Students will utilize their understanding of trigonometry and simulations to distinguish between the mathematical models for a projectile launched horizontally and a projectile launched at an angle.

A projectile’s motion is composed of two independent motions: a constant horizontal velocity and a vertical velocity undergoing constant acceleration.

The goal of this lesson is to help students learn that models can be extended to solve more complex problems. This lesson addresses the HSA-RE1.A.1 standard as a way to effectively construct viable solutions related to the motion of a horizontally launched projectile. This lesson is aligned to HSN-Q.A.3 standard because students choose a level of accuracy when they report data values during their explanation of launching a projectile horizontally.

Students explore concepts related to projectile motion using the NGSS Practices of Using Mathematics and Computational Thinking(SP5), Planning and Carrying out Investigations(SP3), and Analyzing and Testing Data (SP4) to correctly choose and test a solution method for quantifying factors related to horizontally launched projectiles. Students will practice creating visuals to show step-by-step analysis for related problems. 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.

I ask my students to identify connections between the factors that affect a projectile's motion and trigonometric functions they already know.

I show students that:

vy = vi*sin(theta)

vx = vi*cos(theta) are still consistent for a horizontally launched projectile.

Students do not need trigonometry, but understanding that the cos(0) = 1 and sin (0) = 0 helps them mathematically model the physical behavior of the velocity vectors that correspond to a horizontally launched projectile. This relates to (SP5) because students have to leverage skills that they learn during mathematics to extend their physical understanding of the system at hand: the time of flight and range of a projectile launched horizontally from above the ground.

Before we transition to the next portion of the lesson, I discuss the results of the previous lesson's exit slip. In particular, I note that students highlighted Galileo's equations of motion as important models for understanding projectile motion. I ask students to look for and take note of more direct connections between the factors from this week's lessons and the trigonometric identities they study in math class.

5 minutes

At the beginning of each lesson, I have a quick Bell-Ringer Activity to help students focus on the tasks for today's lesson. This portion of the lesson follows a routine to help students focus on the goals of the lesson. Today's additional piece of information is a BIG IDEA which states that a projectile's motion is composed of two independent motions: a constant horizontal velocity and a vertical velocity with constant acceleration. I choose this type of warm-up because it is a routine that they are familiar with which helps to lend structure to an otherwise fluid classroom environment.

I also want students to have a clear idea of the key ideas of the class. In addition, my goal is for students to recognize the connections between ideas that build on one another from past lessons. Within this lesson, I ask students to use a simulation to test their calculations of range for two projectiles.

30 minutes

During this section, I write the phrase Angry Bird Physics and circle it on the interactive whiteboard at the front of the room and 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 students to identify information from previous lessons that we will use to understand physics content later in the lesson. I routinely use this activity to have students summarize their current understanding of a particular topic. Students have completed mind maps on Angry Bird Physics before, so I expect the mind maps that students create during this section to contain more details than the previous ones. After students create mind maps I conduct a share out and create a summary mind map on the interactive whiteboard at the front of the room. I lead a question and answering session focusing on general student understanding of projectile motion.

I then lead a whole class discussion around whether we could predict the range of projectiles launched horizontally from a certain height. I present students with the idea that the vertical and horizontal motions of a projectile do not affect one another and can be treated separately. During the next ten minutes, I lead students through a set of notes that give an example of a horizontally launched projectile. In this section of the lesson, I use direct instruction because I am showing students new material that extends their current level of understanding beyond projectile launched from the ground at an angle.

I spend five minutes calling on students from around the room and write down key ideas and equations based on their input and show step by step how the time of flight could be determined in terms of height instead of vertical velocity using an equation of motion that is quadratic with respect to time. Students spend the last ten minutes of this portion of the lesson applying information from the notes to the related question that I project on the interactive whiteboard at the front of the room. Click here to see an example of student work.

35 minutes

During this section of the lesson, I ask students to produce a visual that explains the idea of projectile motion. I project the Visual requirements on the interactive whiteboard at the front of the room for students to complete. Students may work in teams of 2-4 to create a visual that illustrates the physics behind launching a projectile horizontally.

Each visual must include:

- 2-4 problems
- Related terms and their definitions
- Images that illustrate the physics of the problem
- Annotated solutions to the problems
- Tips for peers on "How to solve similar problems?"

As students are creating their visuals, I walk around and check in with students to ensure they have met all of the requirements. It takes a little longer for some students to get started than others, but after five minutes or so most students decide which visual they are going to create and quickly get to the task at hand.

The materials that can be used for this activity are found in the front of the room at a resource station in containers and includes scissors, rulers, washers, colored pencils, markers, dry erase markers, string, whiteboards, multiple sized unlined paper, and highlighters. I also distribute Chromebooks for students who choose to create a visual digitally using Popplet, Prezi, Powerpoint or Powtoon. Click here to see an example of student work. This student uses Powerpoint to create their visual. This student uses Equation Editor to type the equations for their examples of projectile motion and provides screenshots from the Phet projectile motion simulation within their visual. This work needs edits before the student could move from the competent rating to a proficient rating on our schoolwide 5.0 scale because of errors in the equation for maximum height.

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 materials are readily available for the next lesson.

10 minutes

Throughout this lesson I give students multiple opportunities to listen to one another and to control the process of their learning. With this in mind I include a closing activity for this lesson so that students have an opportunity to identify important and challenging aspects of the lesson. The closing activity is a writing routine called a headlines with which students are familiar that asks students to answer the question "What was the most important part of today's lesson?" in 25 words or less. Click here for an example of student work.

This type of closure activity asks students to highlight connections to their previous understanding and key ideas within the lesson. This activity also works to make student thinking visible regarding the underlying reasons behind their understanding.