Lesson 3

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.

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

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

• 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)

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.

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

• “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

• Invite 1–2 previously identified students to share their equation for Diego’s total.
• Consider asking:
  • “¿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.
• Consider asking:
  • “¿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?”

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.)

• Groups of 2

• “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 \(18 - 10 = 8\))

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?"

• 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.”