Balancing Act

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Objective

SWBAT determine what factors determine whether or not two objects of different mass will be able to balance one another and use those factors to predict balance mathematically.

Big Idea

Can objects of different mass be arranged so they balance one another? Is there a mathematical equation that can predict balance?

The Need for the Lesson

In this lesson students will observe patterns when attempting to balance two objects of different masses on either side of the teeter-totter. There are an increasing number of middle school students who have not had the opportunity to experience physics in action on the playground. I drove around my hometown to look for a teetor-totter at the schools and parks. I found none.

In many ways I think our physics / physical science teachers had an easier time explaining to us how things worked by activating our prior knowledge via experiences on the playground. Students without this prior knowledge will need to have experiences to help them understand abstract concepts. This simulation - Balancing Act - will help students see how passive objects exert forces and by observing patterns understand how proportional reasoning will help them predict how two objects of different masses can balance using mathematics.

Investigation Summary & Preparation

5 minutes

In this lesson students will observe how applied forces can change an objects motion. We are looking at rotational motion as the students make observations to find a pattern that can be used to predict how to balance two objects of different mass. (MS-PS2-2 Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object.)

Disciplinary Core Ideas of Forces and Motion include:

PS2.A The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. And All positions of objects and the directions of forces and motions must be described in an arbitrarily chosen reference frame and arbitrarily chosen units of size. In order to share information with other people, these choices must also be shared. 

The Cross Cutting Concept is Stability and Change.

The simulation include options to view visual displays that will help students strengthen their claims supporting the CCSS ELA standard integrating visuals to clarify understanding and provide evidence to support student claims (SL.8.5 Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest.)

Student engagement is supported as students use the Balancing Act simulation as a model to explain proportional reasoning as a tool to predict balance. Students are also developing perseverance as they extract evidence through inquiry to support their understanding of force and motion. Perseverance is being challenged as students use their data collection to inspire them to use the appropriate mathematical concepts to answer scientific questions. By changing variables to deepen their understanding, students are developing mastery as they use the simulation as an iterative process. (7.RP.A.3 - Use proportional relationships to solve multiple step ratio and percent problems). (SP2 - Using Models) (SP4 - Using Data) (SP5 - Using Mathematical Thinking)

Students will discover that balance can be predicted mathematically by multiplying mass * distance on each side of the fulcrum. If the products are equal, the lever will balance. Students employ the use of two standards of mathematical practice in this lesson. With a model, students will be able to collect the data to support their mathematical findings. (MP4 - Model with mathematics) and (MP2 - Reason abstractly and quantitatively).

Conducting investigations is inherent in all the PhET simulations as they allow for the change of variables that allow students to make changes in their investigation that lead to the discovery of answers to specific questions. Students in this simulation are changing variables in the simulation to understand the relationship between force and motion of objects. (SP3 - Planning and Conducting Investigations)

Throughout their investigations students are asked to collect observations and use the information collected to make conclusions building upon their experiences to develop habits and skills leading towards independent explorations. The lesson asks students to collection observations in a table and use that information to state conclusions about their investigation. (SP8 - Collecting and Communicating Information)

At the end of the lesson, students will replicate their virtual experience with a homemade first class level. pennies and nickels.

A complete materials list is available in the resource section.

Students in Action

40 minutes

Students in Action

Students take a few minutes to answer questions 1, 2 & 3 on today's lesson handout using Turn/Talk/Record. Working with their elbow partner, students will discuss the questions and record their answers. Recording answers provides a level of accountability for the discussion time. It is also building a habit of practice. Since I will soon call on groups to share out their answers, students are vigilant about recording their answers.

When we work as a groups students can easily explain and demonstrate the answers to questions 1 & 2. It seems most all of the students have carried a heavy backpack or other load in one hand and felt themselves leaning in the direction of the load. When the load is balanced - two heavy backpacks, one in each hand, students demonstrate that they are able to walk upright if not somewhat slouched.

Students are hesitant to proclaim that they can predict where the objects of different mass should be in order to balance. 

PhET Simulation - Balancing Act Link

The lesson requires students to find objects of different masses that balance and record the distance from the fulcrum and the mass for each object. The data collected should be sufficient for students to begin to see a pattern. If students multiple the distance and force on the left, it should match the product of the distance and force on the right.

In this video, I share how I model using the simulation for students and the expectations for the type of data they are collecting. I also share an example of student data collection.

As students work, I circulate around the classroom. I want to make sure that the data they are recording is correct so they can make an unencumbered observation to find the mathematical pattern that allows them to predict balance.

When a student says they cannot find a pattern, I read their data out loud in such a way as to help them hear the pattern as I say it. So, you placed 20kg at 1 meter and 10kg at 2 meters and the result was a balance. Look at the numbers on the left 20kg, 1 meter they are equal to the 10kg, 2 meters. What operation can be performed on these two sets of numbers to show they are equal?

Connecting the Learning

15 minutes

I hand out the rulers, fulcrums, and pennies. Providing tools for exploration allows students an opportunity to test their virtual experiences with real world objects. It allows students to apply what they learned to a new situation, answering the question whether this example applies only in certain situations or can I apply the concept to other situations as well.

We use building toys to make our fulcrum - quick, easy and fun!

 

Students should balance the ruler on the fulcrum (first class lever) before adding objects.

I remind students this is our experimental control. Does the ruler balance without additional mass?

 

  

This time I ask students to apply the formula they used to balance the objects in the virtual lab to the pennies and the ruler. I ask students to balance various combinations with multiple pennies stacked one on top another.

  Left Side  Right Side

         1             2

         2             4

         4             6

Does the formula apply to this situation as it did in the virtual lab?

Yes, indeed, we did find the formula applied to the student made lever in the same way it worked in the virtual lab. 

Example:  Left side 1 penny * 6 inches (distance from the fulcrum) = Right side 2 pennies * 3 inches (distance from the fulcrum)

 


I hand out nickels and ask students to balance the teeter-totter using one nickel and one penny. We did not attempt to calculate the mass * distance for the right and left side of the balance to prove what we learned virtually. I am definitely adding that step the next time I use this lesson in class!