The purpose of this activity is for students to solve problems about dividing a whole number by a unit fraction in a way that makes sense to them. The context of quilt making is used so students can visualize a strip of paper that is a whole number length being cut into fractional sized pieces. As students describe how the problems are similar and different, listen for the authentic language they use to describe division. The paper strip, or tape, is a helpful diagram to use when dividing a whole number by a unit fraction because students recognize important relationships between the divisor, dividend, and quotient (MP7). For example, if the length of the strip stays the same, but the size of the pieces gets smaller, then the number of pieces will get bigger.

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

• “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:

  
  
  
• “How do these equations represent the problems about the paper strips?” (The 2 is for 2 feet of paper, and the fractions show the size of the pieces that the paper is being cut into. The 4, 6, and 8 are the number of pieces of each color of paper.)

The purpose of this activity is for students to represent division of a whole number by a unit fraction with diagrams and equations. The context is the same as the previous activity so students can use a tape diagram to solve the problem, if they choose. In the previous activity, students recognized that when the length of paper stays the same and the size of the piece gets smaller, there are more pieces of paper. In this activity, students will consider what happens when the length of the paper changes, but the size of the pieces stays the same.

• “How does your equation represent the situation?”
• Show them and ask, “How does this expression represent the situation?”

• Ask previously identified students to share their solutions.
• Display:
• “How does this equation represent the yellow strip of paper?” (The strip of paper is 2 feet long and it is cut into pieces that are of a foot long, so there will be 12 pieces.)
• Display:
• “How does this equation represent a different strip of paper being cut into equal sized pieces?” (A 3 foot piece of paper is cut into pieces that are of a foot long, so there are 18 pieces.)
• “Why is the quotient larger than the dividend in both of these equations?” (You are cutting a whole number length into fractional sized pieces, so there will be more pieces than when you started.)