Warm-up: Choral Count: Fifteens (10 minutes)
The purpose of this Choral Count is to invite students to practice counting times by 15 minutes and notice patterns in the count. This will be helpful later in this section when students will solve problems involving addition and subtraction of time intervals.
Students have an opportunity to notice regularity through repeated reasoning (MP8) as they count by 15 minutes over a span of 3 hours.
- “Count by 15 minutes, starting at 12:00.”
- Record as students count. Record times in the count in a single column.
- Stop counting and recording at 3:00.
- “What patterns do you see?”
- 1–2 minutes: quiet think time
- Record responses.
- “How much time passed between 1:15 and 1:45?” (30 minutes) “1:15 and 2:30?” (75 minutes)
- Consider asking:
- “Who can restate the pattern in different words?”
- “Does anyone want to add an observation on why that pattern is happening here?”
- “Do you agree or disagree? Why?”
Activity 1: Time at the Bus Stop (25 minutes)
In this activity, students solve problems involving elapsed time in a way that makes sense to them. Although the problem type may be new, students can reason about them using their understanding of time and of addition and subtraction. They can also support their reasoning by drawing on a clock.
In each problem, students are given a start time and an elapsed time of 24 minutes. To find each end time, students may:
- use words to describe their thinking
- write a series of numbers and symbols to show how 24 minutes is added to the start time
- create a table to track changes in time from the start time to 24 minutes later
- show incremental “jumps” that add up to 24 minutes on the clock
- use a linear representation to show incremental changes from the start time to 24 minutes later
To elicit and discuss as many possible strategies and representations for reasoning about the problems, significant time is allocated for this activity. Students may choose to use any of the strategies or representations they see here to solve elapsed time problems in future lessons.
When they determine what time different events occurred based on the initial time and the 24 minutes of elapsed time students reason abstractly and quantitatively(MP2).
Advances: Representing, Conversing
Supports accessibility for: Organization
- Groups of 2
- “Have you ever ridden a bus? When or where?” (I ride a school bus to school. I ride the city bus with my parents. I rode a bus at the airport to get to our car in the parking lot.)
- “What are some things you need to know about when you ride the bus?” (What time will the bus come? How often does the bus come? Where does the bus pick you up? Where are you getting off? How long will your bus ride take? How much does the bus cost?)
- 1–2 minutes: partner discussion
- Share and record responses.
- “Now solve the problems about Kiran and Elena riding the bus. Show your thinking in any way that makes sense to you.”
- 8–10 minutes: independent work time
- As students work, consider asking:
- “How does your work show the 24 minutes Kiran or Elena waited?”
- “How does your work show the time the bus arrived?”
- “How did you know it would be before or after 4:00 when the bus arrived?”
- Monitor for and identify students who use the strategies listed in the activity narrative.
Kiran arrived at the bus stop at 3:27 p.m., as shown on this clock. He waited 24 minutes for his bus to arrive.
What time did his bus arrive? Show your thinking. Organize it so it can be followed by others.
Elena arrived at the bus stop at 3:45 p.m. She also waited 24 minutes for her bus to arrive.
What time did the bus arrive? Show your thinking. Organize it so it can be followed by others.
Advancing Student Thinking
If students say they aren’t sure how to show their thinking, consider asking:
- “What is the problem about?”
- “What representations have we used with addition and subtraction that could be used here to show your thinking?”
- Select previously identified students to share their responses in any order. Display or record their representations for all to see.
- “In Elena’s problem, how does each of the strategies 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.)
Activity 2: Time on the Bus (10 minutes)
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).
- Groups of 2
- Read the problem as a class.
- “How is this problem like the ones we saw earlier?” (They are all about the passing of time and are related to riding the bus. The start time is given in all of them.) “How is this one different?” (The arrival time is given here, and the amount of time that has passed is missing.)
- 1 minute: quiet think time
- Share responses.
- “How would you solve this problem? Explain which strategies or representations you saw earlier that would be useful for solving a problem like this.”
- 5–7 minutes: independent work time
Here’s another problem about time:
At 6:32 p.m., Elena got on a bus to go home. She got off the bus at 7:10 p.m. How long was her bus ride?
Which strategy or representation would you use when solving a problem like this? Explain your reasoning.
- Invite students to share their reasoning and strategies. Display or record different representations for all to see.
“Today we solved problems about time. We saw that we could use many ways to reason about the solutions and different representations to show our thinking.”
“Which strategies would you want to keep in mind when you solve future problems about time?” (Making a table to keep track of the minutes that have passed. Drawing jumps on a clock and writing down the minutes of each jump before adding them up or seeing where the last jump lands. Using the clock to help me see if the time that passes means going into a new hour. Writing addition or subtraction expressions.)
Record students’ ideas and display them in the next lesson.