# Lesson 4

Midamos y ubiquemos

## Warm-up: Observa y pregúntate: Diagramas de puntos (10 minutes)

### Narrative

The purpose of this warm-up is to elicit students’ understanding of line plots, which will be useful when students create and analyze line plots in a later activity. While students may notice and wonder many things about the measurement data, the characteristics of the line plot are the important discussion points.

### 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 compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Student Facing

¿Qué observas? ¿Qué te preguntas?
paciente longitud del pie (cm)
A 12
B 18
C 20
D 18
E 18
F 20
G 17
H 21

### Activity Synthesis

• “¿En qué se parecen el diagrama de puntos y la tabla? ¿En qué son diferentes?” // “How is the line plot the same as the table? How is it different?” (They both represent the lengths of patients’ feet. They both show the same measurements. The table helps you see the length of each patient’s foot. The line plot helps you see the measurements together, but doesn’t show you which patient had which length.)
• As needed, revisit features of a line plot (scale, meaning of each X, titles).

## Activity 1: ¿Puedo sacarle punta a mi lápiz? (20 minutes)

### Narrative

The purpose of this activity is for students to measure the length of objects (pencils) to the nearest centimeter and record their data in a table. Students add and subtract to answer questions about the data in the table and share strategies for how they find sums and differences. The numbers in the chart were chosen to invite students to look for ways to use methods based on the properties of operations and using known sums within 20 to find the total lengths.

Action and Expression: Develop Expression and Communication. Give students access to base-ten blocks or connecting cubes to represent the numbers they will add. Encourage students to build a ten when they can.
Supports accessibility for: Conceptual Processing, Organization

### Required Materials

Materials to Gather

### Required Preparation

• Each students needs an unsharpened pencil.
• The activity works best if it is likely that students will have a range of pencil lengths between and among groups. If necessary, sharpen pencils to different lengths and distribute them randomly to students.

### Launch

• Groups of 3–4
• Give each student an unsharpened pencil and a centimeter ruler.
• “Sin medir, estimen la longitud de un lápiz nuevo” // “Without measuring it, estimate the length of a brand new pencil.”
• 30 seconds: quiet think time
• Share responses.
• “Midan el lápiz al centímetro más cercano” // “Measure the pencil to the nearest centimeter.” (18 cm)
• 1 minute: group work time
• Share responses.

### Activity

• Display the table.
• “En la tabla se muestran las longitudes de los lápices de 4 grupos de estudiantes” // “The table shows the length of pencils from 4 different student groups.”
• “Encuentren la longitud de su lápiz y compártanla con su grupo. Escriban las medidas de su grupo en la tabla” // “Find the length of your own pencil and share it with your group. Record your group’s measurements in the table.”
• 4 minutes: group work time
• “Usen la tabla para encontrar la longitud total de los lápices de cada grupo” // “Use the table to find the total length of each group’s pencils.”
• 4 minutes: independent work time
• Monitor for students who:
• look for ways to make sums by making 10 or finding easier sums

### Student Facing

grupo longitud de los lápices en cm longitud total
A 8 13 12 7
B 9 15 7 10
C 12 13 8 6
D 9 9 11 13
E

1. Mide la longitud de tu lápiz. _______ cm
2. Escribe las longitudes de los lápices de tu grupo en la tabla.
3. Encuentra la longitud total de los lápices de cada grupo.

### Student Response

If students appear to only find the total lengths by adding each length from left to right or if student methods are unclear, consider asking:

• “¿Cómo encontraste la longitud total de los lápices del grupo _____?” // “How did you find the total length of group _____’s pencils?”
• “¿Cuáles longitudes sumaste primero? ¿Por qué?” // “Which lengths did you add first? Why?”
• “¿Puedes pensar en otra manera de encontrar la suma?” // “Can you think of another way to find the sum?”

### Activity Synthesis

• Invite previously identified students to share strategies for how they found the total lengths.
• Record equations to emphasize how students rearranged or decomposed addends to make 10 or find sums.

## Activity 2: ¿Se apuntan a hacer un diagrama? (15 minutes)

### Narrative

The purpose of this activity is for students to plot their measurement data and to use the data to answer questions (MP2). In the activity synthesis, students share the methods they use to add or subtract within 20 and discuss different ways that they can use the data in a line plot.

MLR2 Collect and Display. Synthesis: Direct attention to words collected and displayed from the previous lesson. Add to the display to include more comparison and measurement words. Invite students to borrow language from the display as needed, and update it throughout the lesson.

• Groups of 2

### Activity

• “Usen la tabla de medidas para hacer un diagrama de puntos. Cuando hayan terminado, comparen sus diagramas y resuelvan cualquier desacuerdo con su compañero” // “Use the table of measurements to create a line plot. When you and your partner are finished, compare your plots and work together to resolve any differences.”
• 4 minutes: independent work time
• 2 minutes: partner discussion
• “Juntos, respondan las preguntas” // “Work together to answer the questions.”
• 3 minutes: partner work time

### Student Facing

1. Usa las medidas de los lápices para hacer un diagrama de puntos.

2. ¿Cuál es la longitud más común? _______
3. ¿Cuál es la longitud menos común? _______
4. ¿Cuántos estudiantes tenían un lápiz con una longitud mayor que 10 cm? _______
5. ¿Cuál es la diferencia entre la longitud del lápiz más largo y la del lápiz más corto? Escribe una ecuación que represente la diferencia.
6. ¿Cuál es la diferencia entre la longitud del lápiz más corto y la de un lápiz sin punta? Escribe una ecuación que represente la diferencia.

### Activity Synthesis

• Invite 1–2 students to share methods for how they found the difference between the longest and shortest pencil or the difference between the shortest pencil and an unsharpened pencil. Consider selecting strategies based on making 10 and using known facts.
• “¿Qué otras preguntas podríamos responder usando el diagrama de puntos?” // “What other questions could we use the line plot to answer?” (How many people had a pencil that was _____ cm long? How many more students had a pencil that was _____ cm long than students who had a pencil that was _____ cm long?)
• Display a completed table from the first activity and a line plot from the second activity.
• “¿Qué preguntas son más fáciles de responder usando el diagrama de puntos? Expliquen sus ideas” // “What questions are easier to answer with the line plot? Explain.“

## Lesson Synthesis

### Lesson Synthesis

“Hoy usamos la suma y la resta para encontrar sumas de longitudes y para comparar longitudes. Compartimos maneras de usar los hechos numéricos que ya nos sabemos. También compartimos maneras de formar 10 para hacer que las sumas y las diferencias fueran más fáciles de encontrar” // “Today we used addition and subtraction to find sums of lengths and to compare lengths. We shared ways we used facts we know and ways to make 10 to make sums and differences easier to find.”

Display:

$$14 - 8$$
$$14 - 4 = 10$$

“Mai está encontrando la diferencia entre 14 y 8” // “Mai is finding the difference between 14 and 8.”

“Primero, ella piensa: ‘Sé que $$14 - 4$$ es 10’” // “First, she thinks, ‘I know $$14 - 4$$ is 10.’”

“¿Qué debería hacer ahora?” // “What should she do next?” (take away 4 more because you have to take away 8, find $$10 - 4 = 6$$)

If time, “¿De qué otra manera podrían usar un hecho numérico que ya se saben para encontrar el valor de $$14 - 8$$?” // “What is another way you could use a fact you know to find the value of $$14 - 8$$?” ($$8 + 6 = 14$$)