EXPLORING MATHEMATICS USING THE CLOCK AND TIMEKEEPING
by
Melinda Aresta, Barri Crowley, Nicole Ruoppo, and Danielle Schwass
A MATHEMATICS UNIT PLAN
SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
ISSUES AND TRENDS IN MATH EDUCATION (EDU 532)
Instructor: Dr. Hari P. Koirala
EASTERN CONNECTICUT STATE UNIVERSITY
EDUCATION DEPARTMENT
MARCH 7, 2005
Table of Contents
Content Page
Concept Map 
3

Unifying theme 
4

Assumptions 
4

Grade level 
4

Topics to be covered 
4

Required resources 
4

Unit features 
5

Unit objectives and the standards alignment 
6

Tentative timeline 
9

Lesson 8: “Field Trip to Six Flags” 
25

Worksheet 
2931

Lesson connections 
25

Unit extension and modification 
2627

Unit assessment 
2728

Group work class worksheet 
2930

Quiz/exam

3235 
Observation and interview notes 
36

Bibliography 
39

Unit Framework:
Unified Theme
The theme for this unit is to use the clock to explore mathematical concepts. Time concepts will be used in a meaningful way to reveal to students the relevance of accurate time measurement to their lives and the application of various mathematical concepts.
Assumptions
It is assumed that students will have a basic understanding of time before starting this unit. They should be able to tell time to the hour, minute, and second. They may not however have an indepth or flexible understanding of these units. They may have limited understanding of fractions of an hour, elapsed time, estimation of time, or the geometry associated with the clock. It is assumed that this unit will provide students a more indepth understanding of these concepts.
GradeLevel 46
The lessons in this unit can be modified for grades 28, with modifications for specific groups, or even individual students. The lessons presented here are designed for students in grades 4, 5, or 6.
Topics in this unit include:










Required Resources
Various clocks (both standard and digital), map of US and world with time zones, computer with access to Internet, calculator, analog clock manipulatives, graph paper, protractors, construction paper, straws
Unit features:
Unit Objectives 
Alignment 

NCTM Standards 
Connecticut Standards 

By the end of the unit students will: 


1. Calculate local date and time for places around the world. 
Number & Operations Geometry Measurement Connections Communication Representation Reasoning & Proof 
Number Sense Operations Measurement Spatial Relationships and Geometry Discrete Mathematics Patterns 
2. Explore universal time and issues related to time by visiting Internet sites like U.S. Naval Observatory Data Services page and NASA. Collect data about time, for example, time differentiation (A.M. vs. P.M.), the importance of time in science, related careers, etc. 
Number & Operations Geometry Measurement Data Analysis & Probability Reasoning & Proof Connections Communication Representation 
Number Sense Measurement Spatial Relationships and Geometry Discrete Mathematics Estimation and Approximation
Patterns 
3. Explore and explain variations in measurements of time and individual clocks. 
Connections Measurement Reasoning & Proof Data Analysis & Probability 
Measurement Estimation and Approximation Probability and Statistics Patterns 
4. Communicate time measurement with each other using language arts and manipulatives. 
Number & Operations Communications Measurement 
Number Sense Operations Measurement 
5. Design a clock using a straw compass. 
Problem Solving Measurement Geometry Representation 
Estimation & Approx. Measurement Spatial Relationships and Geometry 
6. Convert analog time to digital time and vice versa. 
Number & Operations Measurement Connections 
Number Sense Operations Measurement 
Unit objectives and alignment to NCTM and Connecticut standards continued
Unit Objectives 
Alignment 

NCTM Standards 
Connecticut Standards 

7. Calculate fractions of time when given digital time or visual of analog clock time. 
Number & Operations Measurement Connections Representation 
Number Sense Operations Ratios, Proportions, and Percents
Measurement 
8. Calculate percentage of an hour when given digital time or visual of analog clock time. 
Number & Operations Measurement Connections Representation 
Number Sense Operations Ratios, Proportions, and Percents
Measurement 
9. Calculate elapsed time by using time stories and analog representations. 
Number & Operations Measurement Connections Representation Algebra Communications 
Number Sense Operations Measurement Discrete Mathematics Algebra & Functions 
10. Design a schedule/trip when given time parameters. 
Number & Operations Algebra Measurement Connections Problem Solving Representation 
Number Sense Operations Estimation and Approx. Measurement Algebra & Functions Discrete Mathematics 
11. Calculate mean, median, and mode of different times. 
Data Analysis & Probability Communication 
Operations Probability and Statistics Discrete Mathematics 
12. Make diagrams (bar graphs/pie charts) to represent how quantities may vary and how schedules are affected due to passage of time. 
Data Analysis & Probability Connections Measurement Communication Representations 
Estimation and Approx. Measurement Probability and Statistics Patterns Discrete Mathematics 
13. Make connections between pie chart and clock face and a circle with all of its geometric parts. 
Geometry Connections Representation 
Spatial Relationships and Geometry 
Unit objectives and alignment to NCTM and Connecticut standards continued
Unit Objectives 
Alignment 

NCTM Standards 
Connecticut Standards 

14. Use knowledge of clocks as circles to determine special angles, calculate angles in degrees, and discuss the relationship between angles and circles. 
Number & Operations Geometry Connections Measurement Representation 
Number Sense Operations Measurement Spatial Relationships and Geometry 
15. Use equations and symbols to solve problems related to time. 
Number & Operations Algebra 
Number Sense Operations Algebra & Functions 
16. Articulate through journals and writing assignments ideas about time and how it affects their everyday life. (Standards addressed will vary depending on student’s personal experiences with this unit, his/her connections to it, and whichever topics he/she chooses to discuss). 
Standards will vary. 
Standards will vary. 
17. Work both individually and in pairs. 
Communication
Representation 

Tentative Timeline for Exploring Mathematics using the Clock
This unit will be comprised of approximately 14 lessons to be completed in about three to four week’s time, with each lesson taking up about 4550 minutes of classroom time, except for the Scheduling lesson, which may take longer. This unit may be introduced in association with science around time measurement, and possibly near about the time for a major field trip. The following is a tentative timeline for the 14 lessons, which may be completed in at least one class period each, depending on school schedule.
Lesson 1: 
Introduction of the history and science behind time measurement, Universal Time and time zones

Lesson 2: 
What time is it? Exploring variations in clocks

Lesson 3: 
Important time terms

Lesson 4: 
Clock face vs. digital time measurement

Lesson 5: 
Fractions/percents of an hour

Lesson 6: 
Elapsed time

Lesson 7: 
Using the clock to explore variables

Lesson 8: 
Field Trip to Six Flags: The making of a schedule

Lesson 9: 
Calculations of mean, median, and mode

Lesson 10: 
Data analysis of time: using bar graphs

Lesson 11: 
Using a schedule to create a pie chart

Lesson 12: 
Introduction of the circle using the created pie chart and clock face

Lesson 13: 
Using the clock to explore angles

Lesson 14: 
Exploring the Internet

Lesson 15: 
Journal writing/disposition 
Individual Lesson Plans:
Lesson 1
History and Science of Time Measurement
Grade 46
Lesson Description: Ask the students first why they think measuring time is important? What do people today base time measurement on? What did people do in ancient times to measure time? What about months and years? The students could be shown a rotating model of the earth, such as a globe against a light source in a darkened classroom. Using a penlight, point out different areas of the globe and ask students to tell you whether it is day or night at any given time. Use the globe to illustrate the difference between local time and universal time. Ask them why it is important to have a single date and time measurement for the entire earth? Point out the International Date Line and ask students what it means. Students then could explore universal time at http://aa.usno.navy.mil/data/docs/earthview.html, where simulated views of partially lit areas of earth can illustrate further the science behind the measurement of time. Hand out both a US and a world time zone map to each student and use historical events to illustrate that events occurring around the globe can be happening at the same moment, but on different dates and local time. In groups of three or four students, use the time zone maps to calculate what the local date and time would be for several places in the world at the exact time of the classroom activity. Have each group report to the class what time it is at two of their places and discuss how they arrived at their answer.
Modifications for diverse learners: Lower ability learners can visualize the day and night cycle using the globe and work with heterogeneous groupings to contribute and reinforce time concepts for them. Higherlevel learners could explore algebraic reasoning by determining an equation for calculating local time around the world from universal time.
Lesson Connections: To this Unit  This lesson, as do Lessons 2 & 3, connects with all of the proceeding lessons because it sets the framework for discussions and later problems involving time. It defines time and what it is used for both in ancient and modern times. To other disciplines  This lesson connects with science and social studies. It can be used to coincide with a unit on the planets and in discussing the publishing of Benjamin Banneker’s first almanac.
Lesson 2
What Time is it?
Grade 46
Lesson Description: In this lesson, students will explore variations in measurements of time on individual clocks in the classroom or school. (i.e. “this clock is fast or slow”) In groups of two or three, students will record time shown for all clocks in the class and write an explanation for the differences. Based on the previous lesson on Universal Time, ask why there is a variation and if it is justifiable. Ask them what situations in life or work require the time to be exact. For homework, have students write down all of the times shown in their own home, or even the car, and write a onepage explanation for the difference and reflect on what it means.
Modifications for diverse learners: This lesson should be basic for most levels of learners. A further challenge could be to have students list when it is acceptable to use time approximations.
Lesson Connections: To this Unit  This lesson also lays the framework for all other lessons in this unit. It helps students understand the importance of properly working equipment, in this case clocks and watches, in order for calculations to be accurate.
To other Disciplines Geography lends itself to this lesson as students study differences in time between different areas of the country and world.
Lesson 3
Important Time Terms
Grade 46
Lesson Description: The purpose of this lesson will be to reinforce knowledge of minutes and hours shown on a clock and the language used to express the time shown. Students will also explore the passing of time, what it feels like to sit still for one minute, 30 seconds, 15 seconds, etc. Ask them why one minute appears to be such a long time. Give small groups of two or three students a small clock manipulative showing minutes and hours. Students will explore different ways to communicate to each other what time it is using the model to illustrate what time they are referring to. For example, ten minutes past one can also be oneten, ten past one, or even 50 minutes before two o’clock. Quarter or half hour intervals can be used as well to introduce fractions of an hour. Homework could include a crossword puzzle with important time definitions and content words associated with time, such as those brought up so far in the unit, as well as familiar words such as afternoon, midnight, AM and PM.
Modifications for diverse learners: This lesson could easily be modified for diverse learners using only on the hour measurement for lower level students. Higherlevel learners could use seconds and individual minutes rather than quarter hours.
Lesson Connections: To this Unit Another framework lesson, this one helps define terms and poise students for understanding the basic dynamics of an analog and digital clock. To other Disciplines Now is a good opportunity to include this in an Art or Music lesson. As part of an Art lesson students can create a collage by cutting out pictures of various types of time telling devices. The lesson could open by reading from a biography of Salvador Dali, best known for his piece The Persistence of Memory, a.k.a. “Melting Clocks”. Discussing and showing pictures of Dali’s surrealist version of time may lead to group talks on the importance of time in Art, both ancient and modern. As part of a Music lesson, the importance of structured timing in this art form can best be heard in classical composer Johann Sebastion Bach’s “Brandenburg” Concertos. Students can listen to and compare his work to some of today’s modern composers. How is timing important in today’s music?
Lesson 4
Clock Face vs. Digital Time Measurement
Grade 46
Lesson Description: Each student will create a straw compass. Cut a straw in half and connect the two halves by inserting a twist tie between one end of each half. Next tie a pencil to one end of the straw. Students can then draw a circle on a piece of paper. Detach the pencil from the straw compass. Now students can use the straw like the hands of a clock (have students label as a 12hour clock). Students may use the straw to show on their analog clock what 2:35 looks like. They can position the straw on their clock and have group members give the digital time. Analog clock worksheets would have students draw the hands on the clock to match the given digital times.
Modifications for Diverse Learners: Having students create miniclocks that they can use may be helpful for some students who need a visual. These, as well as the straw hands/compass, will also be helpful for visual representation during other lessons in this unit.
Lesson Connections: To this Unit This lesson helps students visualize an analog clock and ‘see’ the fractions and percents they will calculate in the next lesson. To other Disciplines Science and history lessons can easily be adapted at this point, namely the beginnings of time telling such the stars, sun dials, early calendars.
Lesson 5
Fractions/Percents of an Hour
Grade 46
Lesson Description: Fractions  Students will be presented with analog clocks depicting different times and asked to give the fraction of an hour that it represents. For example, what portion of an hour is noted in fraction 20/60? Students will reduce to 1/3 and then translate into digital time, such as 1:20. Students will also be given fractions and asked to draw the clock hands that correspond with it. For example, 30/60 = ½ or 12:30. Students may use miniclocks for this lesson. Percents – In addition, students will convert portions, or percentages, of an hour. For example, students will be asked to label clock to show 25%, 50%, 75%, 33.3%, etc. of an hour.
Modifications for Diverse Learners: Label the 3, 6, 9, 12 on an analog clock. In parenthesis, write 15, 30, 45, 60, respectively.
Lesson Connections: To this Unit Students learn the dynamics of basic timetelling in this lesson in order to be able to understand and calculate elapsed time in Lesson 6. To other Disciplines Other disciplines as well as school activities can be tied to this lesson. For example, what fraction/percent of the class attended the school car wash fundraiser? How close has each student come to achieving his/her goal of reading 10 books?
Lesson 6
Elapsed Time
Grade 46
Lesson Description: Students will create 5 to10 short stories consisting of two to three sentences that show at least one instance where time has elapsed. Have students use straw protractors to create 10 sets of two clocks sidebyside. Label as analog clocks. Students will draw minute and hour hands on each clock. Each clock set will show a change in time. When students have completed creating their math elapsed time problems they will exchange with another student and solve the problems.
time: 3:00 time: 9:30 What is the elapsed time?: 6 hrs 30 minutes
Modifications for Diverse Learners: Students with a strong grasp of elapsed time may try using any possible time configurations, for example: What is the elapsed time between 3:02 and 9:36? Struggling students may practice more with hour, half hour, and quarterhour changes. Some students may want to illustrate their stories. All stories, illustrations, and calculations may then be compiled as part of the class math story journal. Students may later use this journal to practice time and other math skills.
Lesson Connections: To this Unit Students gain experience in scenarios by writing their own short time stories and then calculating elapsed time. Both of these timetelling techniques combined with problem solving skills gained from the next lesson will help them accomplish the scheduling exercise in Lesson 8. Creating time stories helps them use time in real world situations. This will help students visualize themselves scheduling time for different events as the next lesson demonstrates. To other Disciplines: Students can discuss time lapses between World War I and World War II, for example. They can discuss the importance of controlling and knowing the exact time during scientific experiments in order to replicate findings. Referring back to the lesson on Music, discuss the importance of timing to all the musicians in a band, for a competitive figure skater, a distance runner, or a baker.
Lesson 7
Using the Clock to Explore Variables
Grade 46
Lesson Description: Have students calculate word problems using addition, subtraction, or multiplication to denote passage of time. For example:
1) Addition: It is 5:15pm. Susan will talk on the phone 6 hours 45 minutes later. What time will she talk?
12:10am 11:00am 11:10am 12:00am
2) Subtraction: It is 9:00am. Stephen played soccer 6 hours and 50 minutes ago. What time did he play soccer?
2:20am 1:10am 1:20am 2:10am
3) Multiplication: Carin runs 1 mile in 14 minutes. How long will it take her to run 7 miles?
3.5 hours 37 minutes 1 hour 45 minutes 1 hour 38 minutes
(See http://www.teachrkids.com/ for more time word problems)
Students may also create their own time word problems and have classmates try to solve.
Modifications for Diverse Learners: Levels of difficulty can vary. Create separate worksheets using a labeling system that is unknown to the students, for example a basic worksheet may be called Exploring World Variables and a more challenging one may be labeled Investigating Variables, etc. In this way, students can be given appropriate worksheets and the teacher is able to track the level of difficulty without the students’ knowledge.
Lesson Connections: To this Unit As with Lesson 6, this lesson helps students use equations and variables to solve real world scenarios like the ones they will be required to do in Lesson 8. To other Disciplines Students can use these types of equations to figure out how long it will take them to conduct a science experiment or read a chapter in a book.
Lesson 8
Amusement Park Trip
Grades 46
Lesson Description: Students will work with a partner to create a schedule of how they will spend their time while on a class field trip to Six Flags. Students will be provided with a list of activities that they can partake in, as well as how long each activity takes. There will be requirements that must be taken into consideration when creating the schedules.
Modifications for Diverse Learners: The requirements that must be included in the schedule could be changed to make it easier or more difficult, depending on the learner. For more advanced learners, the schedule could also be made to include what time the bus would need to leave the school, as well as finding distances and computing travel costs.
Lesson 9
Calculations of Mean, Median, & Mode
Grade 46
Lesson Description: Students can work in groups of five or seven (preferably odd number) to discuss the time, in minutes it took them to complete homework the night before. Students will calculate and answer worksheet questions about the mean, median, and mode of their scores.
Modifications for Diverse Learners: If some students are on a modified homework schedule, offer the class the opportunity to discuss how many hours (or minutes) they watched television the night before, worked on the computer, read a book, etc. (Students may decide on a handful of different activities and then group themselves accordingly to calculate their activity times, for example everyone who read last night would be in one group, everyone who played video games would be in another). Advanced students may be asked to compute their time in fractions of hours instead of using minutes.
Lesson Connections: By calculating the mean, median, and mode of different times, students learn to use time in nontraditional ways; in other words, they gain experience using time values as raw data aside from their original purpose as mere measurement. This connection helps them make the transition to using graphs and charts in Lessons 10 & 11.
Lesson 10
Data Analysis of Time – Bar Graphs
Grade 46
Lesson Description: Students will work in groups of three to four to make six groups. Each group will choose a different beverage served in the school cafeteria, for example: 1) whole milk, 2) skim milk, 3) chocolate milk, 4) orange juice, 5) apple juice, 6) other. Students will tally how many of their beverages are selected by students during tenminute intervals at one breakfast and one lunch period. Data will be placed into bar graphs.
Modifications for Diverse Learners: There is plenty of opportunity for students of all ability levels to participate and learn together. Groups can be teacherselected to support this diversity. The group work offers struggling students ample time to ask questions of their peers. Students with a better understanding of time, data gathering, and graphing will be able to assist with group members less familiar with these topics. Groups will have the opportunity to divide duties, for example, two may choose to do the actual data gathering while the others design and prepare the bar graphs. Students comfortable with public speaking can choose to lead their group’s discussion about their findings. Students who are PowerPoint savvy may choose to compile the class findings on Excel, creating bar graphs, pie charts, etc, and then produce a slideshow of the overall project. This lesson may be taught over three days or modified into a shorter lesson by including data collected on only two beverages during one meal.
Lesson Connections: To this Unit Time hacks are used to help easily collect data and use it to create graphs. This lesson smoothly transitions to the next lesson where students transfer the data into more complex pie charts. To other Disciplines The nature of constructing bar graphs allows students to use Art skills.
Lesson 11
Using a Schedule to Create a Pie Chart
Grade 46
Lesson Description: Students in fourth and fifth grade can create pie charts of their daily school schedule. Sixth graders may try doing this with weekend, extracurricular, or sports schedules. For example a partial school schedule might include:
8:00am – 10:00am Class Work
10:00am – 10:15am Snack
10:15am – 10:30am Silent Reading
10:30am – 11:15am RLA
11:15am – 11:30am Bathroom Break
Circles for pie charts can be created by cutting a straw in half and connecting the two halves by inserting a twist tie between one end of each half and tying a pencil to one end of the straw, creating a compass. Some sample scheduling questions to ask include:
1) How long is language arts class?
2) Today you would prefer to eat lunch one period earlier. How many minutes
earlier would you prefer to eat?
3) How much longer is Class Work time than your Bathroom Break?
4) How long is your school day?
Modifications for Diverse Learners: Having students create straw compasses may be safer to use in the classroom. Students who leave the classroom for resource room time may or may not choose to include these deviations from the class schedule. Students may use Excel to create pie charts and present to class.
Lesson Connections: To this Unit Pie charts are a natural transition for students to start looking at the clock as a circular figure, enhancing its value as a tool for measurement as well as a perfect geometric shape. To other Disciplines The nature of constructing pie charts allows students to use Art skills.
Lesson 12
Introduction of the Circle using the Created Pie Chart and Clock Face
Grade 46
Lesson Description: Have students use their previously created pie charts and clock faces. Discuss clock/pie chart shape and circles. Using straw compasses, have students practice drawing midpoints, radii, and diameters. Discuss how they are related, how the diameter is twice as long as the radius, and how the circle is divided into two equal parts by diameters. Discuss the distance around the circle.
Sample exercises include:
1) Name the center
2) Name each radius
3) Name each diameter
4) Name each central angle
5) Explain how the length of one radius compares to a diameter
6) Draw a chord on the circle and label the new points
7) Draw a diameter and label the new points
Modifications for Diverse Learners: Introduce students to LOGO, a math program that they can use to create programs based on simple or complex commands.
Lesson Connections: To this Unit As students begin to recognize the clock face as a geometric shape, the next natural progression is to discuss it’s relationship with angles. To other Disciplines Students can use what they have learned about circles during their discussion of planets in science.
Lesson 13
Using the Clock to Explore Angles
Grade 46
Lesson Description: Begin asking students general terminology questions about circles and angles. (What is a circle? Are there straight lines in a circle? What is an angle?) Draw a circle. Draw a right angle inside the circle. Discuss acute angles, right angles, obtuse angles, and rays. Have students draw, identify, and discuss the various angles (30°, 60°, 90°) using times on a clock.
Modifications for Diverse Learners: LOGO can again be used to enhance learning for beginning, moderate, and mastery level students.
Lesson Connections: To this Unit This unit closes with exploring angles, a window for students to future math experiences with geometry. Lessons 15 and 16, Exploring the Internet and Journal Writing/Disposition respectively, may be saved for the end of the unit, but will probably best serve students if interspersed throughout the unit. They will help give students deeper understanding, depth, and a chance for thoughtful exploration, as well as an opportunity for teachers to use as assessment tools. To other Disciplines History lessons can include references to the importance of the circle and angles in creating designs, buildings, and other permanent structures.
Lesson 14
Exploring the Internet
Grade 46
Lesson Description: In groups have students explore time related websites that have been previously saved under “Favorites” and reviewed by the teacher. For example, have students investigate the official U.S. Time Homepage: http://www.time.gov. Students can collect data or use this page as a source for further learning on the topic of time. Links from this page range from when and why we have Daylight Savings Time, Ancient to Modern uses of time, and Advances in Timekeeping.
Modifications for Diverse Learners: This is a good site to use with students who are having trouble understanding time differences worldwide. This site offers visuals to help these students grasp this idea. This site is a valuable goto site and offers some details and definitions students may find helpful. Also, this site offers opportunity for further learning to students interested in gaining more knowledge about timerelated issues and careers.
Lesson Connections: By using the Internet as a guide, students can research time concepts safely by exploring sites earmarked under “Favorites” by the teacher. The Internet is a valuable resource and can help students understand the importance of time in world experiences, as well as how it is used in everyday life.
Lesson 15
Journal Writing/Disposition
Grade 46
Lesson Description: Before or after each lesson have students log their thoughts, concerns, questions about time, and its connections with other topics and disciplines. Students can articulate their learning and be free to make suggestions or comments for this unit. Teachers may use these journals as a form of assessment to measure student progress. A final entry may be geared toward student overall ratings of the lessons and unit. This information is invaluable for future teaching of this unit.
Modifications for Diverse Learners: Students may find these exercises helpful as another method to communicate with the teacher about this unit. Students with difficulty writing or those more creatively inclined may wish to include illustrations, a collage from magazine or newspaper clippings, or poetry about this unit. The journals may be compiled into the class Math lesson book for future reference and studying.
Lesson Connections: To this Unit This lesson connects to all other lessons in this unit as it allows the student and teacher a forum for direct feedback and a source for assessment. To other Disciplines Journaling, writing stories, and creating books are directly related to Reading and Language Arts.
In order to accommodate all learners, all above lessons may incorporate the following:
1 Preteaching
2 Coteaching with special education/paraprofessionals when possible
3 Pairing advanced learners with struggling learners when doing group work
4 Incorporating Hunter model of teaching
5 Use of manipulatives and visuals whenever possible
6 Overhead as well as writing on board
7 Verbal as well as written directions
“Field Trip to Six Flags”
Lesson 8  Scheduling
Grade 46
Standard alignment: This lesson aligns with most of the NCTM and Connecticut standards listed previously in the unit objectives.
Required resources: Instruction/scheduling worksheet, clock manipulatives, if needed
Lesson assumptions: It is assumed that students will have a general understanding of previously learned units of time and how they relate to a clock. However, it is not assumed that students will have a deep enough understanding to feel comfortable with adding and subtracting time. One of the purposes of this lesson is to help students learn time measurement concepts.
Objectives: At the end of this lesson, students will be able to:
a) create an accurate time based schedule
(i) by adding and subtracting times
(ii) using a schedule worksheet
b) understand elapsed time via scheduling
Lesson procedure:
Lesson Connections: To This Unit – This lesson serves as a review of elapsed time and shows students the real world usefulness of scheduling. To other disciplines: Scheduling, as a whole, is useful for time management, which is necessary for being successful in school, as well as in the workforce. This could also be related to timelines which could be used in all disciplines (social studies, science, math) or sequencing of stories (reading).
Unit extension and modifications: As mentioned above, the lessons within this unit are well connected to each other and work smoothly. In addition to the lessons discussed, this unit plan is also relevant to other important mathematical topics. For example, time can easily relate to:
a) Computing (students can visit www.POPClocks.com. Clocks show population of the USA as well as world population growth. Over the course of a day, have students log on to obtain new population data).
(i) Have them subtract former totals from new ones to learn number of individuals by which population increased.
(ii) Calculate how many new world citizens are born in a day.
(iii) To challenge advanced students, compute rate of growth by minute or hour.
b) Modular arithmetic (repetitive cycles of numbers and remainders, i.e. cycles of 12 hours on the clock, 60 minutes, 60 seconds).
c) Graphing (Teacher could take class polls on which partnerships went on each ride. Students could then graph the results of the polls. Teacher could also find out what groups went to lunch at what times).
d) Proportional reasoning (find out which groups took a restroom break versus who did not).
e) Astronomy (mathematics was involved in celestial navigation, When you know your time, your location can be determined).
f) Measurement (fractions and decimals  use manipulatives to show 1/2, 1/3, and 1/4, write fractions to represent parts of an object such as a clock, write fractions to represent related pictures, and tells time to the hour, 1/2 hour, 1/4 hour, minute with a standard clock face).
g) Geometry (can introduce students to acute, obtuse, and right angles as well as relationships between angles formed).
Modifications:
Unit assessment: As seen throughout the unit, students will be expected to answer multiple types of mathematics questions. Possible types of questions to be used on quizzes and exams to measure comprehension are noted below.
Another option is to have students work in small groups to create and solve their own word problems. One can also use “Telling Time” worksheets (attached) as quiz material for both reading time on traditional clocks, and drawing hands on clocks for a particular time. If the students have Internet access, some good sites for quizzes are http://www.toonuniversity.com/quiz.asp, http://www.edu4kids.com/clock/time.php, and http://www.teachingtime.co.uk/draggames/y4atod.html. Teachers can also use the students’ ongoing math journals, which were previously mentioned in other lessons to assess their progress and understanding.
Field Trip to the Amusement Park
The entire class is going on a field trip to Six Flags. Before we go, everyone must find a partner and create a schedule of what they will do while they are there. I have provided a list of options that you and your partner may choose from to decide what schedule you will follow.
Before you go crazy, there are some basic requirements that everyone’s schedule must meet. Before you hand your schedule in, PLEASE make sure you meet the following requirements:
Below is the list of things that you and your partner can do during the trip:
Batman Rollercoaster 
3 min. 
Superman Rollercoaster 
4 min.

Typhoon Watercoaster 
5 min. 
Double Trouble Catapult Ride 
4 min.

Colossus Ferris Wheel 
6 min. 
Cyclone Wooden Rollercoaster 
5 min.

Get a caricature done 
15 min. 
Picture taking in booth 
5 min.

Lunch 
20 min. 
Rest room break 
6 min.

Hurricane Harbor Waterpark 
45 min. 
Mr. Six’s Pandemonium Coaster 
3 min. 
Please use the attached blank schedule to write in your activities and times.
DON’T FORGET TO MEET THE REQUIREMENTS!
Time Arrived 
Activity Planned 
Time Left 




































Six Flags Schedule for:
Name #1 ________________ & Name #2_________________
Rubric for Field Trip Scheduling Activity
Schedule starts at 10 am

5 points 
______ 
points 
Schedule has lunch break within 10 min. of noon

10 points 
______ 
points 
Schedule ends by 2 pm

5 points 
______ 
points 
A 10 minute break was scheduled between each activity

10 points 
______ 
points 
Each activity time was properly added to the schedule

10 points 
______ 
points 

Total points earned 
______ 
points 

Total available 
40 
points 

Percentage 
_______ 
% 
Possible test (http://www.edhelper.com/math/time_sg490.htm):
Name _____________________________ 


Date ___________________ 
Time
Draw the two hands on the clock to show the time.




Write the time.




Write the time.




Draw the two hands on the clock to show the time.




Draw the two hands on the clock to show the time.




Draw the two hands on the clock to show the time.




Figure out the elapsed time. Write how much time has passed.


Solve each word problem.


Solve each word problem.


Complete the pattern. Draw the clock hands.

Complete the pattern. Write the time.

Complete the pattern. Write the time.

Complete the pattern. Draw the clock hands and write the time.

Complete the pattern. Draw the clock hands and write the time.

Observation and interview notes:
Task Comprehension
Do the students have an understanding of the problem that is being addressed? Do they have enough background knowledge to solve the problem? Can they proceed with minimal guidance?
Organization
Are they able to isolate what processes they will need to use to solve the problem? Do they have knowledge of the tools needed for this process? Can they organize the tasks into a feasible sequence?
Motivation
Are students able to stay on task with solving the problem? Do they ask questions if they do not understand? Are they engaged in the problem solving?
Communication
Are the students working together effectively? Can they communicate to the teacher and others what they are doing and why? Can they explain their thinking to others?
Self Assessment
Do they reevaluate their understanding as they work? Will they selfcorrect if needed? Are they able to reflect on their work and the organization of their tasks?
Flexibility
Are students flexible in their problem solving? Are they able to vary their approach if it is not working? Will they accommodate each other’s thought processes?
Equality and Accessibility
Do all students have equal opportunity to participate? Are the physical accommodations in the classroom working for all students? Are modifications meaningful to students that require them?
Solution Comprehension
Do students complete the task with an appropriate solution? Do they understand what the solution means in the context of the lesson? Can they explain their thinking?
Extrapolation
Can students generalize their results to a real world context? Do they understand how their solution may fit into their own lives? Can they think ahead?
Learning of Mathematical Concepts
Can the students connect their solution to the mathematical concepts being presented and to other parts of the curriculum? Do they make connections to other content areas? Are they able to build on their prior learning?
Time Themed Books for Further Reading:
A Wrinkle in Time by by Madeleine L'Engle. Science fiction twist on time and space, as well as good and evil.
Berenstain Bears and Too Much Pressure, The by Stan Berenstain, Jan Berenstain. The bears learn to prioritize in a fastpaced world.
Dear Benjamin Banneker by Author: Pinkney, Andrea Davis and
Illustrator: Pinkney, Brian. A picture book depicting Benjamin Banneker’s
struggle to publish his almanac, the first one penned by an African American
author.
Gettin’ Through Thursday by Melrose Cooper, Illustrated by Nneka Bennett. Picture book. This book deals with anticipation, making it a nice inclusion with Lesson 3.
Mr. Tucket by Gary Paulsen. A young boy learns the importance of survival on the Oregon Trail. (Time is important in gauging travel, food, shelter issues).
Running Out of Time by M. Peterson Haddix. A girl caught between 1840 and 1996.
Time Machine, The by H.G. Wells. Classic about the thrill and peril of altering time.
Time Warp Trio, The by Jon Sciezska. Fantasy series of time travel.
Additional Resources
1. Match Time by Attainment Company
Features matching dial clocks with digital time
Four levels of complexity requiring a minimal number of correct answers to move up to the next level.
Level 1 to the hour
Level 2 to the ¼ hour
Level 3 to the minute
Level 4 earlier and later, elapsed time
Learner is assessed as they learn, with increasing difficulty of questions as they master the program.
 Can print our a progress report with percent of correct answers at each level
 Has audible prompts that can support learning for lower level learners.
Has support graphic on the CD that can be used to print out an overlay for Intellikeys adaptive keyboard for some special education students, if needed.
2. Clock Puzzles by Developmental Learning Materials (DLM #354) © 1975
Grade K2 but can be used for highergrade special education students
25 double sided cards with two of jig cut self correcting puzzle pieces where top piece has clock face and bottom has digital time that matches.
Graded in difficulty
Whole and ½ hour on the red side
 Clocks with minutes and before the hour times on the other side (blue).
3. What’s the Time? By Creative
A game for learning how to tell the time
Ages 59
24 players
4 plastic game clocks w/ plastic hands
78 game cards
Learn time from seconds to hours.
4. Quizmo Tell Time by World Class Learning Materials, Media Materials
Played similar to a Bingo game where the teacher says the time and students put markers on the appropriate time shown on the clock until someone has a “Quizmo”.
Grade 14
Ages 69
Can be used in a group of 239 players whole class can play
Objectives:
Develop the concept of telling time by the hour halfhour, quarter hour, or in fiveminute increments. Express the position of the hour and minute hands on the clock face in both numbers and words.
5. Clock and Calendar Skills
Bunnell, J (1996). Clock and calendar skills: Teaching time to special students. Portland, Me: J Weston Publishers.
This is a special education book of reproducible worksheets with lesson plans that may possibly go with some of the lessons if needed.
Bibliography
Connecticut State Department of Education (1999). A guide to K12 program development in mathematics. Hartford, CT: Author.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.