# Lesson 3

Midamos en un mapa

## Warm-up: Observa y pregúntate: De costa a costa (10 minutes)

### Narrative

The purpose of this warm-up is to elicit ideas about length and distance on maps, which will be useful as students measure the distance between cities on maps throughout the lesson activities. While students may notice and wonder many things about the map and map features, comments about the distance between cities, states, or other features on the map are the most important.

If there is a range of background knowledge about maps, cities, and states, it may be helpful to focus the synthesis on sharing what students know about U.S. geography and map features that will be helpful when completing the first activity.

### 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?

### Activity Synthesis

• Based on student responses, answer any questions to clarify the labels for cities and states.
• “¿Qué cosas podríamos medir en un mapa?” // “What are things we could measure on a map?” (lines/borders of the states, the length or width of states, the distance between states and cities, the distance from one side of the country to the other)

## Activity 1: Midamos en el mapa (20 minutes)

### Narrative

The purpose of this activity is for students to measure lengths to the nearest centimeter and to find the total distance each student moves on the map. The synthesis focuses on sharing student methods for addition using properties of operations and the sums they know from memory. When students measure and represent the trips with equations and find the total distance on the map, they reason abstractly and quantitatively (MP2).

Depending on students’ experiences with maps and U.S. geography, it may be helpful to pause during the activity to share the strategies students use for locating cities and states on the map.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk. For example, once students get the measurements for how far a child traveled, check in to discuss their strategy and provide feedback on efficiency and accuracy. Another option is once the students complete numbers 1–3, check in to discuss their strategy for finding the total distance each child traveled.
Supports accessibility for: Attention, Organization

### Required Materials

Materials to Gather

Materials to Copy

• Measurement Map

### Launch

• Groups of 2
• Give each student a ruler and a map.

### Activity

• “Usen el mapa y sus herramientas para medir las distancias que cada estudiante recorre” // “Use the map and your tools to measure the distances each student travels.”
• 15 minutes: partner work time
• As students find the total length for each trip, monitor for students who:
• explain or show methods that create equivalent, but easier or known sums
• explain methods based on using known facts

### Student Facing

Dibuja una recta para representar la distancia que hay entre estas ciudades del mapa. Luego, mide la longitud en centímetros.

1. Noah empezó en Trenton, Nueva Jersey.

1. Primero, viajó a Harrisburg, Pensilvania. _____ cm
2. Luego, viajó de Harrisburg a Indianápolis, Indiana. _____ cm
3. Por último, viajó de Indianápolis a Saint Paul, Minnesota. _____ cm
2. Diego empezó en Sacramento, California.

1. Primero, viajó a Phoenix, Arizona. _____ cm
2. Luego, viajó de Phoenix a Santa Fe, Nuevo México. _____ cm
3. Por último, viajó de Santa Fe a Topeka, Kansas. _____ cm
3. Lin empezó en Austin, Texas.

1. Primero, viajó a Oklahoma City, Oklahoma. _____ cm
2. Luego, viajó de Oklahoma City a Nashville, Tennessee. _____ cm
3. Por último, viajó de Nashville a Augusta, Maine. _____ cm

4. Encuentra la longitud total del recorrido de cada estudiante. Representa el total con una ecuación.

1. Longitud total del recorrido de Lin
2. Longitud total del recorrido de Diego
3. Longitud total del recorrido de Noah

### Activity Synthesis

• Invite 1–2 previously identified students to share their equation for Diego’s total.
• “¿Cómo encontraron la longitud total del recorrido de Diego? ¿Por qué tomaron esa decisión?” // “How did you find Diego’s total? Why did you make that decision?”
• Invite 1–2 previously identified students to share their equation for Lin’s total.
• “¿Cómo encontraron la longitud total del recorrido de Lin? ¿Por qué tomaron esa decisión?” // “How did you find Lin’s total? Why did you make that decision?”

## Activity 2: ¿Cuánto más largo? (15 minutes)

### Narrative

The purpose of this activity is for students to compare the lengths they measured in the previous activity. Students are encouraged to share and compare strategies they use for finding the unknown length.

As students compare lengths, ask them about the methods they are using. In particular, identify students who are using the following methods for finding difference:

• making equivalent, but easier sums or differences (making 10)
• using known facts (changing equations to make known facts, using relationship between addition and subtraction, etc.)
MLR2 Collect and Display. Circulate, listen for, and collect the language students use as they compare lengths. On a visible display, record words and phrases such as: “más largo”, “más corto”, “centímetro más cercano”, “distancia”, “suma” y “diferencia” // “longer,” “shorter,” “nearest centimeter,” “distance,” “sum,” and “difference.” Invite students to borrow language from the display as needed, and update it throughout the lesson.

• Groups of 2

### Activity

• “Ahora respondan las preguntas sobre las longitudes de los recorridos que los estudiantes hicieron en el mapa. Asegúrense de compartir con su compañero cómo pensaron” // “Now answer the questions about the length of the path the students traveled on the map. Be ready to share your thinking with your partner.”
• 4 minute: independent work time
• 2 minutes: partner discussion
• As students find the difference of Lin's and Noah’s trips, monitor for students who:
• use a known addition fact
• explain or show counting up or back to make ten ($$9 + 1 = 10$$, $$10 + 7 = 17$$, $$1 + 7 = 8$$)
• explain or show methods that create equivalent, but easier or known differences (add 1 to 17 and 9 to create $$18 - 10 = 8$$)

### Student Facing

Usa tu mapa y las historias de la actividad anterior para responder las preguntas. Representa cada historia con una ecuación que tenga un símbolo para representar la longitud desconocida.

1. ¿Cuánto más corta es la longitud total del recorrido de Diego que la longitud total del recorrido de Lin?
2. ¿Cuánto más larga es la longitud total del recorrido de Diego que la longitud total del recorrido de Noah?
3. ¿Cuánto más corta es la longitud total del recorrido de Noah que la longitud total del recorrido de Lin?

### Student Response

If students add the lengths of the student trips rather than finding the difference, consider asking:

• “¿Quién hizo el recorrido más largo? ¿Este recorrido es un poco más largo o mucho más largo que los otros recorridos?” // “Who’s trip is longer? Is their trip a little longer or much longer?”
• “¿Cómo podrías usar un diagrama para mostrar la diferencia de las longitudes de los recorridos?” // “How could you use a diagram to show the difference between the lengths of their trips?"

### Activity Synthesis

• Invite previously identified students to share their equation that shows the difference of Lin's and Noah's trips, or display: $$17 - 9 = {?}$$

• “¿Cómo podrían usar un hecho de suma que se sepan para encontrar el número desconocido?” // “How could you use an addition fact that you know to find the unknown?” ($$9 + 8 = 17$$)
• “¿De qué otra forma podrían hacer que esta diferencia fuera más fácil de encontrar?” // “What is another way you could make this an easier difference to find?” (You could think about making a 10. Add 1 to the 9 and think about how many more you would need to get to 17. Add 1 to both numbers and subtract 10.)
• “Estos son dos métodos buenos para encontrar sumas y diferencias con precisión y rapidez: usar hechos de suma que ya se sepan y buscar maneras de formar expresiones más fáciles” // “Using addition facts you know and looking for ways to make easier expressions are two good methods for finding sums and differences accurately and quickly.”

## Lesson Synthesis

### Lesson Synthesis

“Compartan lo que hicieron en el cierre” // “Share your work from the cool-down.”

1 minute: partner discussion

Share responses.