Lesson 16

The purpose of this warm-up is to introduce the context of a world record event about the longest continuous noodle, which will be useful when students solve problems about this event in a later activity. While students may notice and wonder many things about this text and image, the noodle’s length and the number of people sharing the noodle are the important discussion points. 

• Groups of 2
• Consider showing students a Guinness Book world record image or video of the worlds longest noodle.
• Display the image.

• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share and record responses.

• “¿Qué otra cosa tiene aproximadamente 10,000 pies de largo?” // “What is something else that is about 10,000 feet long?” (That is about how high people are when they skydive. It is about 2 miles.)
• “Estas imágenes muestran cómo se hizo el fideo más largo del mundo. Vamos a resolver problemas relacionados con este evento” // “These pictures show the world’s longest noodle being made. We are going to solve some problems about this event.”

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 larger than the numbers students have worked with 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 with the following strategies to share in the synthesis:

• Students use multiplication or division to estimate that each person will get about 25 feet of noodle.
• Students can explain why 25 feet of noodle for each person is a low estimate.

• “¿Qué tipo de fideo les gusta comer?” // “What kind of noodles do you like to eat?” (ramen, spaghetti, fettucini, chicken noodle soup)
• 30 seconds: partner discussion
• “¿Aproximadamente qué tan largo es el fideo que les gusta comer?” // “About how long is one of the noodles you like to eat?” (about 1 foot long)
• Groups of 2

• 5 minutes: independent work time
• 5 minutes: partner discussion
• As students work, consider asking “¿Qué significan los números de tus cálculos, en términos de la situación?” // “What do the numbers in your calculations mean, in terms of the situation?”

• Ask selected students to share in the given order (or use the provided student solutions if needed).
• “¿En qué se parecen los métodos para estimar la cantidad de fideo que recibió cada persona?” // “How are the methods for estimating the amount of noodle each person gets the same?” (They both start by giving each person 10 feet of noodle. Then they give more until they have both given 25 feet to each person. They both find multiples of 400.)
• “¿En qué son diferentes?” // “How are they different?” (One thinks of the process as division and one uses just multiplication.)
• “¿Cómo saben que la estimación de 25 pies es muy baja?” // “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).  

• Groups of 2

• 3–5 minutes: independent work time
• 3–5 minutes: partner discussion

• Display: \(25\frac{119}{400}\)
• “¿Qué significa \(25\frac{119}{400}\) en esta situación?” // "What does \(25\frac{119}{400}\) mean in this situation?" (Each person gets 25 feet of the noodle and then the 119 feet leftover would be divided into 400 equal pieces.)
• Display: \(25\frac{1}{4}\)
• “¿Por qué la estimación de Han es razonable?” // "Why is Han's estimate reasonable?” (Because is \(\frac{119}{400}\) really close to \(\frac{100}{400}\) and \(\frac{100}{400}=\frac{1}{4}\))
• “¿Creen que realmente midieron y cortaron el fideo en partes iguales cuando lo sirvieron?” // "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 if long noodles represent long life they probably want to serve the noodle soup with sections that are one piece of the original noodle.)