# Lesson 11

Solve Problems Involving Time (Part 2)

## Warm-up: Notice and Wonder: Band Practice (10 minutes)

### Narrative

The purpose of this warm-up is to elicit the idea that many different questions could be asked about this situation involving time, which will be useful when students solve problems in a later activity.

### Launch

• Groups of 2
• Display the situation.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• 1 minute: partner discussion
• Share and record responses.

### Student Facing

What do you notice? What do you wonder?

Han ate his dinner before he caught a bus.
When he got off the bus, he had to hurry to get to band practice on time.

### Activity Synthesis

• “Let’s add times to Han’s situation. What times could we add?” (The time he started or finished dinner. The amount of time he was on the bus. How long he waited for the bus. The time his band practice started.)

## Activity 1: On the Bus Again (15 minutes)

### Narrative

The purpose of this activity is for students to solve problems involving addition and subtraction of time intervals when given times on a clock. Students may choose to show or explain their reasoning in any way, but the clocks are given to encourage use of that representation. Monitor for different ways that students represent their thinking, particularly differences in strategies when the problem involves time crossing the hour mark and when it doesn’t.

MLR8 Discussion Supports. Synthesis. Display sentence frames to support whole-class discussion: “Can you say more about . . . ?” “Why did you . . . ?”
Representation: Develop Language and Symbols. Synthesis: Make connections between representations visible. Supports accessibility for: Conceptual Processing, Memory

### Required Preparation

• Display students’ ideas from the lesson synthesis in the previous lesson.

### Launch

• Groups of 2
• Display the clocks showing when Han got on and off the bus.
• “What time could Han have been eating dinner? What time do you think band practice might start?” (Han could have eaten dinner at 5:00. Band practice might start at 6:45 since we know he had to hurry to get there.)
• 1 minute: partner discussion
• Share responses.

### Activity

• “Now take some time to solve these two problems.”
• 5 minutes: partner work time
• “What time did _____ get on [or off] the bus?”
• “How could you show your ideas on the clock?”
• Monitor for students who used different strategies to solve the two problems, or those who noticed that the time crossed the hour mark in the first problem but not in the second.

### Student Facing

1. For how many minutes was Han on the bus? Explain or show your reasoning.

the time Han got on the bus:

the time Han got off the bus:

2. Draw the minute hand to show that Elena waited for the bus for 32 minutes.

the time Elena started waiting:

the time Elena got on the bus:

### Activity Synthesis

• Select previously identified students to share their responses and reasoning.
• “We noticed that when the time does not cross the hour, we can just add or subtract the number of minutes, such as $$36 - 32=4$$ here. When the time does cross the hour in a problem, we need to make sure to keep track of what hour we are in.”

## Activity 2: Math Libs Time (20 minutes)

### Narrative

The purpose of this activity is for students to solve problems involving addition and subtraction of time intervals in minutes. Students fill a name and activity into each problem before they solve it using any representation that makes sense to them. The synthesis draws attention to the different types of problems that have been solved. Students need to read and think carefully about the given information and the unknown, which differ in most of the situations, in order to decide which calculations to perform (MP2).

### Launch

• Groups of 2
• “We have been solving problems about riding the bus. What are some other activities where you would keep track of the time to the nearest minute?” (recess, TV time, baking or cooking time, class time)
• 1 minute: partner discussion
• Share and record responses. Keep displayed for ideas to use in the activity.

### Activity

• “Work with your partner to fill in a name and activity for each problem. Then, solve the problem.”
• 10 minutes: partner work time

### Student Facing

For each problem, fill in a name and an activity, and then solve the problem. Show your thinking. Organize it so it can be followed by others.

1. $$\underline{\hspace{1 in}}$$ started $$\underline{\hspace{3 in}}$$ at 8:25 a.m. and finished at 8:50 a.m. How much time was spent doing that activity?
2. $$\underline{\hspace{1 in}}$$ finished $$\underline{\hspace{3 in}}$$ at 5:38 p.m, after spending 20 minutes. What was the start time?
3. $$\underline{\hspace{1 in}}$$ started $$\underline{\hspace{3 in}}$$ at 10:45 a.m. and finished at 11:18 a.m. How much time was spent on it?
4. $$\underline{\hspace{1 in}}$$ started $$\underline{\hspace{3 in}}$$ at 3:30 p.m and took 45 minutes to complete it. What was the finish time?

### Activity Synthesis

• For each problem, invite groups to share what they filled in and how they solved the problem.
• Keep the problems displayed.
• “How are these problems alike?” (They are all about doing an activity for a certain amount of time.)
• “How are they different?” (They are about different activities and give different kinds of information. Sometimes we know the start time and end time. Other times we know either the start time or end time, and how much time passed. We are solving for different things.)
• Highlight ideas about how the problems had different unknowns (start, end, and time that passed).

## Lesson Synthesis

### Lesson Synthesis

“Today we solved a variety of problems involving time, including finding how much time has passed and when something started or ended.”

“What are some strategies that you found helpful for solving these problems?” (I can use the same counting strategies that I used for adding and subtracting numbers. I can count by 5, 10, 15, or other numbers. I can use a clock, a number line, or a table to help keep track of the counting. I can also write equations or use words.)

## Student Section Summary

### Student Facing

In this section, we learned to tell and write time to the nearest minute. We solved addition and subtraction problems about time.

the time Han got on the bus:

the time Han got off the bus:

Here is one way to find out how much time Han spent on the bus:

• Count up 3 minutes from 5:42 to 5:45, and then 15 minutes from 5:45 to 6:00.
• Count up 30 minutes from 6:00 to 6:30, and then 7 more minutes to 6:37.
• Add the minutes, $$3 + 15 + 30 + 7$$, to get 55.