The purpose of this activity is for students to represent their thinking visually as they compare pairs of fractions with the same numerator. They also locate fractions with the same numerator on number lines and observe the relative locations of the points. Students see that fractions with greater denominators are smaller in size (or are closer to 0 on the number line). Their reasoning here reinforces the idea that the denominator of a fraction determines how many equal parts are in a whole, and that the more parts there are, the smaller each part (MP7).

To compare and , students are likely to draw a diagram or a number line for sixths and a separate diagram or number line for eighths. They may use a single diagram or number line, but likely find it more difficult to partition and represent both denominators.

• Display a set of number lines that a student completed.
• Invite the class to share their observations about the locations of the points.
• “¿Cómo puede ayudar la ubicación de los puntos a decidir cuál es mayor,  o ?” // “How can the locations of the points help you decide which is greater, or ?” (I can see that is located to the right of , so is greater.)
• Consider asking: “¿Por qué la fracción que tiene el menor denominador, 2, es la mayor fracción del grupo?” // “Why is the fraction with the least denominator, 2, the greatest fraction in the set?” (There are only 2 parts in 1 whole. With the other fraction, the denominator is larger than 2 so there are more parts in the whole, which makes the parts smaller.)

The purpose of this activity is for students to compare two fractions with the same numerator. Students use any representation to reason about the number and the size of the parts of each fraction. In the last problem, students may notice that more than one denominator can sometimes work, but do not need to generalize about all the denominators that make each statement true. There is an opportunity for that kind of generalization in a future lesson.

• Select 3 or 4 students to share the denominators they chose for one part in the last problem. Ask them to explain why their chosen denominator makes the statement true.