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.
• “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.)
• “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.”
• “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.
• “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.

• “What fractions could you make with what you rolled?”
• “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
• “If you got these numbers on your last roll, what equivalent fractions could you make?” ( or )
• If needed, ask, “What number should I use for my wild card?”