Modeling Archimedes' Principle

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Objective

Students will be able to build a model to investigate Archimedes’ principle.

Big Idea

Archimedes' principle is a conceptual model of fluid mechanics which connects forces to engineering design.

Warm-Up

5 minutes

I teach this lesson because I believe constructing explanations based on real world models is a skill my students need to attain to be successful in my class and the in external world. Most of my students expressed a desire to study engineering in college, but have not had any practical engineering-based experiences outside of physics class. With this in mind, I have infused concepts from fluid mechanics and engineering design within this lesson.

I emphasize effective collaboration as a way to facilitate learning physics concepts, so at the beginning of the lesson students sit in groups of four at lab stations. During the first five minutes of class, as a bell-ringer activity, I ask students to write down the big idea, the date and the objective for the lesson in their notebooks. I choose this bell-ringer activity because I want students to be aware of the guiding principle for the lesson. I also want students to make connections between their general knowledge, physics driven ideas and key engineering concepts.

After students complete the bell ringer activity, I display the following buoyancy simulation on the interactive whiteboard:

After I load the simulation, I ask students to write predictions in the notebooks regarding whether blocks will sink or float when I drop them into the liquid. After 1 minute has elapsed and students are done writing their initial predictions, I add the blocks into the liquid. I ask students to write whether their predictions were supported or not supported in their notebooks. If their predictions were not supported, I ask students to write suggestions as to why their predictions were not supported. After a minute has passed, I reset the simulation then ask students to write predict what will happen if I change the fluid to something other than water. I change the fluid and repeat the demonstration asking students to record whether their new predictions were supported or not.  

I choose this simulation because I wanted students to have a quick way to test their predictions. This simulation helps students revisit concepts like the forces acting on an object and the idea that less dense objects will float while more dense objects will sink. I chose this simulation to help students front-load concepts related to Newton's Laws of Motion that we cover later in the semester.  I also choose to run this simulation on the interactive whiteboard as a way to have a low pressure way for students to gather evidence that either supports or does not support their hypotheses. 

Guided Question

15 minutes

Several of my students rely heavily on their computational skills of identifying an unknown in an equation. In fact most of my students, regardless of their aptitude, tend to be confident when it comes to substituting values, solving a problem algebraically, then boxing their answers. I use this next activity to give students a protocol that encapsulates a more realistic way to interact with challenging problems.  This protocol asks students to actively read a problem statement, identify the useful information contained within the problem statement, create a visual representation of the system described by the problem statement, determine which relationships will be useful in constructing a solution and communicating this solution in a clear sentence or two after the step-by-step solution. 

Many of my students have trouble "getting started" when word problems are involved. With this in mind, I introduced a protocol that will help them to develop a better conceptual understanding of how to effectively approach and solve word problems. During the first five minutes of this Guided Question section, I project an introduction to the G.I.R.L.S. (Givens, Image, Relationships, Looking For, Solution) protocol for solving physics problems on the interactive whiteboard at the front of the room for students to write in the notebooks. I have students use this protocol when answering word problems or they are creating a solution guide or visual representation of topic we have covered in class. 

Using the G.I.R.L.S. protocol students need to be able:

  • Identify the Givens from the problem statement
  • Sketch an Image of the system being studied
  • Use the appropriate Relationships to solve the problem
  • Identify the unknown that we are Looking For
  • Highlight a Solution to the problem 

 

After students have transferred the provided information into their notebooks on the best way to leverage givens and known relationships to accurately identify unknowns, I have students apply the protocol to the problem that I have projected on the interactive  white board at the front of the room. While students are applying the protocol to the problem, I walk around the room to monitor students progress and answer any clarifying questions that students may have. I spend 3-5 minutes providing one-on-one help to students who need it.  

I spend the final five minutes of this section applying the G.I.R.L.S. protocol to the problem that I have projected on the interactive whiteboard in the front of the room. First I code the example problem statement and solving the example problem. I underline the givens and write a capital G above them, I sketch an image that shows a ball floating in a tank of water, then I write and box the equations related to the volume and density of the ball as well as the mass and weight of the displaced volume of water. I elicit student help for each step in the solution and write the 1-2 sentence summary according to student input. After I have completed applying the protocol to the example problem, I ask students to update their notebooks with any steps that were missing from their application of the G.I.R.L.S. protocol and answer any questions students may have about applying the protocol.

In order to emphasize Practice 6 (SP6), I require that students label each step in their solutions with appropriate units and annotations.  

Archimedes' Principle Investigation

30 minutes

Within this section, I want students to create their own models to investigate Archimedes' principle. Students spend about 25 minutes building aluminum foil boats which they design and test by adding pennies until their prototypes sink. Students refine their designs using information they have gathered during their experiment. During this 25 minute portion of this section, students determine the combined mass of the boat and pennies, isolate the mass of the displaced water and eventually calculate the buoyant force of the water just before their best aluminum foil boat design fails.

I use the interactive whiteboard to project the Archimedes Principle Lab outline. In this task I ask each four member team to create a set of aluminum foil boats, predict the number of pennies that each prototype will be able to successfully carry, and test those predictions.  Each student has to sketch, then design a boat out of the aluminum foil from their team's resources.  After each student had designed and built their prototypes,  students shares their proposed boat design as being able to successfully carry the load of at least 100 pennies.  The students then build their prototypes, measuring the mass of the pennies just before the boat sinks.  Students then rank their designs in order from most successful to least successful. After they have tested each design, I ask students to give supporting details to explain why their claim of building the best aluminum foil boat prototype are supported or not supported based on their understanding of Archimedes' principle in their lab notebooks.  

I choose this activity because I wanted to emphasize the importance of collaboration during scientific investigations.I  have students work in groups of four at lab stations using defined student roles of task manager, resource manager, facilitator and recorder. 

The student with the task manager role reads the procedure aloud and asks me clarifying questions about the required tasks. 

I ask teams to send a resource manager to obtain:

1 tub of water (I use Sterilite containers about the size of a shoe box)  

1 30 cm x 30 cm sheet of aluminum foil  

1 plastic bag that has 100 pennies in it

1 triple beam balance

1 pair of scissors

1 12" ruler

The student with the facilitator role makes sure that everyone participates in the lab activity and keeps the group working toward completing the tasks by the end of the 25 minute time limit. The recorder copies data for the group in a table in his or her lab notebook that includes the trial number, the mass of the boat and the number of pennies added before the boat sinks.  During the last 5 minutes of this section, the recorder then shares the data table with the rest of the team. Each group member then records the team data table into his or her notebook.

Mini Poster

25 minutes

Once students are done organizing their lab notes, I project an Archimedes Mini Poster Guide on the interactive white board (SP6 and SP8). I create this activity because I want my students to learn that buoyancy is directly related to the amount of fluid being displaced by an immersed object. I distribute bins which contain colored pencils, markers, poster paper and Chromebooks to each team. Students are seated in pairs and are tasked with creating a visual within 15 minutes to represent their understanding of Archimedes' principle. I have included an example Mini Poster on Archimedes' Principle that incorporates the G.I.R.L.S. protocol from the previous section. 

After student pairs have created a visual, I ask them to spend 5 minutes working individually on a related Archimedes Principle Challenge Question, taking care to annotate each step of their written components. 

Closure

5 minutes

Once students are done creating their mini posters, I ask them to add their names to the mini-posters and to place them on the resource table. I ask students to clear their immediate area before the next class begins.

Then, I hand out an Exit Slip in which students express their current understanding of the important portions of today's lesson and the Student Role  they chose during this activity. I use the information from student Exit Slips to determine possible new pairings that will help students move more effectively through material. I also keep track of student self reporting of their current understanding levels so that students have information for student led conferences which are discussed further here.

After five to seven minutes have elapsed and students have completed their exit slips, I collect the slips to be graded and returned to students during the first five minutes of the next lesson.