Creating a **working model of real numbers in a tree format** using paper and cardboard is a great way to visually organize and explain the different subsets of real numbers.

Here’s a step-by-step guide for constructing this model:

### Materials Needed:

**Cardboard**(for the base and tree branches)**Colored paper**(to make number categories and labels)**Scissors****Glue or tape****Markers/Colors**(to write labels and decorate)**Ruler****String or thin wire**(optional, to hang labels from branches)

### Real Number Classification:

Before constructing the tree, remember that **real numbers** can be classified into various subsets:

**Real Numbers (ℝ)**:**Rational Numbers (ℚ)**:**Integers (ℤ)**:**Whole Numbers (ℕ₀)**:**Natural Numbers (ℕ)**

**Irrational Numbers**

### Video Steps to Create the Model:

#### 1. **Prepare the Base**

- Cut a large rectangular piece of cardboard to serve as the base of the tree model.
- You can cover the base with colored paper or paint it for a decorative effect.

#### 2. **Create the Tree Trunk**

- Cut out a long rectangle from the cardboard to serve as the
**tree trunk**. - Label the trunk
**“Real Numbers (ℝ)”**since all the other subsets of numbers stem from this category. - Attach the tree trunk to the center of the base using glue or tape.

#### 3. **Make the Tree Branches**

- Cut out
**branches**from cardboard, each representing a different subset of real numbers. - The branches will split as follows:
- The
**first branch**should represent**Rational Numbers (ℚ)**and**Irrational Numbers**. - From the
**Rational Numbers**branch, further split into**Integers (ℤ)**and**Fractions**. - The
**Integers branch**will further split into**Whole Numbers (ℕ₀)**and**Negative Integers**. - The
**Whole Numbers branch**will split into**Natural Numbers (ℕ)**and**Zero (0)**.

- The

#### 4. **Label the Branches**

- Cut out small pieces of colored paper for each label, such as:
**Real Numbers (ℝ)****Rational Numbers (ℚ)****Irrational Numbers****Integers (ℤ)****Fractions****Whole Numbers (ℕ₀)****Natural Numbers (ℕ)****Negative Integers****Zero (0)**

- Use
**markers**or**colored pens**to neatly write the names on the paper, and then glue or tape these labels to the corresponding branches.

#### 5. **Assemble the Tree**

- Attach the
**branches**to the tree trunk. - Make sure each branch splits appropriately, with the subsets connected to the correct categories.
- You can angle the branches in a way that they look like a tree growing outward.

#### 6. **Add Examples on Leaves**

- Create
**leaf-shaped cutouts**from colored paper to represent examples of numbers within each subset:**Natural Numbers (ℕ)**: Examples like 1, 2, 3, 4…**Whole Numbers (ℕ₀)**: Add 0 to the set of natural numbers.**Integers (ℤ)**: Examples like -3, -2, -1, 0, 1, 2…**Rational Numbers (ℚ)**: Examples like 1/2, 3/4, -5, 2.**Irrational Numbers**: Examples like π (Pi), √2, e.

- Attach the leaf cutouts to the appropriate branches to visually show examples of each type of number.

#### 7. **Decorate the Model**

- Add finishing touches to make the tree visually appealing. You can use more colored paper to add leaves, or add designs to the base.
- Optionally, use
**string**or**thin wire**to hang some of the labels or number examples from the branches, giving it a more dynamic look.

#### 8. **Final Layout**

- Ensure that the main branches flow smoothly from
**Real Numbers (ℝ)**at the trunk, splitting into**Rational**and**Irrational Numbers**. - From the
**Rational Numbers**branch, have**Integers (ℤ)**on one side and**Fractions**on the other. - Further split
**Integers**into**Whole Numbers**and**Negative Integers**. - Split
**Whole Numbers**into**Natural Numbers (ℕ)**and**Zero (0)**.

### Explanation of the Model:

**Real Numbers (ℝ)**: All the numbers on the number line, including both rational and irrational numbers.**Rational Numbers (ℚ)**: Numbers that can be written as a fraction (like 1/2 or -3/4), including integers.**Irrational Numbers**: Numbers that cannot be expressed as a fraction, such as π (Pi) and √2.**Integers (ℤ)**: All whole numbers, including positive, negative, and zero.**Whole Numbers (ℕ₀)**: Non-negative integers (0, 1, 2, 3…).**Natural Numbers (ℕ)**: Counting numbers (1, 2, 3…).