The purpose of this Warm-up is to have students consider a new type of data representation, the line plot. While students may notice and wonder many things about the two data representations, describing the differences between the data represented in a bar graph (categorical) and the data represented in a line plot (numerical) should be the focus. This Warm-up will provide a foundation for discussions about the features of a line plot and an understanding of how data is represented in this type of graph.
Launch
Groups of 2
Display the image.
“¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discutan con su pareja lo que pensaron” // “Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
Student Task Statement
¿Qué observas? ¿Qué te preguntas?
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿De qué se tratan estas dos gráficas? ¿Cómo lo saben?” // “What are these two graphs about? How do you know?” (One graph is about the size of gloves. The other graph is about hand spans. I can tell from the title and labels on the graphs.)
As needed, clarify the meaning of hand span.
“Hoy vamos a aprender una nueva forma de mostrar datos que recolectamos midiendo longitudes de objetos. Van a tener la oportunidad de medir sus palmos y hacer una presentación con los datos de la clase” // “Today we are going to learn a new way to display data that is collected by measuring the lengths of objects. You are going to get a chance to measure your own hand spans and create a class data display.”
Activity 1
20 mins
Midamos nuestros palmos
Standards Alignment
Building On
Addressing
2.MD.1
Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
The purpose of this activity is for students to generate numerical data by measuring their hand spans in inches. Students trace their hands and measure their hand spans (the length from the tip of the pinky to the tip of the thumb). The student-generated data is used to demonstrate creating a line plot, as they work collectively to represent their hand spans measured in inches. Students add a representation of the length of their hand spans by drawing an x on a sticky note and adding it to the line plot. They make sense of the way the line plot represents a number of measurements and the size of each measurement (MP2). The class line plot will be used in the next activity to discuss the purpose and features of a line plot.
Engagement: Provide Access by Recruiting Interest. Provide choice and autonomy. Provide students access to colored pencils, markers, colored paper, etc. Supports accessibility for: Attention
Launch
Groups of 2
Give students 12-inch rulers.
Activity
“Vamos a seguir midiendo en pulgadas. Cada uno de ustedes va a medir su palmo” // “We are going to continue measuring in inches. Each of you will measure your hand span.”
Display the image of the traced hand.
“Van a medir su palmo, que es la longitud desde su dedo meñique hasta su dedo pulgar. Primero, tracen su mano y después mídanla, redondeando a la pulgada más cercana” // “You are going to measure your hand span, which is the length from your pinky to your thumb. First, you’ll trace your hand and then measure it to the nearest inch.”
“Después de medir su palmo, revisen las medidas de su pareja” // “After measuring your own hand span, check your partner’s measurements.”
6 minutes: partner work time
“Ahora, vamos a hacer una representación para mostrar las medidas de los palmos de todos” // “Now, we are going to make a representation to show everyone’s hand span measurements.”
Give each student a sticky note that is the same size.
“Ahora tenemos que representar los datos que hemos recolectado. Dibujen una X grande en su nota adhesiva” // “Now we need to represent the data we have collected. Draw a big x on your sticky note.”
As needed, demonstrate drawing an x on a sticky note.
Display the blank line plot.
“Si queremos que esta representación le muestre a otros la longitud de todas nuestras medidas, ¿en dónde creen que debe ir la medida de sus palmos?” // ”If we want this display to show others the lengths of all our measurements, where do you think the length of your hand span should go?”
30 seconds: quiet think time
1 minute: partner discussion
Invite students to come up to add their sticky notes to the chart above the corresponding measurement.
Consider asking students to explain how they place their sticky notes.
Student Task Statement
Activity Synthesis
“Acabamos de hacer un diagrama de puntos. Un diagrama de puntos es una forma de mostrar cuántas hay de cada medida, usando una X para cada medición. La recta y los números sobre la recta representan las unidades que usaron para medir. La recta debe verse como los números de la herramienta que usan para medir” // “We just made a line plot. A line plot is a way to show how many of each measurement using an x for each measurement. The line and the numbers on a line plot represent the units you used to measure. The line should look like the numbers on the tool you use to measure.”
“¿Qué representa cada X en el diagrama de puntos?” // “What does each x on the line plot represent?” (Each x represents a measurement of a student hand span.)
“¿Qué representa el número total de marcas de X?” // “What does the total number of Xs represent?” (Everybody's measurement. It's the same number as the number of people in our class today.)
As needed, “El número total de marcas de X representa el número total de mediciones” // “The total number of Xs represents the total number of measurements.”
“¿Cuántas medidas recolectamos para nuestro diagrama de puntos? Expliquen cómo ven sus datos” // “How many measurements did we collect for our line plot? Explain how you see the data.”
1 minute: quiet think time
1 minute: partner discussion
Share responses.
Activity 2
15 mins
Interpretemos nuestros datos numéricos
Standards Alignment
Building On
Addressing
2.MD.9
Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
The purpose of this activity is for students to interpret data represented in a line plot. They engage in a discussion about what they notice and how a line plot can be used to interpret data. After highlighting the features of a line plot, students answer questions about the lengths of students’ hand spans. In the Synthesis, the importance of making Xs the same size in order to accurately reflect our data is stressed (MP6), as students will create their own line plots in later lessons.
MLR8 Discussion Supports. Synthesis: Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class. Advances: Speaking
Launch
Display the class line plot.
“Acabamos de representar los datos que recolectamos, pero si alguien más los mira, no va a saber de qué se trata este diagrama de puntos” // “We just represented the data we collected, but if someone else looks at it, it is not clear what this line plot is about.”
“Sabemos que las gráficas necesitan un título. ¿Cuál puede ser un buen título para estos datos?” // “We know graphs need a title. What could be a good title for this data?” (Class Hand Spans)
1 minute: quiet think time
Share responses and record a title.
“Cuando hicimos gráficas de dibujos y gráficas de barras, escribimos las categorías para que los demás supieran lo que representaba cada grupo de dibujos o cada barra” // “When we made picture graphs and bar graphs we labeled the categories so others would know what each group of pictures or each bar represented.”
“¿Qué representan los números de nuestro diagrama de puntos? ¿Qué les recuerda la forma en la que los números están organizados?” // “What do the numbers on our line plot represent? What does the way the numbers are arranged remind you of?” (The numbers represent lengths in inches. It reminds me of a ruler. It has tick marks and each tick mark is the same length apart.)
“La línea de la gráfica de puntos representa la unidad que usaron para medir. Ella muestra los números en orden y con la misma longitud entre números, como en una regla” // “The line on a line plot represents the unit you use to measure. It shows numbers in order and the same length apart, just like on a ruler.”
“¿Qué unidad de medida representan los números de nuestro diagrama de puntos? ¿Cómo podemos escribir esto?” // “What length unit do the numbers on our line plot represent? How could we label this?” (The lengths of our hand spans in inches. “measurement in inches”)
1 minute: quiet think time
Share responses and record a label.
“La longitud de la línea entre dos marcas debe ser la misma, pero no tiene que coincidir con la unidad que usaron. Es importante escribir en la línea del diagrama de puntos la unidad que usaron al medir para que otras personas sepan lo que significa” // “The length of the line between two tick marks should be the same, but does not have to match the unit you used. It's important to label the line on the line plot with the unit you used to measure so others know what it means.”
Activity
Hemos usado gráficas para responder preguntas. Ahora ustedes van a usar este diagrama de puntos para responder preguntas basadas en estos datos, que representan los palmos de nuestra clase. Piensen en lo que representan las marcas de X mientras responden cada pregunta. Asegúrense de anotar la unidad en sus respuestas” // “We have used graphs to answer questions. Now, you will use this line plot to answer questions based on our class data representing hand spans. Think about what the Xs represent as you answer each question. Make sure you record the unit in your answers.”
3–4 minutes: independent work time
Student Task Statement
¿Cuál es el palmo más largo de tu clase?
¿Cuál es el palmo más corto?
Escribe otra afirmación sobre los palmos. Usa el diagrama de puntos.
Student Response
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Advancing Student Thinking
If students count the number of Xs to determine the longest hand span, consider asking:
“¿En qué parte del diagrama de puntos ves las longitudes de los palmos?” // “Where do you see the lengths of hand spans in the line plot?”
“¿Qué nos dice el número de marcas de X que hay encima de un número?” // “What does the number of Xs above a number tell us?”
Activity Synthesis
Invite students to share the longest and shortest hand span and how they used the line plot.
Invite 3–4 students to share the statements they wrote about the data.
Consider asking:
“¿Cual longitud de palmo fue la más común?” // “Which hand span length was most common?” (The measurement that has the most Xs represents the length that was most common in our class. This is different from having the most votes. _____ inches was the most common measurement.)
“¿Qué medida de longitud de palmo no tuvo ninguna persona de nuestra clase?” // “What is a measurement that no one in our class had for their hand span?” (Any number with no Xs.)
Lesson Synthesis
“Hoy aprendimos una nueva forma de mostrar datos: un diagrama de puntos” // “Today, we learned a new way to display data—a line plot.”
Display the images from the Warm-up.
“¿En qué se parecen y en qué son diferentes las gráficas de barras y los diagramas de puntos?” // “What is the same and different about the bar graphs and line plots?” (Both graphs have numbers. The numbers go up by ones. The bars and the Xs go up in the graphs.)
“¿En qué son diferentes?” // “What is the same different?” (One graph is about glove sizes and the other is about hand spans. One has bars and the other has Xs. In the bar graph, numbers are on the side. In the line plot, the numbers are on the bottom.)
“¿Qué nos dicen los números de cada gráfica?” // “What do the numbers tell us in each graph?” (The numbers in the Glove Sizes graph tell us how many people have each of the glove sizes. The numbers in the Hand Span of Teachers line plot tells us the length in inches of teachers’ hand spans.)
Have feedback on the curriculum?
Help us improve by sharing suggestions or reporting issues.
Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.
Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.