To explain how Mateo can use the number line to find an equivalent fraction with a denominator greater than 6, here's a step-by-step breakdown:

1. Understand the starting fraction: Identify the fraction Mateo is working with on the number line. For example, if he starts with $\frac{1}{2}$, that is the fraction he needs to find an equivalent for.

2. Divide the number line: Begin by dividing the number line into equal parts based on the denominator of the starting fraction. For $\frac{1}{2}$, the number line is split into 2 equal parts: 0, $\frac{1}{2}$, and 1.

3. Increase the number of divisions: To find an equivalent fraction with a denominator greater than 6, divide the number line into more sections. For instance, instead of 2 parts, divide it into 8 equal parts. Each part now represents $\frac{1}{8}$.

4. Locate the equivalent fraction: Find the same position as the original fraction on the newly divided number line. If $\frac{1}{2}$ was the starting fraction, its equivalent with 8 as the denominator would be $\frac{4}{8}$, as the position of $\frac{1}{2}$ aligns with 4 out of the 8 parts.

5. Confirm the new denominator: Ensure the new fraction has a denominator greater than 6 (in this case, 8) and is equivalent to the original fraction.

This process visually demonstrates equivalence by using equal spacing and alignment on the number line.

Would you like me to provide additional examples, or clarify any part of this explanation?

Follow-up Questions:

1. How can Mateo find fractions equivalent to $\frac{3}{4}$ using a number line?
2. What happens if the new denominator is a multiple of the original one?
3. How does Mateo confirm that the fractions are truly equivalent?
4. Can Mateo use this method to find improper fractions? Why or why not?
5. What are the benefits of using a number line over other methods of finding equivalent fractions?

Tip:

Always ensure that the divisions on the number line are evenly spaced for accurate representation of equivalent fractions.