The purpose of this activity is for students to use a method of their choice, likely multiplication or division, to solve a contextual problem about equal sharing of the longest noodle ever made. The numbers in this activity are greater than the numbers with which students have worked in previous lessons on division. Students estimate the number of feet of noodle each person ate at the record-breaking event. The numbers and context were chosen to encourage students to consider what they know about the meaning of division, to make a reasonable estimate, and to reason about the meaning of the quotient in the context of the situation presented (MP2).

Monitor and select students, who use the following strategies, to share in the Activity Synthesis:

• Multiply or divide to estimate that each person will get about 25 feet of noodle.
• Explain why 25 feet of noodle for each person is a low estimate.

• Ask selected students to share in the given order (or use the provided Student Responses if needed).
• “How are the methods for estimating the same?”(Both start by giving each person 10 feet of noodle. Then they give more until both have given 25 feet to each person. Both find multiples of 400.)
• “How are they different?” (One method uses division and the other uses just multiplication.)
• “How do you know the estimate of 25 feet is too low?” (Because there was still some of the noodle left. There are 119 feet left over.)

The purpose of this activity is to consider a more precise estimate for the length of noodle each person would get if 400 people equally shared a 10,119-foot noodle. This estimate includes a fractional part and encourages students to connect division to what they know about fractions. In the next lesson students will continue to examine fractions and how they relate to partial quotients.

Making an estimate, or a range of reasonable answers, with incomplete information, is a part of modeling with mathematics (MP4).

• Display: 
• "What does mean in this situation?" (Each person gets 25 feet of the noodle and then the 119 feet left over would be divided into 400 equal pieces.)
• Display: 
• "Why is Han's estimate reasonable?” (Because is really close to , and )
• "Do you think they actually measured and cut the noodle into equal pieces when they served it?" (No, because it would take too long and be too difficult. Yes, because they probably want to serve the noodle soup with sections that are one piece of the original noodle.)