The purpose of this activity is for students to explain equivalence, using a number line. Students are given situations in a measurement context and have to determine whether the distance is the same. Students are encouraged to use a number line to provide an opportunity to explain fraction equivalence as fractions that are at the same location. They may choose to use two number lines for each question (one for each fraction). Choosing to use one number line or two will be discussed in the Synthesis of the next activity. 

When they identify whether or not two fractions of the same trail represent the same distance, students reason abstractly and quantitatively (MP2).

• Display a student-created number line that shows and at the same location.
• “¿Cómo muestra esto que Jada y Kiran corrieron la misma distancia?” // “How does this show that Jada and Kiran ran the same distance?” (The points that represent them are at the same location between 0 and 1 on the number line.)
• “Aprendimos que dos fracciones son equivalentes si tienen el mismo tamaño. Ahora también sabemos que dos números son equivalentes si están en la misma ubicación en una recta numérica. Como  y  están en la misma ubicación, podemos decir que son equivalentes” // “We’ve learned that two fractions are equivalent if they are the same size. Now we also know that two numbers are equivalent if they are at the same location on a number line. Because  and are at the same location, we can say they are equivalent.”
• “¿Cómo podemos usar el signo igual para escribir fracciones que son equivalentes?” // “How could we use the equal sign to record fractions that are equivalent?” (, )
• Share and record responses.

The purpose of this activity is for students to locate fractions on the number line, and find pairs of fractions that are equivalent. Students can use a separate number line for each denominator, but they also can place fractions with different denominators on the same number line to show equivalence. Focus explanations about why fractions are equivalent on the fact that they share the same location. In the Activity Synthesis, discuss how one number line or two can be used to compare fractions.

• Select previously identified students to display how a single number line or separate number lines can be used to show equivalent fractions.
• “¿Cuándo tiene sentido usar una sola recta numérica y cuándo ayuda usar dos rectas numéricas?” // “When might it make sense to use a single number line and when might it be helpful to use two number lines?“ (One number line might make sense if one fraction can be partitioned to get to another, like halves to fourths. If a number line is too crowded or has fractions that could be hard to partition together, like halves and thirds, it might be helpful to use two number lines.)

The purpose of this activity is for students to practice generating equivalent fractions. The goal of each round is to use the numbers on the number cubes to complete a statement that shows that two fractions are equivalent. Students roll 6 number cubes and try to use 4 of the numbers to create a statement that shows two equivalent fractions. If students roll a 5 (or a blank), they may choose any number to use. Students may choose to re-roll any of their number cubes up to 2 times. Students get a point for every true statement they make. Students may choose to use fraction strips, diagrams, or number lines to prove that their fractions are equivalent. If students choose to use diagrams, monitor to make sure they are drawing equal-size wholes.

• “¿Qué fracciones puedes hacer con lo que sacaste?” // “What fractions could you make with what you rolled?”
• “¿Cómo puedes usar tus tiras de fracciones para decidir si algunas de las fracciones son equivalentes?” // “How could you use your fraction strips to decide if any of the fractions are equivalent?”

• Display number cubes showing 1, 1, 4, 2, 2, 5
• “Si sacaran estos números en su último lanzamiento, ¿qué fracciones equivalentes podrían hacer?” // “If you got these numbers on your last roll, what equivalent fractions could you make?” ( or )
• If needed, ask, “¿Qué número debo usar para mi comodín?” // “What number should I use for my wild card?”