## Distance over Time

### Sandi KingBay District Schools

#### Description

What is velocity and how is it determined? In this lesson plan, students are actively involved in experiments to measure and calculate the magnitude of speed, known as velocity using algebraic terms.

#### Objectives

The student selects an appropriate measurement unit for labeling the solution to real-world problems.

The student selects and uses the appropriate tool for situational measures (for example, measuring sticks, scales and balances, thermometers, measuring cups, gauges).

The student solves problems involving equations or simple inequalities using manipulatives, diagrams, or models, symbolic expressions, or written phrases.

The student translates problem-solving situations into expressions and equations using a variable for the unknown.

The student knows that velocity describes a change in distance over time.

The student uses tools to measure changes in position, direction, and speed of an object after a push or pull has been applied.

#### Materials

- Vocabulary cards from the attached file
- One set of Used to Measure Posters from the attached file
- A variety of measuring tools for each type of measurements (Time = stopwatch, large class clock with a second hand, wristwatch, timer, calendar; Distance = ruler, yardstick, meter stick, tape measurers all in both metric and English units; Volume = beakers, various measuring cups and spoons; Mass = various balances, a balance with cups on each side and a balance with gram weights to establish the exact mass, spring scales, bathroom scales, etc.)
- One set of vocabulary cards from the attached file
- Calculator Review sheets from the attached file (one per student)
- One calculator per pair of students
- One overhead calculator (if possible)
- One roll of masking tape
- Rolling Marbles instructions and data chart from the attached file (one per person)
- One marble per pair of students
- Students’ Formative Assessment Checklists used on previous days of this unit
- One softball per pair of students
- How Slow Can You Go? Instructions and data chart from the attached file (one per person)
- A long hallway or flat surface on the playground such as the basketball court
- Summative Assessment #1 from the unit’s attached files (one per student)
- Summative Assessment #3 from the unit’s attached files (one per student)

#### Preparations

1. Download and print one copy of the vocabulary cards from the attached file.
2. Download and print one set of Used to Measure Posters from the attached file.
3. Locate a variety of measuring tools for each type of measurements (Time = stopwatch, large class clock with a second hand, wristwatch, timer, calendar; Distance = ruler, yardstick, meter stick, tape measurers all in both metric and English units; Volume = beakers, various measuring cups and spoons; Mass = various balances, a balance with cups on each side and a balance with gram weights to establish the exact mass, spring scales, bathroom scales, etc.). Stop watches may be borrowed from the PE department.
4. Download, print, and duplicate the Calculator Review sheets from the attached file for each student.
5. Locate one roll of masking tape.
6. Locate one calculator per pair of students.
7. Locate one overhead calculator if possible.
8. If the overhead calculator is used, an overhead projector will be needed.
9. Download, print, and duplicate the Rolling Marbles instructions and data chart from the attached file. You need one per student.
10. Locate one marble per two students.
11. Locate one softball per three students.
12. Locate a long hallway or flat surface on the playground such as the basketball court.
13. Download, print, and duplicate the How Slow Can You Go? instructions and data chart from the attached file. You need one per student.
14. Locate the students’ Formative Assessment Checklists used on the previous days of this unit.
15. Download, print, and duplicate the Summative Assessment #1, Racing Velocity, from the unit’s attached files. You need one per student.
16. Download, print, and duplicate the Summative Assessment #3, I Am Responsible, from the unit’s attached files. You need one per student.

#### Procedures

Note: This is lesson four of seven in the Beacon Learning Center unit, A Television in My Room. This lesson covers science and math content and is to be done on the fourth, fifth, and sixth days of the unit.

Session One: (Day four of the unit)

1. Gain the students’ attention by showing one of the pictures of simple machines in the real world. Ask what kind of simple machine is shown and what task it makes possible. Mark the formative assessment checklists.

Making everything relevant -

2. Begin the lesson by thinking out loud . . . I’ve been thinking about Brian hitting Mrs. Bailey yesterday in our reading. He came off a rail that was an inclined plane, then used a wheel and axle to ride along the sidewalk and hit Mrs. Bailey. She was knocked down, but was not badly hurt. I wonder how fast Brian had to be going on the skateboard in order to knock Mrs. Bailey down. (Note the reference to simple machines as well as velocity.)

3. Review the unit question and scenario from the lesson plan, Responsibility, completed on day two of the unit and now on display on the wall of the classroom.

4. Review the charts made yesterday and on display that list ways to be responsible to self and others.

5. Review the chart that displays the two ways that were chosen by students as the main ways to demonstrate responsibility to others involving having televisions in their own rooms. Those are: 1) My television must be turned off when I leave the room or fall asleep. 2) The volume will not bother others.

6. Remind students that we are beginning our focus on thinking about how to be sure our television is turned off at the appropriate time. It was decided yesterday that we would need a machine to turn off the television. Students were asked to think about what this machine might be like.

7. Guide a discussion of devices that might achieve this goal. As students share ideas, keep these thoughts in mind when giving feedback: 1) The machine must be automatic because if they fall asleep, they won’t be able to push a button. 2) Students should identify which simple machine will be used in the device. 3) Since our discussion and learning concept will move towards the study of velocity, encourage students to think about how hard a button must be pushed, or how fast an object must move to push a button, or lift a lever, or how hard will the pull have to be to pull the plug, or whatever the students dream up.

8. Think out loud to the students:

* Since we know that we are going to have to be able to push a button, or pull a chord, to somehow get the television off, do you think we should learn about how to tell the speed of objects?

* That reminds me again of poor Mrs. Bailey. I wonder how fast Brian was going when he hit her.

Science and Math –

Note: One main purpose of this lesson is for students to be able to answer the question, “What does velocity describe?” At the end of these three days of instruction, students should know that velocity describes a change in distance over time.

9. Display the vocabulary words, speed and velocity. Explain that velocity is what we mean when we use the word speed. Velocity is the rate of motion in a particular direction. Speed is the average velocity, not counting the acceleration separately, but figured into the total. This average velocity is called constant, or uniform velocity and can be determined, just as speed can, by measuring the distance covered by the time taken to travel that distance. Although students may seem confused by this at this moment, the experiments and activities to follow will make this definition clear to students. Put the words and definitions of the word wall for this unit.

10. Begin the study of velocity by giving a mini-lesson in measurement. Have a variety of measuring tools at hand including the large class clock that has a second hand.

* Hang the Use to Measure posters from the attached file.
* As each tool is displayed, call on a student to tell what the tool is and what it is used to measure.
* Ask about the measurement label that would be used with the tool. For example, a ruler might measure centimeters.
* The tool is then placed under the appropriate poster.
* Write the measurement tool and unit of measure on the poster. As the units are written, point out the abbreviations for the labels such as, while writing centimeter, write cm.
* Write large enough that the students will be able to use these posters as references.
* Give formative feedback both affirming correct answers or guiding students toward correct answers.

11. Now that the measurement tools have been classified and sorted, guide the students toward discovering the relationship of certain measurement tools and finding the velocity. Ask the focus question, “What does velocity describe?”

* Start by reminding students which two measures will be used to find the velocity (distance and time).

*Ask the question: When finding the velocity of a fast moving object, which tool for measuring time would be most appropriate? Review each tool and its unit of measure and guide the class to a consensus that the unit to use would be second, so the wristwatch with a second hand, or a stopwatch are the appropriate tools.

* Follow the same procedure to find the measurement tool for measuring distance. Since the experiments will be done in the classroom, inches or centimeters will be the appropriate units and rulers, or tape measurers will the appropriate tools.

11. Lead a discovery as to how to set up an experiment to find velocity.
* While students watch the experiment, the teacher should have a running dialog of what is being done and why. Special points should be made to discuss the selection of the unit of measure and tools to use, the formula for finding the velocity, and the completion of the formula, including the label of the unit of measure.
* Write the formula for calculating the velocity on the board. v = d/t
* Decide what will be moving. Locate a ball, can of pop, miniature car taken from a student, bottle of lotion, or any other object that will roll.
* Next, mark a beginning line, measure five feet and mark an ending line. Masking tape on the floor will mark the beginning and ending lines.
* As you are measuring and marking, discuss the selection the units of measure and measurement tools for both the distance and time.
* Under the formula (remembering to line up the equal signs) write v = 5 ft./ ____ sec.
* Select a student to roll the object. Use a watch with a second hand, or a stopwatch and time the objects roll from the beginning line to the ending line.
* Complete the formula. It will now be something like v = 5 ft./ 3 sec.
* Use a calculator to do the division, 5 ft. divided by 3 sec equals 1.67 feet per second.
* Read the velocity to the students so they actually hear what the answer sounds like. Tell students that the velocity is 1.67 feet per second.

12. Ask the focus question, “What does velocity describe?”
Repeat this experiment procedure above using a ramp made from one book with another book angled from the top book to the floor. Begin at the ending line and measure back 5 feet. Remember to measure the floor and up the ramp to the top where the object will begin the roll. Repeat the procedures described in procedures number 11 above.

13. Give a mini-lesson in use of a calculator to divide. Use a calculator made for demonstration on an overhead projector if possible. Discuss the fact that the / is another way of writing divided by. The math sentence 5 feet/ 3 seconds means 5 feet divided by 3 seconds. As you read the math sentence, punch the keys on the calculator so the students see the correlation of what they are reading in the math sentence and what they touch on the calculator. Give a few examples such as 4 feet / 2 seconds, 27 centimeters / 3 seconds, 8 meters / 3 seconds. As each answer is found, have the student read the answer using the correct unit of measure label.

14. Students complete the Calculator Review sheet from the attached file and turn it in.

15. Ask the focus question, “What does velocity describe?”

16. Students complete their daily journal entries by discussing what they have learned about tools needed to measure velocity.

17. Collect the journals and give formative feedback as to whether the student understands which tools are needed to measure velocity. You are assessing whether students understand which measurement tools are needed to measure velocity. Mark the Formative Assessment Checklists. (See Extensions of this lesson plan for a suggestion for managing the review and feedback.)

18. Use the Calculator Review sheet to formatively assess. Although these standards state that the student is in a problem-solving situation, this is a prerequisite to using this knowledge to problem solve. Give formative feedback by conferencing with the student, if possible, and by writing notes on the individual papers. Remember that formative feedback both tells the students why they are correct; "Yes, you remembered to label your answers." or guides them towards the correct answers; "You divided correctly, but forgot your labels." Mark the Formative Assessment Checklists.

Session Two: (Day five of the unit)

19. Gain the students’ attention by showing one of the pictures of simple machines in the real world. Ask what kind of simple machine is shown and what task it makes possible. Mark the formative assessment checklists.

20. Review the unit question and scenario. Review the chart that tells the two ways that were selected to show that we are responsible enough to have a television in our room. Question students as to why knowing how to find velocity is useful when showing that they are being responsible for the television.

21. Ask the focus question, “What does velocity describe?”

22. Pass back the Calculator Review sheets that now have formative feedback. Review the posters of measurement tools.

23. Yesterday students observed and assisted as the teacher performed experiments to find the velocity. Announce that today students will be measuring, labeling, and calculating to find the velocity as they perform the experiments.

24. Pass out Rolling Marbles Experiment instructions and data charts. Have marbles available.

25. Allow 20 minutes for students to select a partner, select measuring tools to use, and complete the experiments as described on the worksheet.

* Teachers should be able to locate enough distance measuring tools, however, finding enough stopwatches will be a problem.
* Remind students that they can use the second hand on their watch, or use the large class clock and its second hand when measuring time.
* Although students will be working in pairs, they each need their own worksheets. If students do not agree, they can write their individual answers on their own sheets. These will later be used as study guides for the summative assessment, so each student will need his/her own.

26. Circulate among the students and perform a formative assessment giving oral formative feedback, as the students complete their experiments. Take time to correct any misconceptions or misunderstandings. If necessary, have students change partners so that peer tutoring can occur. Mark the Formative Assessment Checklists.

27. Students complete their daily journal entries by discussing the follow question; What have you learned about the measurement tools used to measure velocity?

28. Collect the journals and give formative feedback as to whether the student understands that velocity describes a change in distance over time. You are not assessing exact velocities and/or facts, but whether students understand the concept of velocity and what tools are used to measure velocity. Mark the Formative Assessment Checklists. (See the extensions area of this lesson plan for a suggestion for managing the review and feedback.)

Making everything relevant:

29. Distribute Summative Assessment #3, I Am Responsible. Discuss the requirements and rubric. Write the date due in the appropriate space.

Session Three: (Day six of the unit)

30. Gain the students’ attention by showing one of the pictures of simple machines in the real world. Ask what kind of simple machine is shown and what task it makes possible. Mark the formative assessment checklists.

31. Review the unit question and scenario. Review the chart that tells the two ways that were selected to show that we are responsible enough to have a television in our room. Question students as to why knowing how to find velocity is useful when showing that they are being responsible for the television.

32. Remind students of the assignment given yesterday, Summative Assessment #3. Ask for questions about the assignment.

33. Ask the focus question, “What does velocity describe?” By now students should know that velocity describes a change in distance over time.

34. Review the posters of measurement tools.

35. Remind students that yesterday they performed experiments to find the velocity of a rolling marble. Yesterday, the distance was given, but students had to determine the time it took the marble to roll the distance, then calculate the velocity. Today, the time will remain the same, but students will have to measure the distance in order to calculate the velocity.

36. As a review, and to model today’s experiments, demonstrate finding the velocity of a rolling softball.
* Begin by taking the class out to the hall, or to a flat hard surface on the playground such as a basketball court.
* Mark a beginning point with a piece of tape.
* Tell the students that you will roll the softball, then measure how far it goes in 5 seconds.
* Select a student to be the timekeeper and another to be the measurer.
* When the timekeeper says go, gently roll the softball.
* When the timekeeper says stop, put your finger to mark the ball’s location.
* The measurer then measures the distance the ball traveled.
* Write the distance on a piece of paper. Be sure to write the unit of measure label.
* Tell students that they will be using the measurements to find the velocity when they return to the classroom.

37. Tell students that in all previous examples of velocity, we have discussed how fast things moved. Since velocity describes any change in distance over time, velocity also describes how slow things move. In today’s activities, we will be measuring the velocity of slow moving items.

38. Follow the directions in the attached file for the activity, How Slow Can You Go?

39. Allow 20 minutes for students to select partners (students are in groups of 3), select measuring tools to use, and complete the experiments as described on the worksheets.
* Teachers should be able to locate enough distance measuring tools, however, finding enough stopwatches will be a problem.
* Remind students that they can use the second hand on their watch, or use the large class clock and its second hand when measuring time.
* Although students will be working in pairs, they each need their own worksheets. If students do not agree, they can write their individual answers on their own sheets. These will later be used as study guides for the summative assessment, so each student will need his/her own. They are only writing measurements at this time and will be doing the calculations back in the classroom.

40. Circulate among the students and perform a formative assessment giving oral formative feedback, as the students complete their experiments. Take time to correct any misconceptions or misunderstandings. If necessary, have students change partners so that peer tutoring can occur. Mark the Formative Assessment Checklists.

41. Upon returning to the classroom, write the formula v=d/t on the board. Insert the measurements for your demonstration softball roll. Complete the calculation for your velocity. Remember to put your measurement label. It is important to verbally describe what you are doing and why as you calculate your velocity in order to reach both auditory and visual learners.

42. Now that you have given a review of how to calculate the velocity, allow students time to calculate the velocities for the three softball rolls from their group. These calculations should be done individually. Circulate and assist as needed. Give formative feedback to both affirm correct calculations and to correct miscalculations. Mark the Formative Assessment Checklists.

43. Students complete their daily journal entries by discussing the following question; What is velocity?

44. Collect the journals and give formative feedback as to whether the student understands that velocity describes a change in distance over time. You are not assessing exact velocities and/or facts, but whether students understand the concept of velocity. Mark the Formative Assessment Checklists. (See the extensions area of this lesson plan for a suggestion for managing the review and feedback.)

45. Distribute and review Summative Assessment #1, Racing Velocity. Discuss the various items on the assessment. Ask for any questions. Collect the assessments and have students mark their homework notebook as a reminder to study for the assessment to be given tomorrow. Students put their Rolling Marble Experiment and How Slow Can You Go? papers in their homework folder to use as study guides in preparation for tomorrow’s Summative Assessment #1.

#### Assessments

Formative assessments with formative feedback will be administered throughout the lessons. The Calculator Review worksheet, Rolling Marble Experiments, and How Slow Can You Go? Experiments will all be used as formative assessment evidence. Criteria from the Formative Assessment Checklists from the unit’s attached file will be used to document progress.

Summative Assessment #1, Racing Velocity, will be given on the day following the last session of this lesson. Instructions and criteria for this assessment are included in the assessment document.

Summative Assessment #3, I Am Responsible, is presented. This tool assesses standards taught in this lesson. The instructions and rubric are discussed and a due date is agreed upon.

#### Extensions

1. Individual assistance may be necessary for some students.

2. A parent volunteer may observe students and give assistance as needed.

3. If working in partners is a problem with your students, this can be done individually.

4. Small groups rather than partners may be used.

5. If the quantity of measurement tools needed is not readily available, students may need to do the experiments in shifts.

6. When reading journal entries, the feedback can be given in a color code system. Highlighted yellow means the response is right on target. Pink highlight means bring your journal and let’s talk. Using this method is fast for the teacher, gives student affirmative feedback, and allows for student/teacher conferences on concepts or misconceptions that need further explanations.

7. The Beacon Unit Plan associated with this lesson can be viewed by clicking on the link located at the top of this page or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=3262. Once you select the unit’s link, scroll to the bottom of the unit plan page to find the section, “Associated Files.” This section contains links to the Unit Plan Overview, Diagnostic and Summative Assessments, and other associated files, (if any).

8. Take students outside and time them running a certain distance so they can calculate their own velocity.

#### Attached Files

Vocabulary cards.     File Extension: pdf

Worksheet: Calculator Review.     File Extension: pdf

Data sheet for the Rolling Marble Experiments.     File Extension: pdf

Instructions and the data sheet for the activity, How Slow Can You Go?     File Extension: pdf