Standard Benchmarks and ValuesHeat and Thermodynamics – Understand the laws of thermodynamics, and their applications. Std PS5 a 5.6 (heat, temperature, heat energy, heat engine, 1st law of thermodynamics)

HS-PS3-4. - Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform

energy distribution among the components in the system (second law of thermodynamics).

HS-ETS1-2. - Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.

Photo by Jeff KubinaPhoto by Tetra Pak

Ethnomathematics 2

THERMODYNAMICS:

Melissa Montoya

11th - 12th Grade4 - 5 Blocks

FOOD PACKAGING DESIGN

What are the best materials to use for an insulated shave ice container that will be both cost-efficient and environmentally-friendly?

Enduring Understandings• Students will go through the engineering design process to design the best

insulated shave ice container.• Students will test different materials to see which combination is the best

design for insulation.

Critical Skills and Concepts• Students will be able to compute the rate at which the ice melts with

different materials.• Students will graph the date to compare.• Students will predict which materials to use in their own packages and predict the

“m” value (insulating capacity) for their package.• Students will design an insulated container to hold the shave ice using a different

combination of materials.

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ONAuthentic Performance Task• Students can compare different insulating materials that are good

insulators and those that are less effective as insulators.• Students will interview people outside the school to determine what

proper attributes food packaging for shave ice should have.• Students will compare their “m” value of their designed package to others’

packages in the class to determine who had the best design.• Students will compare the materials used as cost-efficient and

environmentally-friendly.

• The school community which includes other students, teachers, and parents. Students can also contact local shave ice vendors to suggest ideas towards being cost-efficient and environmentally-friendly.

• Completed lab reports and design connection reports, which include proper calculations and graphs to compare data.

Authentic Audience

Other Evidence

Procedure, Data, Observations1. Use a thermometer to measure

the air temperature. Record this temperature in your data table.

2. Examine a paper cup and experimental material. Use a hand lens to take a close look at the two materials. Cut each one so that you can examine a cross section of each material. Record

any similarities and differences you notice in your data table.

3. Measure 200mL of shave ice. Use it to mark the 200-mL level on the inside of two of the paper cups.

4. Make a small hole in the center of the bottom of another two paper cups. The

Learning Plan - Part AIn a group, students will work through prediction questions:• How is heat transferred?• What factors affect the rate of heat transfer?• How do materials that are good insulators differ from materials that are

poor insulators?• Design Connection: How could you modify a package to increase

its effectiveness as an insulator? How could you reduce its insulating properties?

Ethnomathematics 4

LESSON

Questions Answered in Lab ReportInterpretations of the Data1. Which of the containers that you tested “gained” heat more slowly?2. Which materials that the class tested had the lowest m values?Reflections3. How did the class results compare with your predictions? How would you

explain any differences?4. What are some possible sources of experimental error?

hole should be just large enough for a thermometer or Vernier to fit through.

5. You will construct two containers from the paper cups. Determine how to completely wrap one paper cup container with one layer of your experimental material. The other paper cup container will be your control. Keep in mind that you need to be able to put 200 mL of shave ice into your containers.

6. Pour 200mL of shave ice into the bottom of your containers. Place the paper cups from Step 4 on top so that they are rim to rim to make one complete container. The hole you made in Step 4 should now be at the top of each container. Use masking tape to join the top and bottom. Be sure the seam between is tightly sealed.

7. Insert a thermometer or Vernier through the hole in the top of each container. Wait for the temperature to reach the lowest point. Record that temperature as the 0 minutes in your data table. Take a temperature reading every minute for twenty minutes. Record your data.

8. Graph both sets of data on the same piece of graph paper so

you can compare them. Plot time (independent variable)on the x-axis and temperature (dependent variable) on the y-axis.

9. The rate at which the ice in each container melts depends on the insulating capacity of the container as well as the difference in temperature between the ice and water inside and the air outside the container. You can use the following equation to determine the insulating capacity, or m-value, for each container tested: T2 = T1 – m (T1-Tair) delta-t , where T2 is the temperature reading from your set of data; T1 is a temperature reading taken one minute earlier than T2; T air is the air temperature; delta-t is the change in time between T1 and T2; and m is a decay constant that reflects the insulating capacity of the container. The larger m is, the faster the cool escapes the container.

10. Share your data with other groups by posting on the front board. In a class data table, record the m values for each of the materials tested in your lab report. Each group has a different material. Some groups may have more than one material to test.

Learning Plan - Part B

Procedure, Data, and Observations

Interpretations

Reflections

Designing an Insulating PackageIn this part of the activity, you will try to design a package that insulates better than any of the materials tested in Part A. Then, using class results, you will draw conclusions about the characteristics of insulating packaging.

PredictionsDecide which materials you will use in your package. Then predict what m-value your package will have. Give reasons for your predictions.

Design Process: EmpathyInterview at least three people outside of the class to see what attributes they want to see in a shave ice food package.

1. Decide on a design for an insulating package that you think will have a lower m value than the materials tested in Part A, in other words, a package that will insulate better. Your package should hold 200 mL of shave ice and not exceed the following dimensions: 20cm x 20cm x 20cm. Your package can only have three layers of material from what we tested. Draw a labeled diagram of your package design in your data table. List the materials used.

2. Construct the package and test it. Record your data in a data table. Then graph the data as you did in Part A.

3. Calculate the m value for your package.4. Share your results with other groups. Record your results in a class

data table. Through class discussion, identify the characteristics of successful insulating packages.

1. Were you able to construct a package with a lower m value (closer to zero(0)) than any of the materials tested in Part A? If so, how? If not, why do you think the design you chose failed to insulate better?

2. What group’s package insulated best? Describe the package and explain why you think it was so successful.

3. How did your results compare with your prediction? How would you explain any differences between your prediction and your results?

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Putting It All Together

Design ConnectionSuppose you had to design an insulating package using only materials that could be easily recycled. Describe your package design and explain your choice of materials.Extension: Students can research and describe how long it would take for each item of the container to decompose. Students can describe cost of each container given the materials they choose to work with.

1. Based on class results, which types of materials are good insulators? What are properties of those materials?

2. What differences did you notice in the construction of packages that were good insulators and those that were less effective?

Ethnomathematics 6

LESSON

Materials Needed• Shave Ice Machine• Ice• 2 cups per group for the control• 2 cups per group for each material

they are testing for Part A• 1 thermometer for each group

• 2 cups per student for design of Part B (each design is individual)

• Materials for insulation: cellulose paper, foil, bubble wrap, foam sheets, Styrofoam peanuts, cardboard, cardboard, etc…

• Timer