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# Introducing Gravitational Field Strength

Lesson 10 of 11

## Objective: Students will define gravitational field strength and variables that affect its value.

## Big Idea: Gravitational field strength is directly proportional to a celestial body's mass and inversely proportional to a celestial body's radius squared.

*75 minutes*

This lesson addresses standards HS-PS2-4 and HSA-CED.A.1 because it asks students to create mathematical expressions for the gravitational field strength of a celestial body and solve problems using this expression. It also aligns with the NGSS Practices of Using Mathematical Reasoning (SP5) and Developing and Using Models (SP2) for Science because students use mathematical logic to create visuals that demonstrate their understanding of the relationship between the radius of a celestial body and its gravitational field strength.

The concept of gravitational field strength is useful in constructing an explanation of concepts like free fall, projectile motion, and forces like weight and the normal force later on in the curriculum. This introductory lesson on gravitational field strength precedes lessons on the Law of Universal Gravitation and Planetary motion. Within this lesson, students obtain information for a mathematical model of the gravitational field strength from a set of video notes with pause points. Students then use their understanding of mathematical models to calculate the gravitational field strength of a set of celestial bodies given their masses and radii. Finally, students work in teams of 2-4 to create visuals that illustrate the gravitational field strengths of 9 celestial bodies and predict which celestial body corresponds to which mathematical model. 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.

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#### Warm-Up

*5 min*

At the beginning of each lesson, I have a quick Bell-ringer activity to get students focused on the tasks for today's lesson. There is a slide with the date, the objective and an additional prompt projected on the interactive whiteboard with a red label that says "COPY THIS" in the top left-hand corner.

Sometimes the additional prompt is a BIG IDEA for the lesson, or the Quote of the Day or a Quick Fact from current events that is related to the lesson. The red label helps my students easily interact with the information as soon as they enter the room and avoids losing transition time as students enter the classroom. Today's BIG IDEA is that the gravitational field strength is inversely proportional to the square of the radius of a celestial body.

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Within this lesson, I introduce a mathematical model for the gravitational field strength. I include a set of notes that I project at the interactive whiteboard in the front of the room for this section below. This part of the lesson focuses on the mathematical model for gravitational field strength. For the first ten minutes, I play the notes at the front of the room for the entire class and pause at the pause points I embed as green question marks in the video.

During the first ten minutes, students take notes in their notebooks. I ask students if they have any questions or concerns about the methods discussed in the video. We have a whole class discussion for 2-4 minutes. During the last minute of this section of the lesson, I email this video and notes to the entire class so that students can watch, pause and replay the video outside of class. During the next section, students are given a set of practice problems related to these notes to complete in pairs.

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During the first 5 minutes of this section, I distribute a set of 9 scenarios and project a table of the gravitational field strengths for 10 celestial bodies on the interactive whiteboard at the front of the room. I ask students to spend 30 minutes working in pairs to use mathematical reasoning to determine which celestial body corresponds to each scenario.

I create this problem with more choices than solutions because I want students to use mathematical reasoning to determine gravitational field strength and assign celestial body names afterward. This way students are making assertions based on logic instead of by guessing or rote memorization. Once students are done with determining the gravitational field strength for each scenario, I ask students to create a summary poster or white board that summarizes their findings about which scenario corresponds to each celestial body.

While students are working, the whiteboards are available to them at the front and side of the room. I also allow one student per lab station to grab resources from the resource table including handheld whiteboards, dry erase markers, calculators, chart paper, markers and colored pencils to use as they construct their explanation of which celestial body corresponds to each scenario. Click here to see an example of student work.

After 30 minutes elapse, I ask students to spend 5 minutes writing a summary of how to identify the gravitational field strength for a celestial body in their notebooks.

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#### Closure

*10 min*

I provide students with an Exit Slip with a set of writing prompts for a routine called a 3-2-1, where I task students with both identifying their personal level of understanding of key ideas within the lesson and identifying the underlying reasons behind their understanding. Some student responses include:"Remembering to use parenthesis during calculations is important", "Learning how to calculate the gravitational field strength without knowing which planet your numbers represent is important." While other student responses include suggestions of "Watch the video and follow along with a Chrome book or you'll be lost", "Write your calculation step by step in your notebook or your numbers will not make sense"

After ten minutes elapse, I collect the slips to grade them. I use this type of closure activity because it encourages students to consider multiple viewpoints on a scientific topic. To wrap up the lesson, I remind students that I will grade and return the exit slips at the beginning of the next lesson.

#### Resources

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- LESSON 1: Lessons from Galileo
- LESSON 2: Investigating Basic Types of Physics Graphs
- LESSON 3: Motion in Terms of Position and Time
- LESSON 4: Introduction to Linear Motion
- LESSON 5: Modeling Motion Using Motion Maps And Position vs Time Graphs
- LESSON 6: Modeling Motion in Terms of Velocity vs Time Graphs, Part 1
- LESSON 7: Modeling Motion in Terms of Velocity vs Time Graphs, Part 2
- LESSON 8: Finding the Slope of a Position vs Time Graph
- LESSON 9: Finding the Slope of a Velocity vs Time Graph
- LESSON 10: Introducing Gravitational Field Strength
- LESSON 11: Galileo's Equations of Motion