This Warm-up prompts students to carefully analyze and compare the features of line plots. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminology students use to talk about the characteristics of line plots with fractional measurements, which students have seen 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 3 diagramas de puntos que vayan juntos. Prepárense para compartir por qué van juntos” // “Pick 3 line plots that go together. Be ready to share why they go together.”
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.
¿Cuáles 3 van juntos?
A
B
C
D
Student Response
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Advancing Student Thinking
Activity Synthesis
Display Line Plot D.
“¿Qué les dice este diagrama de puntos sobre los datos?” // “What does this line plot tell you about the data?” (A total of 8 items were weighed in pounds. All weights were less than 1 pound. Only 1 item weighed half a pound, and 1 item was less than half a pound. Most of the weights were more than half a pound.)
If it doesn’t come up in the discussion, ask:
“¿Cómo podemos saber cuáles son las fracciones de una libra que muestran las marcas del diagrama?” // “How can we tell which fractions of a pound are shown in the marks of the diagram?” (The number line has 8 partitions, so it’s eighths. Each part represents one-eighth. The data shows , or , , or .)
“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
Standards Alignment
Building On
Addressing
5.NF.A.1
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, . (In general, .)
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 Activity 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
Launch
Groups of 2
Display the number line image from the student book.
“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 book. Let’s practice.”
Demonstrate how to use the pencil and the paper clip to make 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 marcas de 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.
Jueguen “Suma de fracciones” con su compañero.
Hagan girar la ruleta dos veces.
Sumen las 2 fracciones.
Marquen la suma en el diagrama de puntos.
Jueguen por turnos hasta que tengan 12 puntos de datos entre los dos.
¿Cómo supieron dónde ubicar las sumas de octavos?
¿Cuál es la diferencia entre el número mayor y el número menor que marcaron?
¿Qué observan acerca de los datos que recolectaron?
Student Response
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Advancing Student Thinking
Activity Synthesis
Ask previously identified students to share their thinking.
“¿Alguien marcó un 1? ¿Qué números sacaron?” // “Did anyone record a 1? What did you spin?” (I got 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 to, to , and to , and none of those is possible.)
“¿Cuál fue el mayor número que marcaron?” // “What is the greatest number you recorded?” (, )
“¿Es posible obtener más de ?” // “Is it possible to get more than ?” (No, the biggest number is , and two of those is .)
“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?” (, , or any other fraction with a denominator that is not a factor or a 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
Standards Alignment
Building On
Addressing
5.MD.B.2
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
The purpose of this activity is for students to use measurement data to make a line plot, and then to 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 ounces is interesting because it uses two fractions referring to different quantities: is a fraction of the eggs and is their weight in ounces. The focus of the Activity 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. Advances: Reading, Representing
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:
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 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 of 12 and then counted the number of eggs that weighed ounces. Both were 3, so Jada is correct.)
If students do not write an equation matching Jada’s response, consider displaying the equations and .
“¿Cómo está representado el razonamiento de Jada en estas ecuaciones?” // “How do these equations represent Jada’s reasoning?” (Both show that of the 12 egg measurements is 3 eggs. One equation uses multiplication and the other equation uses division.)
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 Responses for the two 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. All fractions are 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 . There is more variation in the weights of the eggs.)
Standards Alignment
Building On
Addressing
Building Toward
5.MD.B.2
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Estos son los pesos de unos huevos, en onzas. Úsalos para hacer un diagrama de puntos.
Jada dice que de los huevos pesa onzas. ¿Estás de acuerdo? Explica o muestra cómo razonaste.
¿Cuánto más pesa el huevo más pesado que el huevo más liviano? Explica o muestra cómo razonaste.
Student Response
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Advancing Student Thinking
Building Toward
5.MD.B.2
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.