The purpose of this activity is for students to measure lengths on a map to the nearest centimeter and to find the total of three lengths. 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 lengths on the maps with equations and find the total length, 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.

• 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?”
• Make sure all students have the correct totals recorded because they will use these totals in the next activity.

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 lengths.

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

• Make equivalent, but easier sums or differences. (Example: Making a ten.)
• Use known facts. (Example: Change a subtraction equation to an addition equation with an unknown addend.)

• “¿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 entre sus longitudes?” // “How could you use a diagram to show the difference between their lengths?"

• Invite previously identified students to share their equation that shows the difference of Lin's and Noah's trips, or display:

• “¿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?” ()
• “¿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?” (Think about making a ten. Add 1 to the 9 and think about how many more we 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.”