Status: Published
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Resource ID#: 51000 Primary Type: Lesson Plan
Motion: Speed and Velocity In this lesson students should be able to : Identify appropriate SI units for measuring speed. Compare and contrast average speed and instantaneous speed. Interpret position-time graphs. Calculate the speed of an object using slopes.
Subject(s): Mathematics, English Language Arts, Science Grade Level(s): 9, 10, 11 Intended Audience: Educators
Suggested Technology: Graphing Calculators, Computer for Presenter, Computers for Students, Probes for Data Collection, Basic Calculators, LCD Projector, Microsoft Office
Instructional Time: 2 Hour(s) Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: speed , average speed, instantaneous speed, velocity, vector, slope, formula, graph, graphing Instructional Component Type(s): Lesson Plan, Problem-Solving Task, Assessment, Data Set, Formative Assessment Instructional Design Framework(s): Demonstration, Predict-Explain-Observe-Explain, Structured Inquiry (Level 2) Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS 7_Unit 1 Assessment ( Version 1 ).docx Unit 1 Self Assessment (Version 1 Answer Key ).docx 3_The Notion of Motion.docx
LESSON CONTENT Lesson Plan Template: General Lesson Plan Learning Objectives: What should students know and be able to do as a result of this lesson? As a result of this lesson students should be able to: 1. Identify appropriate SI units for measuring speed. 2. Compare and contrast average speed and instantaneous speed. 3. Interpret distance-time graphs. 4. Calculate the speed of an object using slopes. 5. Describe how velocities combine.
Prior Knowledge: What prior knowledge should students have for this lesson? At the beginning of this section students should know: Motion is described as a change of position in relation to a frame of reference.
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How to distinguish between distance and displacement. How to calculate simple vector operations as addition and subtraction. How to identify positive and negative integers on a number line. Basic graphing skills. Be aware of the common misconception of speed and velocity--students often confuse them and think they are the same quantity.
Guiding Questions: What are the guiding questions for this lesson? The teacher will ask questions about the previous lesson: 1. What is a frame of reference? A frame of reference is made up of three components an object of reference (fix or attach to the ground), a coordinate system (x, y), and a clock to record time. 2. What two things must you know to describe the motion of an object? You must know the direction the object is moving and how fast the object is moving. 3. Compare and contrast distance and displacement. Distance is the length of a path between two points, whereas displacement is the direction from a starting position and the length of a straight line from the starting point to the final position. 4. How are scalars and vectors similar or different? Scalars are defined by a number (magnitude) and its unit, otherwise vectors are defined by a number (magnitude) and its unit as well as the direction. 5. When is an object moving with constant motion? An object is moving with constant motion when it's covering equal distances in equal amounts of time.
Teaching Phase: How will the teacher present the concept or skill to students? The teacher will present the concept of speed using an inquiry based demo. The Notion of Motion from Bioscope (See attachment file). Recall how motion can be described in terms of changing position in relation to a frame of reference, how far or close an object is from the starting position (distance or displacement) or how fast or slow this change occurred at a time interval. To help students grasp the concept of speed, the teacher should first introduce the concept of constant motion, (an object covering equal distances in equal amounts of time-naturally motivates the concept of speed). A good way to introduce this concept could be obtained from the buggy car demo above. Ask students to explain the opposite of constant, and then introduce non-constant motion, (an object that does not cover equal distances in equal intervals of time--this provides the motivation to develop the concept of average speed). Asked students to provide examples to arrive at this conclusion: their school bus, walking from their homes to the school, etc. Explain to students that we can translate this observation into the language of math and then introduce the equation to calculate average speed. Discuss with the students that average speed is useful because it lets you know how long a trip will take. Sometimes however, such as when you are driving you need to know how fast you are going at a particular moment. The car's speedometer gives your instantaneous speed. Define instantaneous speed, v, is the rate at which an object is moving at a given moment in time. After students are clear about constant speed and average speed, the teacher will: Let a buggy car move across table and ask for observations. List observations and then ask which items are quantifiable. Lead them to observe that the buggy car moves at constant speed; i.e., that it travels equal distances in equal time intervals. The dependent variable is position (x). Emphasize that we are dealing with position, not displacement or distance traveled. The independent variable is time (t). Emphasize time as a clock reading and not an interval. Why make time independent? Because when time is graphed on a horizontal axis, the slope will be equivalent to velocity. Stopwatches and battery-powered vehicles are easier to use than "stomper" cars and photogates. (Honors classes may be able to handle use of photogates at this stage.) Teachers may choose to have the students collect the data (position and time). They should be reminded to perform multiple trials with at least 6 data pairs/trial. Averaging the values of position helps them develop a sense of the precision they should carry through the analysis. Otherwise they are guilty of adhering to Lillenthal's Laws: 1. If reproducibility is a problem, conduct only 1 test. 2. If a straight line plot is required, collect only two data points. Focus discussion on the position versus time relationship. (Linear) Use slope-intercept form to write equation of line (e.g. mx+b). Discuss the slope of the line as being a constant. Introduce the label units of slope (m/s). Identify v (velocity) as the slope in the slope-intercept equation. Discuss the vertical intercept and the "5% rule-of-thumb". In most cases, the intercept is negligible. From the specific equation, write general mathematical model. Discuss displacement when initial position is not zero.
Guided Practice: What activities or exercises will the students complete with teacher guidance? Among many activities that students are supposed to complete for this lesson with the teacher guidance are: Reading Focus, Venn Diagram (Speed and Direction ) Look for samples of Venn Diagram on the web. The Notion of Motion Demo or The Buggy Demo: here students will record and graph data for position and time. Interpret a graph of position vs. time, the meaning of slope, y-intercept; the teacher will explore positive, negative and zero slopes. Math Skills: The teacher should guide students into a problem solving strategy. Math practice problems are found in any core textbook. Example: While traveling from Miami to Orlando on a vacation trip, you recorded the following data for distances and time to cover them. You travel the first 150 Kilometers in 2.5 hours, and the second part of the trip, 100 kilometers in 1.4 hours. What was your average speed for this trip? 1. Read and Understand What information is given?
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Total distance d= 150 km + 100 km = 250 km Total time t= 2.5 h + 1.4 h = 3.9 h 2. 2. Plan and Solve What unknown are you trying to calculate? Average Speed v-? What equation contains the given quantities and the unknown? Replace or substitute each variable with its known value. 3. Look back and Check Is your answer reasonable? Yes, 64.10 km/h is a typical highway speed.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson? Students should be able to complete the following exercises and problems to reinforce the concepts and skills developed in the lesson: 1. Define speed and average speed. 2. How is instantaneous speed different from average speed? 3. A student walked 2.5 km in 50 minutes on the way to school, and then, realizing he was late, ran the remaining 0.5 km on 2.5 minutes. Calculate his average speed on the way to the school. 4. What does the slope of a line on a position-time graph represent? 5. How do speed and velocity differ?
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson? The teacher will close the lesson by asking questions about what students learned in class today. What is speed? How is it calculated? What is average speed? What is the relationship between steepness of the slope of a distance-time graph and speed? What is velocity? How is it calculated? What are the SI units for speed and velocity? Finally the teacher should review the misconception that speed and velocity are the same thing.
Summative Assessment The teacher will determine if the students have reached the learning targets for this resource by taking traditional multiple-choice, true/false, and/or fill in the blank assessments. One such assessment, the Bioscopes Unit 1 Self Assessment (attached), is an excellent test to monitor students gains in graphical analyses and critical thinking.
Formative Assessment Among many activities for teachers to gather information, formal and informal, student understanding may be demonstrated by: Focus activity (recommended to build vocabulary) Engage students to draw a Venn Diagram (a visual aid that compares and contrasts ideas) showing how the key terms of the section are related to each other (Speed and Direction). The teacher should walk around the room to check student work, using questions to guide them toward the main idea. Student diagrams should show circles labeled Speed and Direction. The area in which the circles overlap should be labeled Velocity. Speed might include magnitude, units, scalar etc. and direction might include north, south, east, west, right, lefty, up, down, vector. At this point the teacher should be monitoring students progress by their drawings. The teacher may ask the student with the best Venn Diagram to draw it on the board and to explain it to the rest of the class, then an open discussion about the presentation with the guide of the teacher will wrap this activity up (Inclusion and ESOL students might have trouble finding the answers). Teacher will informally monitor students progress verbally. Venn Diagrams can be created manually or electronically. Electronic Venn Diagrams can be created at sites such as: http://www.matm/Venn_Diagram/Venn_Diagram_Template_Two_Set.html A more formal assessment to gather data about students progress in this content is attached. (See Attachments)
Feedback to Students Students will get feedback about their performance or understanding during the lesson in different stages during and after the class time by: Encouraging them to check their findings with a classmate and the teacher during the exploration and explanation of the Venn Diagram; Checking the core textbook for reinforcement; Homework will reinforce their learning and provide feedback over their understanding of the content as well.
ACCOMMODATIONS & RECOMMENDATIONS Accommodations: ESOL students will create a word wall: Students can relate the concepts in this section to the vocabulary words by creating a word wall. Write the words speed, average speed, instantaneous speed, and velocity on the board. Then, as students work through the section in the core textbook or additional resource physics book, magazine, etc., ask them to define each word in their own words. Discuss their definitions and write acceptable definitions on the board next to each word. Students may also draw a graph or paste a magazine picture next to the corresponding word. Inclusion students will get extended time to complete the Venn Diagram and to graph the data collected for position and time. They will only do one trial, using three
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points to complete the line. The math treatment might be very simple for them: slope is the rise over the run. Gifted students should take data using the data recording device and compare their data with the data from teacher demo, also they should explain the meaning of the y-intercept from their graph of Position-Time.
Extensions: The teacher should challenge their students by graphing lines on position vs. time graph. with positive, negative , zero slopes. lines with different steepness that intercept at one point or are parallel to each other. a line with different slope, and explain the meaning of each part of the path. This lesson can be integrated with Earth Science as well: How can continents move? Suggest the idea proposed by Alfred Wegener, a German meteorologist, that all Earth's continents were once part of a single landmass called Pangaea, meaning "all Earth". Suggested Technology: Graphing Calculators, Computer for Presenter, Computers for Students, Probes for Data Collection, Basic Calculators, LCD Projector, Microsoft Office
Special Materials Needed: The materials for the demo are: any slow-moving battery powered toy vehicle stop watches meter sticks masking tape graph paper High Tech Demo: Graphical Analysis for data collection (Vernier Software Technologies-Logger Pro recommended, or you might use Excel Spreadsheet to record students data and graph) http://www.vernier.com/ Computer or data interface Interval timer/marker
Further Recommendations: Some things to keep in mind when implementing this lesson/topic: 1. It is important to describe motion in terms of position and time, rather than distance. Position is much less ambiguous than distance (sometimes regarded as the path length, sometimes as displacement). Some authors use 's' to describe this variable; we prefer 'x' for horizontal motion (and 'y' when the motion is vertical). We advise against the use of 'd'. When it comes time to discuss the slope of the position-time graph, the definition for velocity naturally arises. Change in position is superior to change in distance; the latter is a difference of differences. Change in position is the definition of displacement, the quantity that helps distinguish velocity from speed. Displacement can be (+) or (-), distance is by definition (+).
2. When discussing the meaning of the graphs, be sure to use a wide variety of examples. Induce the students to describe the motion in full detail (e.g., the object starts somewhere to the right of the origin and moves to the left at constant speed). 3. Using an enlargement of one of their graphs, have the students manually calculate the slope and compare to the value obtained by graphical analysis. Students have been conditioned to think of slope only as "rise over run" or "change in y" over "change in x".
4. Make sure that they have a thorough grasp of the relationship between slope and velocity. The answer "1's slope is greater than 2's" is not a guarantee of understanding. It would be helpful to have students model the behavior of the object represented by a variety of graphs. If you have an ultrasonic motion detector, this is great fun.
Additional Information/Instructions By Author/Submitter This resource could be valuable to teach speed and velocity for student taking physical science at first time, also for a regular physics course at a beginning level. For first time teachers, this resource might guide you to a better understanding of speed and velocity, analytically, and graphically.
SOURCE AND ACCESS INFORMATION Contributed by: Rafael Suarez Name of Author/Source: Rafael Suarez District/Organization of Contributor(s): Miami-Dade Is this Resource freely Available? Yes Access Privileges: Public License: CPALMS License - no distribution - non commercial
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Related Standards Name
Description Distinguish between scalar and vector quantities and assess which should be used to describe an event. Remarks/Examples:
SC.912.P.12.1:
Distinguish between vector quantities (e.g., displacement, velocity, acceleration, force, and linear momentum) and scalar quantities (e.g., distance, speed, energy, mass, work). MAFS.912.N-VM.1.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors. Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference) as functions of time. Remarks/Examples:
SC.912.P.12.2:
Solve problems involving distance, velocity, speed, and acceleration. Create and interpret graphs of 1-dimensional motion, such as position versus time, distance versus time, speed versus time, velocity versus time, and acceleration versus time where acceleration is constant. Florida Standards Connections: MAFS.912.N-VM.1.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors. Recognize that time, length, and energy depend on the frame of reference.
SC.912.P.12.9:
LAFS.910.RST.2.4: LAFS.910.SL.2.4: MAFS.912.N-Q.1.1: MAFS.912.N-Q.1.3:
Remarks/Examples: The energy E and the momentum p depend on the frame of reference in which they are measured (e.g. Lorentz contraction). Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. ★ Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. ★
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