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# Using Open Number Lines to Determine Elapsed Time

Lesson 5 of 11

## Objective: SWBAT use an open number line to manipulate time, in 30-minute intervals, and to measure elapsed time of ten-minute intervals.

## Big Idea: Open number lines are a versatile and simple mental model for measuring elapsed time. This lesson develops students' analog knowledge using the skills they are close to mastering.

*63 minutes*

#### Warm-Up

*15 min*

Students are given a number line time warm up, with carefully crafted problems that serve the dual purpose of getting them thinking about what 30 minutes represents while also providing me with diagnostic information about remediation needs. We are practicing a 2nd grade standard (2.MD.7).

Before I move them back up to "crossing the 12," I need to insure that the fundamental skill set for reading and recording analog time is in place. I record data on how the students approached this warm-up, both while they are working on it and when I review it after school.

After I collect papers, I make a short list of some of the students' ideas about activities that take approximately 30 minutes, without making any comments other than those needed for clarification. Later, they will be able to reflect on their original analysis of each time interval to determine if it has changed.

Then, for fun, we play briefly with the idea of 30 SECONDS. I pick a handful of children to be "watchers". The rest close their eyes when I say, "go," and raise their hand when they think 30 seconds have passed. I stop timing them anywhere between 45 seconds and 1:10 minutes so that the end time isn't a confounding factor. I repeat this a few times.

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I introduce students to an open number line. If your students have already worked with open number lines, you can skip this section.

I demonstrate the following examples:

**Adding** adding 5 hours to 2 pm and 5 hours to 9 pm.

**Subtracting** 8 hours from:

9 p.m., 4 p.m.

**Determining the length of an activity with a given start and end point:**

If an activity starts 9 a.m. and ends at 1 p.m., how long was the activity?

How about if the activity starts at 6 p.m. and ends at 11 p.m.?

Using a number line to compute elapsed time is a helpful tool, but may not be the best introduction to open number lines because, technically, it represents an iterative 12-hour cycle.

Also, although a number line is an excellent model to demonstrate mathematical thinking as well as an effective strategy, if students are not accustomed to using them I recommend that you practice several times to ensure that students know how to use them. You'll be glad you did because you can continue to use open number lines when introducing multiplication and they are particularly useful in teaching fractions.

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Now we are ready to begin using an open "time" number line as a tool when reasoning with time. I give students the following problems and quickly go over each one. The primary goal here is to make sure students understand how to use not only an open number line, but one that is special to the context of time. It also is a reteach for those who are still developing their concept of elapsed time, to the hour, and crossing 12 noon and 12 midnight.

Adding 3 hours to:

9 p.m., 11 p.m., 5 a.m.

Adding on 7 hours to:

1 p.m., 10 p.m.

Subtracting 4 hours from:

5 p.m., 10 p.m., 12 p.m.

Subtracting 9 hours from:

11 p.m., 3 p.m. 6 p.m.

If an activity starts at _____ and ends at _______, how long was the activity?

7 a.m. - 12 p.m.

11 a.m. - 4 p.m.

*expand content*

I demonstrate the following examples:

Adding on 30 minutes to:

2 p.m., 9 p.m.

Subtracting 30 minutes from:

9 p.m., 4 p.m.

If an activity starts at _____ and ends at _______, how long was the activity?

6 p.m. - 11 p.m.

9 a.m - 1 p.m.

*expand content*

We work through the following examples together. Students write their answers on individual whiteboards or scrap paper. It is critical to continue to closely monitor student responses.

Add 30 minutes to:

2:00, 3:30, 5:20, 6:50, 7:45, 8:35, 9:50, 10:01, 11:47

Subtract 30 minutes from:

2:00, 3:30, 5:20, 6:50, 7:45, 8:35, 9:50, 10:01, 11:47

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#### Wrap Up

*4 min*

I ask students to (silently) think about how they would teach this to a child who hasn't yet worked with open number lines and time. Then I have them explain their strategies to a partner.

*expand content*

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- UNIT 1: 1st Week: Getting to Know Each Other Through Graphs
- UNIT 2: Addition and Subtraction
- UNIT 3: Multiplication
- UNIT 4: Introduction to Basic Division
- UNIT 5: Division in Context
- UNIT 6: Time
- UNIT 7: Rounding
- UNIT 8: Place Value Practice
- UNIT 9: Fractions
- UNIT 10: Math and Me: Nutrition, Health and More
- UNIT 11: Geometry in Architecture
- UNIT 12: Time Cycle 2
- UNIT 13: Patterns in Math
- UNIT 14: Area and Perimeter
- UNIT 15: Solving Mult-Step Word Problems Using the Four Operations
- UNIT 16: Musical Fractions
- UNIT 17: Volcanoes (Data Collection, Graphs, Addition & Subtraction)

- LESSON 1: It's Time We Begin
- LESSON 2: Time Pictures
- LESSON 3: Lucky Luggage Tags: Elapsed Time to the Hour
- LESSON 4: Lucky Luggage Tags: An International Challenge
- LESSON 5: Using Open Number Lines to Determine Elapsed Time
- LESSON 6: Fractional Parts of an Hour: An Investigation
- LESSON 7: Fractional Parts of an Hour (Day 1)
- LESSON 8: Fractional Parts of an Hour (Day 2)
- LESSON 9: Review of Telling Time to 5 Minutes
- LESSON 10: Time to the Minute
- LESSON 11: Time Midway Assessment