In this activity, students solve problems involving elapsed time in a way that makes sense to them. In each problem, students are given a start time and an elapsed time of 24 minutes. Although the context of elapsed time may be new, students can reason about the situations using their understanding of time and of addition and subtraction. They can also support their reasoning by drawing on a clock.

Monitor for and select students with the following approaches to share in the Activity Synthesis:

• Show counting on or adding 24 minutes with incremental “jumps” on the clock.
• Show counting on or adding 24 with incremental “jumps” on a linear representation.
• Show adding 24 minutes in incremental steps with words or a series of numbers and symbols.
• Show adding 24 minutes in incremental steps with a table.

The approaches are sequenced from more concrete to more abstract ways of showing how students might think about counting on or adding in incremental parts of an hour, with a focus on reasoning about getting to the next hour. To elicit and discuss as many possible approaches for reasoning about the problems and organizing their thinking, significant time is allocated for this activity. Students may choose to use any of the approaches they see here to solve elapsed-time problems in future lessons. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven't shared recently.

• Invite previously selected students to share in the given order. Record or display their work for all to see. If no students use one of more of the given strategies, consider demonstrating them.
• Connect students’ approaches by asking:
  • “¿En qué se parece esta forma de encontrar la hora a la que llegó el bus a otras formas de encontrar la hora? ¿En qué es diferente?” // “How is this way of finding the time the bus arrived the same as the other ways? How is it different?”
  • “¿Cómo podemos ver que pasaron 24 minutos en total? ¿Cómo podemos ver la hora a la que llegó el bus?” // “How do we see that a total of 24 minutes has passed? How do we see the time the bus arrives?”
• Connect students’ approaches to the learning goal by asking:
  • “En el problema de Elena, ¿cómo nos ayuda cada una de las formas de encontrar la hora a saber que el bus va a llegar después de las 4:00?” // “In Elena’s problem, how does each of the ways we shared help us see that the bus would come after 4:00?” (If we add the minutes and get a sum that is more than 60, we know that it’s a new hour. On the clock, we can see that there are only 15 minutes until 4:00, so 24 minutes would be past 4:00.)

In this activity, students encounter another type of elapsed-time problem in which the start and end times are given but the elapsed time is not. Students consider possible strategies they saw earlier that could be used to find elapsed time. Although they are not required to solve the problem, students may choose to do so as they think about ways to reason abstractly and quantitatively about the solution (MP2).

• Invite students to share their reasoning and strategies. Display or record different representations for all to see.
• If time allows, invite students to use the strategies they just described to solve the problem.