
Lesson Plan Template:
PredictObserveExplain

Learning Objectives: What will students know and be able to do as a result of this lesson?
Students will:
 become proficient in understanding the behavior of a pendulum by measuring the amount of time it takes for the pendulum to swing back and forth once, known as the "period", when the mass and length of the pendulum are varied.
 predict what the two graphs (mass versus period, and length versus period) will look like by drawing a line that represents their prediction of what that line will look like after plotting the actual data points collected.
 learn how to collect and analyse data collected from observations of actual pendulum behavior under different conditions.
Optional followup activity: Students will use the collected data to calculate the value of acceleration due to gravity by applying the formula that represents the algebraic relationship between length of period, measured in seconds, and length of pendulum, measured in meters.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students should have prior knowledge of the math skills necessary to rearrange an equation to solve for an unknown. This is usually covered in basic algebra. It is also helpful if students understand what mathematical relationships are represented by the shape of the line produced on a graph from the data points. For example  the slope of a straight line can be found by dividing the rise over the run. This can produce the value for "m" in the formula for a straight line relationship between the "x" and "y" data and is represented by y=mx+b where b is the "y" intercept. This is also taught in basic algebra.

Guiding Questions: What are the guiding questions for this lesson?
EQ 1: How does varying the mass hanging from the end of a pendulum impact the length of the period when the length of pendulum remains constant. What formula would represent that relationship?
EQ 2: How does varying the length of a pendulum impact the amount of time it takes the pendulum to swing back and forth once when the mass hanging from the pendulum remains constant? What type formula would represent that relationship mathematically? Note: For the purpose of this lab, it is not essential that the students know the actual formula. The formula can be provided after the students have predicted the nature of the mathematical relationship, which it turns out is square root and not linear (as most students will predict).
EQ 3: How can we use the formulas for pendulum behavior to calculate the value of acceleration due to gravity? What is the derived value of gravity?

Predict: What event, related to the focus topic, that may surprise students, will the students make a prediction about?
Note: having the students complete the prediction step is critical for student engagement and learning gains from the lab.
In this inquiry based lab, students make predictions, observe and collect data, and then explain the graphs of the time it takes a pendulum to swing back and forth once, known as the "period," as the length of the pendulum and the mass hanging from the pendulum are varied. Students will make a prediction for a graph of the relationship between the length of period to mass and for the graph of length of period to length of the pendulum. The PowerPoint presentation provides a lesson flow for completing the lesson in one class period. If the optional activity is carried out, an additional class period is required and includes time to address any misconceptions still held by the students after the first part of the lab is completed. Reviewing the summative assessment (the exit ticket) from the first day's lesson should identify any misconceptions the students may still have.
The graph lines represent the mathematical relationship between the two variables. The lab presents a nondiscrepant event and it is likely the student predictions will be incorrect. A typical prediction is that increasing the mass, while leaving the length of the pendulum the same, will increase the length of a period in a linear fashion (reflected in a straight line drawn on their prediction graph). The observed data, when analyzed, will show that the amount of mass has no impact on the length of the period reflected as a straight line parallel to the x axis. The normal prediction for the changing the length of the pendulum, while leaving the mass the same, is that increasing the length will increase the period in a linear fashion reflected in a prediction of a straight line with a positive slope. The actual result produces a square root relationship represented by a line curving up and and bending to the right.

Observe: What will the students observe and/or infer during this step of the lesson? How will students communicate their observations and inferences?
Working in small groups of 23, students will collect actual data regarding pendulum behavior by working at an assigned lab station and following the written procedures to collect and record their data.
Since each group will only collect data from a single lab station, they are instructed to collect the data from one of two other groups to facilitate discussion within their small group.
Students are able to observe data patterns as results from each lab station are plotted on the board for all to see. It is important that the instructor plot the data from the largest values to the smallest.

Explain: How will students be encouraged to develop explanations using their observations and scientific or mathematical concepts or principles?
Students will take part in the construction of graphs of the data collected. The graph will be created on the board one at a time and there is also a spot on the student hand out for the students to recreate the plot for themselves.
There will be one graph plotting mass (xaxis) versus time (yaxis) and one graph for plotting length (xaxis) versus time (yaxis). It is important to start by plotting the graph of mass versus time as this graph will reveal the discrepant event. The graph will reveal that the mass has no impact on the time for a pendulum to swing back and forth once (the period). This will be reflected as a straight line graph with no slope. Most students will have predicted that the mass will have an impact on time and will have drawn a straight line with some slope to it. Once the correct outcome is revealed, ask the small student groups to write out an explanation explaining the discrepancy between what they predicted versus what the data reveals. Discuss the replies as a class. Follow the same process when plotting the length versus time graph. Most students will have predicted that the length versus time graph will have slope and follow a linear relationship. While the plotting of the data for the length versus time graph will reveal a slope, it will also reveal that the line is not straight but curved. Have the students provide explanations to explain this behavior and discuss before sharing with the students the square root relationship (and the formula) between length and time of period.
When looking at each graph, ask for student conclusions after 34 data points have been plotted. After that, add one data point at a time and ask the students to consider further revisions to their hypothesis. It is also very important to start plotting data from the higher values to the lower values as this approach provides a better explanation for the graph of length versus time. Plotting from the outside in will initially suggest that the student predictions of a straight line relationship is correct. Only after plotting the data points for the 25 cm length and then the 12.5 cm length will it be revealed that the graph does not produce a straight line linear relationship.
After students have produced written explanations that explain what actually happened versus what they predicted would happen, it is time to have the students move to the exit ticket activity. Allow time for the students to complete this section as it is the summative assessment for the lesson. Collect all handouts at the end of the period  nothing should go home. The teacher needs to review the results of the exit ticket activity to determine what might need to be reviewed and retaught in the next class period.

Summative Assessment
The lab has an exit ticket activity that provides a summative assessment for the teacher to review after the lesson. The activity also includes a math calculation so the teacher can assess how well the students mastered the math portion of the lab.
It is suggested that the teacher review the cumulative replies from their review of the exit tickets during the following class period and incorporate into that review any common misunderstanding identified. There is a followon math related activity that can be included in the next class period if the students turn out to need more math practice.

Formative Assessment
In this inquiry based lab, students are to make a prediction, prior to the start the lab, as to what they believe the graphs of the lab data will look like after the lab has been conducted. It is important that each student commit to a prediction prior to starting the lab. This "prediction" activity is the basis for the teacher's formative assessment. While the students are drawing their predictions, the teacher needs to move about the room to make sure everyone has committed to a prediction and to collect an overall initial assessment as to what the collective class predictions look like. Since this lab activity highlights a discrepant event, one where the outcome is counterintuitive, only a few students are likely to draw (make) the correct prediction, but it is important to know who they are.
For the definition of a "period" section of the lab, which takes place at the start of the lesson prior to data collection, the formative assessment comes from class discussion and a teacher provided working definition with a visual demonstration to make sure all students are on common ground before heading off in their groups to collect data and observe the behavior.
During the data analysis section of the lesson, contributions from the individual groups will provide feedback to the teacher as to where the level of understanding is within each group. It is important that the teacher collect feedback from each group during this section.

Feedback to Students
The first part of the lesson is focused on defining what a "period" is, as it relates to the behavior of a pendulum. The students share their personal descriptions. The students are given feedback when the teacher provides the formal definition after the discussion. The students can then compare their answer to the formal definition and the class moves forward with a common definition going into the lab portion.
During the data collection portion of the lab, the teacher provides feedback by circulating among the groups to check for understanding of the lab procedures, observe if the data collection process is being carried out correctly, suggesting adjustments as needed, and raising questions for the students to consider about the lab. Each group is only collecting data from a single lab station so this portion of the lesson needs to well monitored and pushed along. The feedback from the teacher needs to help students complete the data collection and return to work in their groups as quickly as possible.
During the small group portion of the lab, which is focused on analyzing data, the students receive feedback from each other as well as teacher feedback.
During the large group portion of the lesson, where the collected data is plotted on the board for all to review, student feedback is provided by comparing what is being plotted to their predictions, written answers to questions, teacher questioning of the large group, and student contributions to the discussion.
Students also receive feedback from the teacher's review and comments on the summative assessment (the exit ticket activity).