To explain how Mateo can use the number line to find an equivalent fraction with a denominator less than 6, follow these steps:

1. Mark the Fraction on the Number Line: Start by identifying the original fraction. For example, if Mateo is working with $\frac{4}{6}$, divide the number line into 6 equal parts to represent sixths, and locate $\frac{4}{6}$ on the number line.

2. Simplify the Fraction Visually: To find an equivalent fraction with a smaller denominator, combine the parts into larger equal segments. For instance, instead of dividing the number line into sixths, try dividing it into thirds (a smaller denominator). Each interval on the number line now represents $\frac{1}{3}$.

3. Relocate the Equivalent Fraction: Check how many thirds fit into the same point as $\frac{4}{6}$. Since $\frac{4}{6} = \frac{2}{3}$, you’ll find $\frac{2}{3}$ matches the same point.

4. Verify: Ensure the equivalence by confirming that both fractions represent the same point on the number line.

By visualizing and combining segments, Mateo can confidently identify $\frac{2}{3}$ as an equivalent fraction with a denominator smaller than 6.

Would you like me to provide further examples or additional clarification?

Here are 5 related questions for deeper understanding:

1. How can Mateo identify equivalent fractions using multiplication or division?
2. What are other methods to simplify fractions without using a number line?
3. Can Mateo find equivalent fractions with a denominator greater than 6 using the same method?
4. Why is it important to simplify fractions in math problems?
5. How does identifying equivalent fractions help in real-world applications?

Tip: Practice with different fractions on a number line to strengthen your understanding of equivalency and simplification.