NoS – Modeling

Models are both a goal and a tool of science. Scientists often seek to produce a model of the phenomenon they are studying that makes predictions that match observations. Then those scientists or other scientists can use the model to engage in further study. Sometimes the model is good enough that non-scientists can use it as a tool to benefit or understand their own lives. Google Maps is one such example of a model that became a tool for everyday use. Personalized music or movie recommendations are another model we see applied in our everyday lives.

Modeling is part of both the CCSS Math Practices and the NGSS Practices. The following activities directly address modeling and are therefore reasonable to include in any math or science class.

This section references two resources:

These resources can be used during one entire 60+ minute period or each part below could be used as a sponge activity on three different days. Each part below was conceived as requiring approximately 20 minutes.

Part 1

Parable of the Polygons is one of my favorite resources. It teaches a valuable social lesson and it is an incredibly clear model. Hart and Case’s post could be equally at home in a social studies class, a science class, or a math class. I think it is particularly important to include resources like this in science and math class to expose students to social and justice issues and trouble any notion that math and science are neutral fields. The post utilizes a cellular automata model to illustrate what happens when members of a population have small individual biases towards other members of that population. Students can interact with the post and watch as the simple, sensible cellular preferences cause the entire population of cells to segregate from each other. The post refers to itself as a simulation, so a possible point of discussion could be the difference between a simulation and a model.

Parable of the Polygons image

 

Students should be given at least 10 minutes to browse and play with the post. For classrooms that may need some language support, the teacher can project their screen to the board and work through the first four panels, as they contain the text that explains the model/simulation.

Students should consider the following questions while they are exploring the post:

  • What is being modeled here?
  • How is that phenomenon being modeled?
  • What are strengths and limitations of this model?
  • Is this a good model? Why or why not?

Once students have had some time to explore and play with the post, they should answer the above questions. This could be done in a class journal where they write regularly, as a quick write assignment, or as small group discussions.

Part 2

Matt Parker contributes content to the YouTube channel Numberphile as well as to his own channel, standupmaths. This stand-up routine featuring spreadsheets is from his channel.

This video is entertaining and engaging and spreads the love for spreadsheets, which don’t get enough appreciation in general, and definitely not from middle and high school students. In the video, Matt builds up to revealing that the spreadsheet he’s sharing which just seems like a random jumble of red, green, and blue colored cells, all of varying brightnesses, actually creates an image when the user zooms out far enough. Matt then makes this a hands-on exercise by providing a website where anyone can create a spreadsheet out of an image.

While students watch the video and then make their own spreadsheet images, they should consider the following questions:

  • What is being modeled here?
  • How is that phenomenon being modeled?
  • What are strengths and limitations of this model?
  • Is this a good model? Why or why not?

Once students have had some time to create their own spreadsheet images, they should answer the above questions. This could be done in a class journal where they write regularly, as a quick write assignment, or as small group discussions.

Part 3

Students, having been exposed to two different robust but approachable models, should now begin to think about what it takes to create a model. Below is a brief overview of an activity that will guide students through considering a model of their own. Students can do this activity individually, or in small groups.

  1. Students choose a phenomenon to be modelled.
    • Examples: student paths through the school, school lunches purchased/consumed throughout the month, how fast a rider has to pedal to go different speeds on a bike.
  2. How could the phenomenon be modelled?
    • A spreadsheet? An equation? A drawing?
  3. What information would be needed in order to create the model?
  4. How could that information be collected?

This activity could be expanded and extended to allow the students to actually collect information and create their models. This could be the basis for a multi-day lesson on modelling should time allow.

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