Math worksheet designed to help students compare and order unit fractions using visual aids and a fraction wall.

Problem Overview:

The task involves comparing and ordering unit fractions. Unit fractions are fractions with a numerator of 1 (e.g., \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4} \)). The worksheet is divided into two sections:

1. Section A: Color the shapes to represent each fraction and determine which fraction is greater.
2. Section B: Compare pairs of fractions using \( <, >, \) or \( = \).

Solution:

#### Section A: Colour in the shapes to show each fraction, then decide which one is greater.

##### 1) \( \frac{1}{4} \) vs. \( \frac{1}{2} \)
- Shape for \( \frac{1}{4} \): Divide the square into 4 equal parts and color 1 part.
- Shape for \( \frac{1}{2} \): Divide the square into 2 equal parts and color 1 part.
- Comparison: Since \( \frac{1}{2} \) represents half of the whole, it is larger than \( \frac{1}{4} \), which represents one-fourth of the whole.
- Answer: \( \frac{1}{2} \) is greater.

##### 2) \( \frac{1}{8} \) vs. \( \frac{1}{5} \)
- Shape for \( \frac{1}{8} \): Divide the circle into 8 equal parts and color 1 part.
- Shape for \( \frac{1}{5} \): Divide the circle into 5 equal parts and color 1 part.
- Comparison: Since \( \frac{1}{5} \) represents a larger portion of the whole compared to \( \frac{1}{8} \), \( \frac{1}{5} \) is greater.
- Answer: \( \frac{1}{5} \) is greater.

##### 3) \( \frac{1}{9} \) vs. \( \frac{1}{4} \)
- Shape for \( \frac{1}{9} \): Divide the triangle into 9 equal parts and color 1 part.
- Shape for \( \frac{1}{4} \): Divide the triangle into 4 equal parts and color 1 part.
- Comparison: Since \( \frac{1}{4} \) represents a larger portion of the whole compared to \( \frac{1}{9} \), \( \frac{1}{4} \) is greater.
- Answer: \( \frac{1}{4} \) is greater.

##### 4) \( \frac{1}{3} \) vs. \( \frac{1}{5} \)
- Shape for \( \frac{1}{3} \): Divide the rectangle into 3 equal parts and color 1 part.
- Shape for \( \frac{1}{5} \): Divide the rectangle into 5 equal parts and color 1 part.
- Comparison: Since \( \frac{1}{3} \) represents a larger portion of the whole compared to \( \frac{1}{5} \), \( \frac{1}{3} \) is greater.
- Answer: \( \frac{1}{3} \) is greater.

#### Section B: Compare each pair of fractions using either \( <, >, \) or \( = \).

To compare unit fractions, remember that as the denominator increases, the value of the fraction decreases. For example, \( \frac{1}{2} > \frac{1}{3} > \frac{1}{4} \), and so on.

##### 1) \( \frac{1}{7} \) vs. \( \frac{1}{8} \)
- Since 7 < 8, \( \frac{1}{7} > \frac{1}{8} \).
- Answer: \( \frac{1}{7} > \frac{1}{8} \)

##### 2) \( \frac{1}{10} \) vs. \( \frac{1}{6} \)
- Since 10 > 6, \( \frac{1}{10} < \frac{1}{6} \).
- Answer: \( \frac{1}{10} < \frac{1}{6} \)

##### 3) \( \frac{1}{2} \) vs. \( \frac{1}{3} \)
- Since 2 < 3, \( \frac{1}{2} > \frac{1}{3} \).
- Answer: \( \frac{1}{2} > \frac{1}{3} \)

##### 4) \( \frac{1}{6} \) vs. \( \frac{1}{5} \)
- Since 6 > 5, \( \frac{1}{6} < \frac{1}{5} \).
- Answer: \( \frac{1}{6} < \frac{1}{5} \)

##### 5) \( \frac{1}{12} \) vs. \( \frac{1}{8} \)
- Since 12 > 8, \( \frac{1}{12} < \frac{1}{8} \).
- Answer: \( \frac{1}{12} < \frac{1}{8} \)

##### 6) \( \frac{1}{3} \) vs. \( \frac{1}{4} \)
- Since 3 < 4, \( \frac{1}{3} > \frac{1}{4} \).
- Answer: \( \frac{1}{3} > \frac{1}{4} \)

##### 7) \( \frac{1}{11} \) vs. \( \frac{1}{9} \)
- Since 11 > 9, \( \frac{1}{11} < \frac{1}{9} \).
- Answer: \( \frac{1}{11} < \frac{1}{9} \)

Final Answers:

Section A:
1. \( \frac{1}{2} \)
2. \( \frac{1}{5} \)
3. \( \frac{1}{4} \)
4. \( \frac{1}{3} \)

Section B:
1. \( \frac{1}{7} > \frac{1}{8} \)
2. \( \frac{1}{10} < \frac{1}{6} \)
3. \( \frac{1}{2} > \frac{1}{3} \)
4. \( \frac{1}{6} < \frac{1}{5} \)
5. \( \frac{1}{12} < \frac{1}{8} \)
6. \( \frac{1}{3} > \frac{1}{4} \)
7. \( \frac{1}{11} < \frac{1}{9} \)

\(\boxed{\text{See detailed explanations above.}}\)