1. **State the problem:** We need to compare the fractions $\frac{1}{4}$ and $\frac{1}{8}$ to determine which is greater. 2. **Explain the concept:** When comparing fractions with the same numerator, the fraction with the smaller denominator is larger because the whole is divided into fewer parts. 3. **Compare denominators:** Here, $4$ and $8$ are the denominators. Since $4 < 8$, the parts are larger in $\frac{1}{4}$ than in $\frac{1}{8}$. 4. **Alternative method - common denominator:** Find a common denominator to compare directly. 5. The least common denominator of $4$ and $8$ is $8$. 6. Convert $\frac{1}{4}$ to eighths: $$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$$ 7. Now compare $\frac{2}{8}$ and $\frac{1}{8}$. 8. Since $2 > 1$, $\frac{2}{8} > \frac{1}{8}$, so $\frac{1}{4} > \frac{1}{8}$. 9. **Conclusion:** $\frac{1}{4}$ is greater than $\frac{1}{8}$. This method helps peers understand fraction comparison by either reasoning about denominators or using a common denominator.