers)**: This is the base of the tree, connecting all other branches.**Branch 1 (Rational Numbers)**: Includes natural numbers, whole numbers, and integers.**Branch 2 (Irrational Numbers)**: This branch represents numbers that cannot be expressed as a ratio of integers (e.g., √2, π).

#### 2. **Prepare the LED Lights**

**Color Coding**: Use different colored LEDs to represent each number set:**Natural Numbers (1, 2, 3, …)**: Green LEDs**Whole Numbers (0, 1, 2, 3, …)**: Yellow LEDs**Integers (…-2, -1, 0, 1, 2, …)**: Red LEDs**Rational Numbers (fractions, decimals, integers)**: Blue LEDs**Irrational Numbers (π, √2, e, …)**: White LEDs

**Plan the Circuit**: Map out where each LED will be placed on the tree and how they will be wired. The LEDs should be arranged along the branches so that each subset of numbers lights up when activated.

#### 3. **Install LEDs on the Tree**

**Drill or Cut Holes**: Use a small cutter or drill to create holes in the cardboard or foam board where the LEDs will be inserted.**Insert LEDs**: Place each LED into its corresponding hole, aligning them with the labeled branches of the tree. For example, place green LEDs on the branch representing natural numbers, red LEDs on the integers branch, and so on.**Secure the LEDs**: Use hot glue or tape to hold the LEDs in place on the backside of the board.

#### 4. **Connect the Wiring**

**Connect the LEDs to the Power Supply**: Connect the positive (anode) lead of each LED to the positive terminal of the battery pack or power supply and the negative (cathode) lead to the negative terminal.**Use Resistors**: Add resistors in series with each LED to prevent them from burning out. A common value would be a 220Ω resistor, depending on the voltage of your LEDs and power source.**Wiring in Parallel**: Since you want the LEDs to light up independently for each number set, wire them in parallel. Each set (natural numbers, whole numbers, etc.) should have its own circuit.

#### 5. **Add Switches or Buttons**

**Place Switches on the Tree**: For each category of numbers (natural, whole, integers, rational, and irrational), add a corresponding switch or button. This will allow you to light up only that specific set of LEDs when the switch is pressed.**Wire the Switches**: Connect the switches in such a way that pressing one button completes the circuit for the corresponding LED group. For example, pressing the “natural numbers” button will light up all the green LEDs on that branch.

#### 6. **Test the Circuit**

**Turn On the Power**: Connect the battery pack or power source and test each switch to ensure the LEDs light up correctly for each number set.**Check the Connections**: Make sure all LEDs light up when their respective switches are pressed and that no LEDs are lighting up unintentionally.

#### 7. **Final Assembly and Labeling**

**Add Descriptions**: On each branch, write a brief description of the number sets it represents. For instance:**Natural Numbers (N)**: Numbers used for counting (1, 2, 3, …).**Whole Numbers (W)**: Natural numbers plus zero (0, 1, 2, …).**Integers (Z)**: Positive and negative whole numbers (… -2, -1, 0, 1, 2 …).**Rational Numbers (Q)**: Numbers that can be expressed as fractions (½, 0.75, etc.).**Irrational Numbers (I)**: Numbers that cannot be written as fractions (π, √2, etc.).

**Decorate the Tree**: You can add additional decorations to the tree to make it more visually appealing for the exhibition. Use bright colors, paints, or even 3D elements to make it stand out.

### Key Concepts:

**Real Numbers**: The entire tree represents real numbers, which includes both rational and irrational numbers.**Rational Numbers**: The right branch will show numbers that can be written as a fraction, including integers, whole numbers, and natural numbers.**Irrational Numbers**: The left branch will display numbers like √2 and π, which cannot be expressed as a ratio of two integers.

This working model is interactive and engaging for exhibitions, allowing observers to press buttons and light up different branches, making abstract math concepts more tangible.