The goal of this lesson is to help students use their understanding of Galileo's equations of motion to construct ideas related to the motion of an angry bird in terms of time of flight, maximum height and range. This lesson addresses the HSA-REI.A.1 standard because it asks students to show the connections between the factors that affect a projectile's motion and Galileo equations of motion in a step-by-step manner. It aligns with the NGSS Practice of Constructing Explanations for Science because students will create summaries to explain factors that are related to a projectile's motion. This lesson also is aligned with the NGSS Cross-Cutting Idea of Patterns because students must recognize that the horizontal and vertical components of a projectile's velocity are independent of each other.
Within this lesson, students will begin constructing an explanation of the equations of motion highlighted during the lessons from Galileo portion of our curriculum using a Mindmap. Students will then use their understanding of mathematical models from algebra and the idea that a projectile's vertical and horizontal motions are independent of each other to solve Galileo's equations for the time of flight, range, and maximum height of a projectile. Finally, students use group roles work in teams of 2-4 to complete a set of practice problems that connect their new equations to generate testable data. During this lesson, I ask students to focus on stretching their prior algebra and physics knowledge to address the factors related to a projectile's motion. I assess student understanding throughout the lesson using informal check-ins, and will assess each student's work at the end of the school day.
During this portion of the lesson, I ask students to write the objective and the BIG IDEA in their notebooks. I ask my students that, instead of focusing on the "right answer", they focus on the patterns in their results and not simply substitute values into certain math models that we discuss in this lesson. Students can sometimes focus too much on substituting values into equations that they do not recognize when a result is improbable or goes against mathematical reasoning. For example, a student should recognize that neither of the components of a resultant velocity vector is larger than the resultant velocity vector. This relates to (SP5) because students have to leverage skills that they have learned from mathematics to extend their physical understanding of the system at hand: a projectile launched from the ground at an angle.
Today's additional piece of information is a BIG IDEA which states that Galileo's experiments can be used to find mathematical expressions for the two-dimensional motion of a projectile. Later on within this lesson I ask students make several choices which lead them down unique paths where they create ways to meet the objectives of the lesson. I want students to learn that models can be extended to solve more complex problems.
During this section, I write the phrase "Lessons From Galileo" and circle it on the interactive whiteboard at the front of the room. I ask students to create a mind map in their notebooks of key ideas, diagrams, descriptions and equations that come to mind when they hear the phrase. This activity asks them to identify information from previous lessons that we will use to understand physics content later in the lesson.
In this section of the lesson, I inform students that the equations we learned in the second unit could be extended to two-dimensional motion. During this section of the lesson, I use direct instruction because I am showing students new material that extends their current level of understanding. I project a set of notes that have step by step derivations for time of flight, range and maximum height on the interactive whiteboard at the front of the room. I ask students to write this information in their lab notebooks.
I spend 5 minutes calling on students from around the room to check their understanding of how equations of motion can be manipulated to determine the range, total time of flight and maximum height of an Angry Bird's path. During this time, students may also respond to the feedback from other students and share out what stuck with them and what still puzzles them about this section of the lesson.
Students spend the last ten minutes of this portion of the lesson transferring this information into their lab notebooks. I have an inclusive classroom with ~15% of students with IEPs who do not write or process the information at the same pace and I give extra time for students to process what we discuss in this section of the lesson. This strategy of allotting extra time allows all students to have the opportunity to process key information before moving to the next section of the lesson.
I lead a whole class discussion for five minutes about the equations we just derived for maximum height, time of flight and range. During the next twenty minutes, students work on Modeling The Motion of an Angry Bird. Students use the equations from the previous section to generate a set of data tables where they test the effect of the initial velocity and launch angle on a projectile's motion. I include an example of student work here that show students applications of equations and a generated data table for the motion of 5 Angry Bird launches. Students calculate the values using calculators or a computer-based spreadsheet and answer a set of analysis questions based on their calculations. Students can then test their calculations using a laptop and the PhET simulation.
I make sure to ask clarifying questions as I circulate in order to push students into supplying evidence to support their claims about the factors an Angry Bird's motion. For example, I might ask to one team "I heard you say that the horizontal and vertical velocity are always the same for this data, what makes you say that?" in order to help students focus on the idea that cos(45) = sin (45) because 45 degrees is its own geometric and trigonometric complement.
Students work in groups of 2-4, although student groups with size less than 4 will have to double up on the established roles of facilitator, task manager, recorder/reporter and resource manager. Students use these roles whenever they work in groups to ensure that there is equity in the workload. After students complete their data tables, I circulate and students spend the next twenty minutes creating a summary. Each summary includes a problem, the physics of the problem, a step-by-step solution and tips for peers on how to analyze similar problems in the future. Click here for an example of student work that includes a summary of projectile motion. I remind students of the digital resources available to them and then ask for resource managers to gather the materials provided at the front of the room where the equipment is kept.
The front resource station holds equipment in labeled drawers or containers and includes scissors, rulers, meter sticks, washers, colored pencils, markers, dry erase markers, string, whiteboards, multiple sized unlined paper and highlighters. Once we have discussed the requirements for the summaries and all of the materials have been distributed to each group, students begin working in groups at a location of their choice. I ask students to summarize the connections between Galileo's experiments and the mathematical expressions of an Angry Bird's air time, range and maximum height. I circulate the classroom with my classwork assessment clipboard and make notes of groupings and answer clarifying questions for students.
At the end of this section, I pause and ask students to return the materials they used during this section to the front resource station. A resource manager returns each material to a bin or labeled drawer so that they are readily available the next time the materials are needed.
Throughout this lesson, I give students multiple opportunities to listen to one another and to control the process of their learning. The closure is a writing prompt for a routine called a Free Write with which students are familiar. I ask students to: "Write everything that comes to mind when you hear the phrase projectile motion...".
This type of closure activity asks students to highlight connections to their previous understanding and key ideas within the lesson and also works to make student thinking visible regarding the underlying reasons of their understanding. Click here to see an example of student work for the closing activity.