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Grade 3Lesson Title: Elapsed Time

Unit 1: Addition and Subtraction Applications within 100 (Lesson 2 of 4) Time Frame: 5 to 7 daysEssential Question: How does elapsed time help us plan and organize real life responsibilities?Targeted Content Standard(s): Student Friendly Learning Targets3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

I can… Use a number line to represent and

solve problems involving elapsed time. Solve elapsed time problems by reading

a schedule. Solve for start unknowns, change

unknowns, and final unknowns in problems involving elapsed time.

Targeted Mathematical Practice(s): Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for an express regularity in repeated reasoning

Supporting Content Standard(s): (optional)2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Explanation of Rigor: (Fill in those that are appropriate.)Conceptual:Students will develop the concept of elapsed time.

Procedural:Students will tell and write time to the nearest minute. Students will determine elapsed time using analog and digital clocks.

Application:Students will model elapsed time on a number line.

Vocabulary:Elapsed timeMinuteHour

a.m.p.m.

half hour (half past)quarter hour (quarter to, quarter past)

Evidence of Learning (Assessment):

Pre-Assessment: Time Pre Assessment (Lesson 1), Sequencing Time Cards, What’s the question? (Informal)

Formative Assessment(s): The Hours Go By, The Minutes Go By, Pizza Deliveries, Transportation Schedules, Elapsed Time

Summative Assessment: Elapsed Time Assessment, Time Assessment

Self-Assessment: Time Assessment Self-Assessment

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Unit 1: Addition and Subtraction Applications within 100 (Lesson 2 of 4) Time Frame: 5 to 7 daysEssential Question: How does elapsed time help us plan and organize real life responsibilities?

Lesson Segments:1. Sequencing times on a human number line, card set of times in both analog and digital. Students find their

place on line. (before and after) 2. Represent elapsed time in hours on number line diagram, (elapsed time, start time, end time), introduce

elapsed time for minutes on clocks. 3. Represent elapsed time in minutes (within an hour) on number line diagram, (elapsed time, start time, end

time) where’s the unknown? (minutes within an hour ex. 3:15 to 3:42, minutes across an hour ex. 3:45 to 4:08, minutes and hours ex. 1:36 to 4:23) Rich context to thin context

4. Solving elapsed time problems with hours and minutes. 5. Time Assessment

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Unit 1: Addition and Subtraction Applications within 100 (Lesson 2 of 4) Time Frame: 5 to 7 daysEssential Question: How does elapsed time help us plan and organize real life responsibilities?Lesson Procedure:Segment 1

Approximate Time Frame:

50-60 minutes

Lesson Format: Whole Group Small Group Independent

Modeled Guided Collaborative Assessment

Resources: Game Time by Stuart Murphy Telling Time by Jules Older Judy Clocks Sequencing Time Cards

Focus: Sequencing times on a human number line, card set of times in both analog and digital. Students find their place on line. (before and after)

Modalities Represented: Concrete/Manipulative Picture/Graph Table/Chart Symbolic Oral/Written Language Real-Life Situation

Math Practice Look For(s): MP1 Make sense of problems and persevere in solving them. Students will make sense of real-life situations involving time.MP4 Model with mathematics. Students will use and/or create clocks and number lines to model times.MP5 Use appropriate tools strategically. Students will use clocks and number lines to model elapsed time and solve problems. MP7 Look for and make use of structure. Students will look for the structure of our time measurement system.

Differentiation for Remediation: Have students use the Minute Time Cards from Lesson 1 for additional practice in sequencing times.

Differentiation for English Language Learners:

Differentiation for Enrichment: Advanced students may extend times into seconds.

Potential Pitfall(s):

Students may have difficulty with before and after the hour.

Students may have difficulty with a.m. and p.m.

Independent Practice (Homework):

Steps:1. What’s the Question: Write 3:15 on the board. Tell students, this

is the answer to a question. Have them discuss with a partner what the question could be.

2. Students share the questions with the class. Record all of the possible questions. Some examples may be:

“What time do we get out of school?” “What time did the thunder wake me last night?” “How long is the drive to my cousin’s house?” (3 hours 15

minutes) The purpose of this opener is not only to start having students think about time, but also to pre-assess if they are aware that elapsed time can be written in this format.

Teacher Notes/Reflections:

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3. To set the stage for work with elapsed time, read the story Game Time, by Stuart Murphy.

Story synopsis: Last year, the Falcons were the soccer league champs. Can the Huskies beat them this year? The big game is only seven days away—just one week. Then, it's only one day away—24 hours. Then, it's only an hour away—60 minutes. At first, the Falcons come on strong; scoring during the first 15-minute quarter. Will the Huskies catch up by the half: 30 minutes into the game? It's a nail-biter! Right down to the last second!

If this book is unavailable, Telling Time by Jules Older is an alternative resource.


4. Tape a blank number line onto the floor. (You may want to do this before starting Segment 1, so you do not need to waste instructional time.) Give 1 student the 12:00 p.m. (Noon) card and one student the 12:00 a.m. (Midnight) card. Have one of them stand on the end of the number line and the other student stand in the middle of the number line.

5. Distribute cards to the other students so that each student has 1 card. Students must sequence themselves on the number line.

6. Once the students have found their places, ask the students to bend their line so that they form the circle to show that the number line repeats itself in a cycle.

7. Have students write in their journals or on an exit slip to pick a time and record what they would be doing at that time if it was a.m. and what they would be doing at that time if it is p.m. (You may wish to have them use the same time of the card they picked for the sequence.)

For example:

2:35 a.m. I would be sleeping.

2:35 p.m. I would be getting ready to go home from school.

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Segment 2


50-60 minutes



Resources: Geared Clocks The Hours Go By Before and After Optional: Elapsed Time Rulers

Focus: Represent elapsed time in hours on number line diagram, (elapsed time, start time, end time) where’s the unknown?


Math Practice Look For(s): MP1 Make sense of problems and persevere in solving them. Students will make sense of real-life situations involving time.MP4 Model with mathematics. Students will use clocks and number lines to model times.MP5 Use appropriate tools strategically. Students will use clocks and number lines to model elapsed time and solve problems. MP6 Attend to precision. Students should use precision when counting and recording times to the minute. They are also asked to interpret and use precise language to discuss time. MP7 Look for and make use of structure. Students are being asked to make sense of the clock by studying the structure of the clock. Teachers should be looking for students to make connections between the clock and the number line.

Differentiation for Remediation: Some students may benefit from moving the hands on the clock to count the hours or minutes. Then they can record the elapsed times on the number line diagrams.

Differentiation for English Language Learners:Include time measurement vocabulary (hours, minutes).

Differentiation for Enrichment: Students extend understanding of basic time structures to seconds.

Potential Pitfall(s): Independent Practice (Homework): Exit Slip to be completed in class: How will you explain how a number line is used to show elapsed time to someone at home?

Steps:1. Using the large geared clock, demonstrate for students how to

find elapsed time with hours by counting how many hours have passed from 3:00 p.m. to 6:00 p.m.

2. Give each pair of students a geared clock. Have them take turns giving each other a starting hour and an ending hour to find the


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elapsed time. 3. While students are working, circulate to listen to their

conversations and address any misconceptions. Debrief the activity with the whole group.

4. Give students The Hours Go By and have them record the elapsed times by working collaboratively with their partners. Some students may choose to check by using their clocks. Try to encourage students to use the number line rather than counting by 1 hour units on the clock. You may choose to do a number line problem that crosses between a.m. and p.m. together before giving students the page to do collaboratively. For example: Start time 9:00 p.m. End time 2:00 a.m. 3 hours 2 hours

9:00 p.m. 12:00 a.m. 2:00 a.m.

5. Explain to students that, now that they know how to find elapsed times in hours, they can also solve problems involving start or end times if they’re given the elapsed times. For example: If Sam’s practice starts at 4:00 p.m. and takes 2 hours, what time does it end? 2 hours

4:00 p.m. ?

Or, If Tammy’s play practice is 3 hours long and ends at 2:00 p.m., when did it start?

3 hours

? 12:00 p.m. 2:00 p.m.

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6. Give students the small geared clocks. Have students show 5:22 on the clock. Ask students to show you 16 minutes after 5:22. (5:37) Have them put the clock back to 5:22 and show you 35 minutes before 5:22 (4:47)


7. Give students set 1 of the Before and After Activity. Students take turns reading the cards to their partners, having their partners show the times, and checking to see if they agree.

8. When students finish the 1st set, they will match the times for set 2 of the Before and After cards. This can be done by just matching, or by playing a Memory Match game.

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Segment 3




Resources:Pizza DeliveriesThe Minutes Go By

Focus: Represent elapsed time in minutes (within an hour) on number line diagram, (elapsed time, start time, end time) where’s the unknown? (minutes within an hour ex. 3:15 to 3:42, minutes across an hour ex. 3:45 to 4:08, minutes and hours ex. 1:36 to 4:23) Rich context to thin context


Math Practice Look For(s):

MP1 Make sense of problems and persevere in solving them. Students will make sense of real-life situations involving time.MP4 Model with mathematics. Students will use and/or create clocks to model times.MP5 Use appropriate tools strategically. Students will use clocks and number lines to model elapsed time and solve problems. MP6 Attend to precision. Students are also asked to understand the precise language used to discuss time.MP7 Look for and make use of structure. Students are being asked to make sense of the clock by studying the structure of the clock. Teachers should be looking for students to make connections between the clock and the number line.

Differentiation for Remediation: Modeling of more basic addition and subtraction situations on a number may be a necessary precursor for some students.

Differentiation for English Language Learners:Modeling of more basic addition and subtraction situations on a number line may be a necessary precursor for some students.

Differentiation for Enrichment:Some students will be ready for more complex story situations involving extended periods of time that span the 12 o’clock hour or could involve multi-step situations.

Potential Pitfall(s):Some students may struggle in seeing a real-world example represented on a number line.

Independent Practice (Homework): Additional practice representing elapsed time situations on number lines.

Steps:1. Teacher will model elapsed time on an actual clock. Give students

a time, and ask them, “How you would show 20 minutes later on this clock. Have students represent the times on their individual clocks.

2. Draw a number line diagram to represent the same situation for elapsed time on the diagram.

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2. They can now find elapsed times for minutes. For example: Tracy’s team started playing basketball at 4:35 p.m. and played for 42 minutes. What time did they finish their basketball game? 35 minutes 7 minutes

4:25 5:00 5:07 p.m. p.m. p.m.

3. Give students the Pizza Deliveries task to work on collaboratively with partners. Students Sort the cards by question type. Then they solve each problem for the missing value and record the answers next to the appropriate questions.-


4. Have students discuss how they knew which questions were being asked for the situations. Have then describe the similarities and differences between the number line models that they sorted.

5. Give each student a copy of The Minutes Go By record sheet. Give each group of students a set of The Minutes Go By cards. Students record the Card letter for each problem they do. They use the number line diagrams to represent each situation. Then will need to find either the start time, elapsed time, or end time. Have them circle the answer for each situation.

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Segment 4


45-60 minutes



Resources:Transportation SchedulesGeared ClocksBlank Number Lines (optional)Dry Erase boards and markers (optional)

Focus: Solving elapsed time problems with hours and minutes.


Math Practice Look For(s): MP1 Make sense of problems and persevere in solving them. Students will make sense of real-life situations involving time.MP4 Model with mathematics. Students will interpret real-world situations using number line diagrams and/or equations.MP5 Use appropriate tools strategically. Students will use clocks and number lines to model elapsed time and solve problems.

Differentiation for Remediation: Students may need to use clocks and/or number lines with guidance.

Differentiation for English Language Learners:Students may need to use clocks and/or number lines with guidance.

Differentiation for Enrichment:Some students will benefit from more complex elapsed time situations and/or multi-step problems. (Example: Train leaves at 8:07 a.m. and arrives at 10:23 p.m. If the train stops for maintenance for 1:15 minutes at 6:30 p.m., how much time was spent traveling?)

Potential Pitfall(s): Independent Practice (Homework):

Steps:1. Introduce the problems to student groups by writing chart on board.

Create equations where appropriate.Person Task Time Taken

Dad Showers, shaves, brushes teeth

20 minutes

Marie Takes a shower, dries her hair, brushes teeth

Half hour

Mom Takes a bath, dries her hair, brushes teeth

40 minutes

Emmanuel Showers, brushes teeth

Quarter hour

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2. Ask these questions: Who spends the most time in the bathroom? Who spends the shortest time in the bathroom? How long do Dad and Emmanuel spend in the bathroom in all?

(Show work.) How much longer does Mom spend in the bathroom than

Emmanuel? Everyone has to be done in the bathroom by 8:30 a.m. What time

does the first person have to enter the bathroom? (Show all your work.)

Have students share problem-solving strategies and solutions for above questions.


3. Post or project the large bus schedule and give students the Transportation Schedules page. Have students work in pairs plan how they would find the answer to the first question. Have students share out their strategies. Continue this process for questions 2, 3, and 4. For number 5, have students write a question that can be answered using the information on the schedule. Ask students to trade questions and answer their partners’ question.

4. Give each group of 3-5 students a set of train and bus schedule cards. Students choose 1 train schedule and 1 bus schedule to use when completing the tables. They may work on this collaboratively in partners or independently. You may want to have marker boards and dry erase markers available for them to use, in case they want to draw number line diagrams.

5. Have students share some of their observations about the bus and train schedules. Ask them to share some of their strategies for making sense of the schedules.

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Segment 5


50-60 minutes



Resources:Elapsed Time Group ProblemsElapsed Time Assessment

Focus: Solving elapsed time problems with hours and minutes.


Math Practice Look For(s): MP1 Make sense of problems and persevere in solving them. Students will make sense of real-life situations involving time.MP3 Construct viable arguments and critique the reasoning of others Students will share and justify conclusions about their problem solving strategies while listening and critiquing others’ solutions.MP4 Model with mathematics. Students will record number line and equation models to represent the real-life situations.MP5 Use appropriate tools strategically. Students will use number lines to model elapsed time and solve problems. MP6 Attend to precision. Students are also asked to understand the precise language used to discuss time.MP7 Look for and make use of structure. Students will look for the structure of the word problems in relation to our time measurement system.

Differentiation for Enrichment:

Some students will benefit from more complex elapsed time situations and/or multi-step problems. (Example: Train leaves at 8:07 a.m. and arrives at 10:23 p.m.)

Differentiation for Remediation:

Times may need to be adjusted for some students or direct instruction of problem solving situations.


Some students may need direct modeling and direct instruction on problem solving situations.

Potential Pitfall(s):

Some students may struggle in solving real-world example involving elapsed time.

Independent Practice (Homework):

Steps:

1. Give students a problem like the one pictured here to solve:


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- from Teaching Children Mathematics / August 2008

NOTE: Writing an equation to model the elapsed time will assist students in developing the connection to addition and subtraction on the number line.

2. You may use this as an example:A train left the Union station at 4:35 p.m. and arrived in Hershey, Pennsylvania at 10:00 p.m. How long did the trip take?

+ 25 minutes + 5 hours

4:35 p.m. 5:00 p.m. 10:00 p.m.

25 minutes + 5 hours = 5 hours and 25 minutes

3. Here is another sample to use:Samantha is going to visit her cousin in Orlando and visit Walt Disney World. An airplane leaves her hometown at 4:45 p.m. and arrives in Orlando at 7:15 p.m. By train, she can leave at 8:00 a.m. and arrive @ 10:00 p.m. By car, it takes the same amount of time as by plane and train combined.

How long does the car take to get to Florida?


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As students work in groups, circulate and assist where needed.

4. Give each group an elapsed time problem to solve using chart paper. Have the groups present their problems, solutions and strategies to the class. Encourage each group to show their diagram, equation and solution (with appropriate labels). Request that they identify the unknown location when they share (start time, elapsed time, end time).

5. Give the Elapsed Time assessment for students to do independently as a formative assessment.

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Segment 6


50-60 minutes



Resources:Time Assessment

Focus:

Time Assessment


Math Practice Look For(s):

MP4 Model with mathematics. Students will use number line models and equations to model elapsed times.MP5 Use appropriate tools strategically. Students will use analog clocks to show times and number lines to model elapsed time situations. MP6 Attend to precision. Students attend to precise mathematical language to model elapsed time.MP7 Look for and make use of structure. Students will use number lines and equations to interpret the structure our time measurement system.

Differentiation for Enrichment:

Differentiation for Remediation:


Potential Pitfall(s): Independent Practice (Homework):

Steps:

Administer the Time Assessment. This is to be done independently.


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