Shipping and Packaging with Math


Kim Brassfield

Unit Title:

Shipping and Packaging with Math


9 - 10



Estimated Duration:

8 50 - minute class periods

Unit Activities:


July 9, 2016

The Big Idea (including global relevance)

Shipping and packaging in the twenty-first century.

Just about everyone around the world has had something shipped to them or packaged something to be shipped to someone else. Shipping and packaging methods have vastly changed throughout the course of time. People today live in a fast-paced environment where they want things given to them as quickly as possible. In addition, engineers are finding ways to ship just about anything. With the need for shipping rates to be much faster and objects to be packaged in various ways with an assortment of materials, how can drones play a role in this process? How can packaging materials be more cost effective when shipping?


The Essential Questions:
  • How has shipping and packaging things changed as time has passed in order to make shipping more efficient and packaging more cost effective, safe, and presentable?
  • How long have they been using the postal service for shipping?
  • How was shipping done in the past?
  • What types of shipping methods are there?
  • Are there certain packages used for specific shipping methods?


Justification for Selection of Content:

✓ Students previously scored poorly on standardized tests, end-of term test or any other test given in the school or district on this content.

✓ Misconceptions regarding this content are prevalent.

✓ Content is suited well for teaching via CBL and EDP pedagogies.


The Hook:

A FAA Cerftified sUAS Pilot will come in and fly a drone at levels higher than the general public can fly a drone. He will then engage in conversation with my students about drone technology and how it is used with shipping today.


  • Students often struggle with calculating the surface area of three-dimensional figures.
  • Students may think they have to use a prism (box) to package their object since this is the traditional method seen.
  • Students may think that they all must have the same package container design in order for them to be successful.
The Challenge and Constraints:


Description of Challenge (Either Product or Process is clearly explained below):

List the Constraints Applied

Students will work in teams to design a shipping container to safely ship a flower so that the flower is still presentable after shipment. The package must also be able to be carried by the drone across the length of the football field without being damaged in any way. The surface area will be calculated to analyze the cost of their materials. Students are trying to yield the smallest cost in their design.

Students may only use:

  • Carnations
  • Cotton balls
  • Plastic
  • Paper towels
  • Rubber bands
  • String
  • Paper clips
  • Cardboard
  • Scotch Tape
  • Newspaper
  • Plastic Wrap
  • Foil
  • Wooden Dowels

Each seam may be taped with one thickness of tape


Anticipated Guiding Questions (that apply to the Challenge and may change with student input.):
  • How can we create a package container that is cost effective and maintains the appropriate package dimensions for our object being shipped and shipping device, a drone?
  • What types of materials are using for packaging containers?
  • What materials would be most cost effective?
  • When did they start using bubble wrap?
  • How do we calculate how much material we have used?
  • What are some pros and cons of using a drone to ship materials?
  • What is necessary to keep a package container from breaking?
  • What makes a package presentable upon arrival?


Engineering Design Process (EDP):

How will students test or implement the solution? What is the evidence that the solution worked? Describe how the iterative process from the EDP applies to your Challenge.

  • Students will have to design and build their own package container that fits on the drone, does not break, and keeps their flower damage free.
  • After the test flight, students will see if their container successfully shipped the flower – did not damage the container or flower.
  • The evidence that the solution worked is if the package is still completely intact and the flower is not damaged.
  • Modifications will be made for the following reasons:
  • If the packaging container is not damaged nor is the flower, students will determine how they could redesign to minimize the cost.
  • If the packaging container and/or flower is damaged, students will redesign.


How will students present or defend the solution?  Describe if any formal training or resource guides will be provided to the students for best practices (e.g., poster, flyer, video, advertisement, etc.) used to present work.

  • Students will present their original design, evaluation of design, modifications made to packaging container to the students via a 2-minute “Ted Talk” using chart part to display their design sketches and computations.
  • Students will also be responsible for showing their calculations of finding the surface area of their packaging container.
  • Students will be given a rubric on how they will be graded.


What academic content is being taught through this Challenge?

    Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*
    Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*
    Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.


ACS (Real world applications; career connections; societal impact):

Real world applications:

The challenge is strongly real world related due to the fact that just about everyone has had a package shipped to them or shipped a package. In addition, Engineers must design packaging differently for different items. When an item must remain fresh (such as flowers) or alive (such as an organ scheduled for transplant) the packaging requires planning and engineering to make sure the product survives. Optimizing packaging and shipping and keeping the cost minimized impacts lives globally.


What activities in this Unit apply to real world context?

The challenge


Societal Impact:

Shipping and packaging of various materials for personal reasons, medicinal, business-related, war-related, weather-related, among many other reasons is prevalent worldwide. The need for various designs of packaging and shipping methods that expedite the shipping process are important in our continuously growing, changing, and fast-paced world.


What activities in this Unit apply to societal impact?  

The challenge


Careers:  What careers will you introduce (and how) to the students that are related to the Challenge? (Examples: career research assignment, guest speakers, fieldtrips, Skype with a professional, etc.)

  • The hook will shed light on what UAV pilots do with maneuvering drones for agricultural, construction, crime, and various other reasons and how it is done. The challenge will open student’s eyes to what material engineers do in designing packaging to meet the needs of various objects, time constraints, and material constraints.


Unit Academic Standards:
Next Generation Science Standards (NGSS):

Science and Engineering Practices:

Crosscutting Concepts:
Ohio’s New Learning Standards for Science (ONLS):


Ohio’s Learning Standards for  Math (OLS) or Common Core State Standards -- Mathematics (CCSS)

☒ Make sense of problems and persevere in solving them

☒ Model with mathematics

☒ Use appropriate tools strategically


Pre Test

Post Test

Additional Resources:



Post Implementation- Reflection on the Unit:

Students were given a pre and post-test that were both comprised of 4 questions. The first two questions were basic surface area problems and the last two questions were composite surface area questions. Both assessments were out of a total of 24 points. The following graph depicts the comparison of pre- and post- test scores.


shipping and packaging reflection

As one can see, there was a definite growth that occurred amongst my students when comparing the pre- and post-test percentages. In addition, through observation and via PowerPoint presentations and EDP Google docs that were submitted, students ability to work in teams, collaborate, and communicate information grew, as well.

Due to many weather-related and timing issues, this unit did not go 100% as planned for the revision.  I ended up flying the drone right outside my classroom instead of having someone come in or taking them out to the football field due to the weather. Students were still extremely engaged and were fascinated and curious about the drone and how it would play a role in the Geometry classroom. Upon finishing flying, we went back into the classroom and watched YouTube videos about Amazon and another company that utilizes drones for shipping. This led to great discussion about how shipping has changed, privacy with shipping, efficiency etc. Students were then given a Google form to fill out to brainstorm a possible challenge and essential question to answer based on the discussion we had that day and the current topic we had been learning in class – surface area. The following day, I showed students how they had all come up with a common theme of designing a package to ship on the drone and minimize the surface area.

    With their idea, I had them discuss guiding questions. I first had them think of guiding questions independently, then, I had them add them to a google doc that was shared amongst their team members. As a result, students were able to discuss these questions in their groups prior to sharing out with the entire class. We then had a class discussion of various guiding questions and then students were set off to research about the Phantom 3 drone we were using and questions about shipping and packaging via drones. Students were also given a formal challenge introduction and rubric and were tasked to come up with at least two different-shaped designs to bring to class the following day (two per each team member).  It was also required that they come to class with the surface areas calculated in their designs as well. This allowed for more math content to be practiced.

                When they got to class the next day, the team members communicated what they had created and a final prototype was chosen and sketched. Students were then required to work together to determine which materials they wanted to use and the amount, while still adhering to the material constraints outlined in class. Once finalized, I approved the list and students began building. The building process was completed in two days.

   Due to the weather, we could not go outside and fly their packages with the carnation inside across the football field, but instead, used the basketball court. I had another person come in (whom was better with the drone than I) to fly their final designs. This way, I could focus on the teams testing outcomes and fill in the rubric for each group as each team‘s package was flown. When teams were finished with their testing, I encouraged them to get on their Chromebook in the gym and begin filling in the refinement section of the engineering design process Google doc while the successes and shortcomings of their testing phase was fresh in their mind. Students finished this piece for homework, if needed. It was beneficial that this document was on a Google doc and could be accessed simultaneously by all while away from the classroom.

                Spring break occurred at this point, upon arrival back to school 10 days later, students compiled a PowerPoint presentation with the original sketch, surface area calculation, testing successes and shortcomings, reflection and refinements, new sketch design and new surface area calculation. Due to time constraints, these presentations were simply shared with me and not presented to the class. This same day, students were able to take the Post-test.

Students have loved this project both years it has been completed. Using a drone in math is fascinating to them as many of them have not seen one in use so close to them before.  When doing this again next year, I would like to redesign it to also incorporate volume to get more Geometry standards embedded within the project. Otherwise, I would not change a thing. I highly enjoy doing this project and have had so much success with it.