The purpose of this activity is for students to compare quotients of quantities based on the relative size of the dividend and the divisor. Students should be encouraged to use whatever strategy makes sense to them to order situations about sharing beads. The numbers were intentionally chosen so that students don’t have to perform any complex calculations to solve the problem which encourages them to think about the relative size of the numerator and denominator in order to compare the quotients. In upcoming lessons, students will divide a unit fraction by a whole number and a whole number by a unit fraction.

This activity uses MLR2 Collect and Display. Advances: Reading, Writing.

• “How can you draw a diagram to represent each situation?”
• “How are the diagrams the same? How are they different?”

• “Are there any other words or phrases that are important to include on our display?”
• As students share responses, update the display, by adding (or replacing) language, diagrams, or annotations.
• Remind students to borrow language from the display as needed.
• Display:
  3 students equally share 45 beads.
  3 students equally share 42 beads.
  3 students equally share 24 beads.
  3 students equally share 6 beads.
• “What is the same? What is different?” (The same number of students are sharing different numbers of beads.)
• “How does the number of beads each person gets change in each situation?” (It gets smaller because there are fewer beads to share.)
• Display:
  14 students equally share 42 beads.
  7 students equally share 42 beads.
  6 students equally share 42 beads.
• “What is the same? What is different?” (The number of beads being shared is the same. The number of students sharing is different.)
• “How does the number of beads each person gets change in each situation?” (When fewer people share the same number of beads, each person gets more beads.)

The purpose of this activity is for students to look for patterns in division by the same divisor. The numbers in these problems were intentionally chosen so students see that the quotient gets smaller as the dividend gets smaller (MP7). Display the poster of the language students used to describe the relationship between quotient, dividend, and divisor during the previous activity. In the last question, students think about what it means to divide a fraction by a whole number which will be the focus of upcoming lessons.

• Ask previously identified students to share their solutions.
• “Why does the quotient get smaller as the dividend gets smaller?” (There are a smaller number of things being split into the same number of groups, so there will be fewer in each group.)
• “Why is going to be smaller than ?” ( is being divided into 3 equal pieces.)
• Display student diagrams like the ones in student responses.
• “How do the diagrams show ?” (They show a third divided into 3 equal pieces.)