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:
- Identify appropriate SI units for measuring speed.
- Compare and contrast average speed and instantaneous speed.
- Interpret distance-time graphs.
- Calculate the speed of an object using slopes.
- 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.
- 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:
- 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.
- 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.
- 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.
- 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.
- 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:
- If reproducibility is a problem, conduct only 1 test.
- 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.
The teacher should guide students into a problem solving strategy. Math practice problems are found in any core textbook.
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?
- Read and Understand
What information is given?
Total distance d= 150 km + 100 km = 250 km Total time t= 2.5 h + 1.4 h = 3.9 h 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.
- 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:
- Define speed and average speed.
- How is instantaneous speed different from average speed?
- 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.
- What does the slope of a line on a position-time graph represent?
- 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.
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.
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.