# Lesson 14

Representemos fracciones en un diagrama de puntos

## Warm-up: Cuál es diferente: Diagramas de puntos (10 minutes)

### Narrative

The purpose of this warm-up is for students to recall the line plots with fractional measurements which they have studied in prior courses. This prepares them to do more arithmetic with fractions using the data from line plots in the next two lessons.

### Launch

• Groups of 2
• Display the image.
• “Escojan uno que sea diferente. Prepárense para compartir por qué es diferente” // “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

### Activity

• “Discutan con su compañero cómo pensaron” // “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

### Student Facing

¿Cuál es diferente?

### Activity Synthesis

• “¿Por qué el diagrama B es diferente?” // “Why doesn’t B belong?” (There are no fractions marked and there is no data with fractional values.)
• “Hoy vamos a trabajar con diagramas de puntos que tienen datos fraccionarios y vamos a usar lo que hemos aprendido sobre las fracciones para resolver problemas” // “Today we are going to work with line plots with fractional data and use what we have learned about fractions to solve problems.”

## Activity 1: Sumas de fracciones (15 minutes)

### Narrative

The purpose of this activity is for students to make a line plot and answer questions about the data collected. The numbers that students plot come from spinning a spinner twice and adding the fractions on the spinner. The denominators are chosen so that 8 can be used as a common denominator. Students observe and think about patterns and then discuss them during the synthesis.

Engagement: Provide Access by Recruiting Interest. Synthesis: Revisit math community norms to prepare students for the whole-class discussion.
Supports accessibility for: Attention, Social-Emotional Functioning

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs 1 paper clip and one pencil.

### Launch

• Groups of 2
• Display the number line image from student workbook.
• “Van a jugar un juego con su compañero. Van a usar un clip y un lápiz para hacer una ruleta con la imagen que está en su libro. Practiquemos” // “You are going to play a game with your partner. You will use a paper clip and a pencil to make a spinner out of the image in your workbook. Let’s practice.”
• Demonstrate how to use the pencil and paper clip as a spinner. Spin twice and record the fractions you landed on for all to see.
• “Necesito encontrar el valor de la suma de estas dos fracciones” // “I need to find the value of the sum of these two fractions.”
• Demonstrate how to record the sum on the number line with an X.
• “¿Cuál número creen que tendrá más ‘X’ si giran la ruleta muchas veces? ¿Por qué?” // “Which number do you think will have the most Xs if you spin the spinner a lot of times? Why?”
• 1–2 minutes: partner discussion

### Activity

• 1–2 minutes: quiet think time
• 6–8 minutes: partner work time
• Monitor for students who:
• partition the number line into eighths
• use common denominators to convert fractions with unlike denominators to fractions with like denominators

### Student Facing

1. Jueguen “Suma de fracciones” con su compañero.

• Jueguen por turnos con su compañero.
• Hagan girar la ruleta dos veces.
• Sumen las dos fracciones.
• Marquen la suma en el diagrama de puntos.
• Jueguen hasta que tengan 12 puntos de datos entre los dos.

2. ¿Cómo supieron dónde ubicar las sumas de octavos?
3. ¿Cuál es la diferencia entre el número más alto y el número más bajo que marcaron?
4. ¿Qué observan acerca de los datos que recolectaron?

### Activity Synthesis

• Ask previously identified students to share their thinking.
• “¿Alguien marcó un uno? ¿Qué números sacaron?” // “Did anyone record a one? What did you spin?” (I got $$\frac{1}{2}$$ on both spins.)
• “¿Hay alguna otra manera de obtener 1 como una suma?” // “Is there any other way to get 1 as a sum?” (No. I would need to add $$\frac{3}{4}$$ to$$\frac{1}{4}$$, $$\frac{7}{8}$$ to $$\frac{1}{8}$$, and $$\frac{3}{8}$$ to $$\frac{5}{8}$$ and none of those is possible.)
• “¿Cuál fue el número más grande que marcaron?” // “What is the largest number you recorded?” (Sample responses: $$1\frac{2}{8}$$, $$1 \frac{1}{8}$$)
• “¿Es posible obtener más de $$1\frac{2}{8}$$?” // “Is it possible to get more than $$1\frac{2}{8}$$?” (No, the biggest number is $$\frac{5}{8}$$ and two of those is $$1\frac{2}{8}$$.)
• “Mencionen una fracción que hubiera hecho que el juego fuera más retador si hubiera estado en el tablero de números. ¿Por qué habría hecho que el juego fuera más retador?” // “Name a fraction that would have made the game more challenging if it were on the number mat. Why would this have made the game more challenging?” ($$\frac{2}{3}$$, $$\frac{4}{5}$$, or any other fraction with a denominator that is not a factor or multiple of 8. It would be more challenging because we could not use 8 as a common denominator to easily add the fractions.)

## Activity 2: Muchos huevos (20 minutes)

### Narrative

The purpose of this activity is for students to use measurement data to make a line plot and then solve problems about the data presented in the line plot (MP2). The line plot is blank so students will choose which whole numbers to label and which fractions to label in between. They will use their understanding of equivalent fractions (halves, quarters, and eighths) to accurately make the line plot. Jada’s statement about the eggs that weigh $$1\frac{7}{8}$$ ounces is interesting because it uses two fractions referring to different quantities: $$\frac{1}{4}$$ is a fraction of the eggs and $$1\frac{7}{8}$$ is their weight in ounces. The focus of the synthesis is on how students reason about Jada’s statement. As students reason through Jada’s statement, they critique the reasoning of others (MP3).

MLR8 Discussion Supports. Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.

### Launch

• Groups of 2
• Display the image.
• “¿Qué observan?” // “What do you notice?” (It is a chicken. There is an egg. There are numbers and units.)
• “¿Qué se preguntan?” // “What do you wonder?” (What is it for? Is it a scale? Why does it say small, medium, large, X-Large?)
• “Esta es una balanza para pesar huevos. ¿Qué pueden decir sobre el huevo que está en la balanza?” // “This is an egg scale. It is used to weigh eggs. What can you say about the egg on the scale?” (It's small. It weighs less than 2 ounces.)
• “Ahora van a hacer un diagrama de puntos y a responder preguntas sobre los pesos de los huevos” // “Now you will make a line plot and answer questions about the egg weights.”

### Activity

• 5 minutes: independent work time
• 5 minutes: partner work time
• Monitor for students who use either of these expressions to determine if Jada is correct:
• $$\frac{1}{4}\times12=3$$
• $$12\div4=3$$

### Student Facing

1. Estos son los pesos de unos huevos, en onzas. Úsalos para hacer un diagrama de puntos.

$$1\frac{7}{8}$$, $$2 \frac{1}{2}$$, $$2\frac{3}{8}$$, $$1 \frac{3}{4}$$, $$2\frac{1}{4}$$, $$2\frac{4}{8}$$, $$2 \frac{1}{8}$$, $$1\frac{7}{8}$$, $$2\frac{1}{4}$$, $$1\frac{6}{8}$$, $$2\frac{1}{8}$$, $$1\frac{7}{8}$$

2. Jada dijo que $$\frac{1}{4}$$ de los huevos pesa $$1\frac{7}{8}$$ onzas. ¿Estás de acuerdo? Explica o muestra cómo razonaste.
3. ¿Cuánto más pesa el huevo más pesado que el huevo más liviano? Explica o muestra cómo razonaste.

### Activity Synthesis

• Ask previously selected students to share their response to Jada's statement.
• “¿Cómo supieron cuántos huevos pesó Jada?” // “How did you know how many eggs Jada weighed?” (I could count the measurements or count the marks on the graph.)
• “¿Cómo decidieron si la afirmación de ella era correcta?” // “How did you decide if her statement was correct?” (I found $$\frac{1}{4}$$ of 12 and then counted the number eggs that weighed $$1\frac{7}{8}$$ ounces. They were both 3 so Jada is correct.)
• If students do not write an equation matching Jada’s response, consider displaying the equations $$\frac{1}{4} \times 12 = 3$$ and $$12 \div 4 = 3$$
• “¿Cómo está representado el razonamiento de Jada en estas ecuaciones?” // “How do these equations represent Jada’s reasoning?” (They both say that $$\frac{1}{4}$$ of the 12 egg measurements is 3 eggs. One uses multiplication and the other one uses division.)

## Lesson Synthesis

### Lesson Synthesis

“Hoy hicimos diagramas de puntos y respondimos preguntas sobre los datos de los diagramas de puntos” // “Today we made line plots and answered questions about the data in line plots.”

Display line plots from the student solutions for the 2 activities or use student-generated examples.

“¿En qué se parecen los diagramas de puntos?” // “How are the line plots the same?” (They both show data that is measured in fractions. The fractions are all eighths. There are 12 measurements in each line plot.)

“¿En qué son diferentes los diagramas de puntos?” // “How are the line plots different?” (The numbers for the game are just numbers. The other ones are weights. The numbers for the game only go up to $$\frac{10}{8}$$. There is more variation in the weights of the eggs.)