SummaryTo display the results from the previous activity, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. They problem solve and apply their understanding of see-saws and lever systems to create balanced mobiles.
Students must think like engineers to design mobiles that balance their boxes.
After this activity, students should be able to:
- Make a balanced mobile that displays their work and communicates their mathematical observations with others.
- Apply previous knowledge of lever systems to creative problem solving involving spatial relationships.
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Each TeachEngineering lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.
All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN),
a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics;
within type by subtype, then by grade, etc.
Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
- Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback!
- Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback!
- 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. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback!
- Design is a creative planning process that leads to useful products and systems. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback!
- Requirements for design are made up of criteria and constraints. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback!
- Apply a design process to solve problems in and beyond the laboratory-classroom. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment? Thanks for your feedback!
- boxes and leftover scraps from the New Boxes from Old activity
- ~20 36-inch dowel rods, 3/16ths of an inch diameter; available in hardware stores and hobby shops for ~30 cents each
- 2 or 3 utility knives, or inexpensive paring knives
- 1 or 2 single-hole punches
- 2 or 3 spools of regular sewing or heavy thread
- white glue and/or clear nail polish, a few bottles
- several sheets of poster paper, in a variety of colors
Today you will be making mobiles! (Show students a completed mobile that you made yourself. Looking at an actual model gives them a clearer idea of what the finished product might look like, as well as establishing a standard for neatness and craftsmanship.)
(Give students a brief, informal review of levers, which may be helpful as they try to balance the different components of their mobiles.) Have you ever played on the see-saws at a playground? What happens if a child (or an adult) on one end of the see-saw is a lot heavier than the child on the other side? (Listen to student stories.) How could they be evened out? (Listen to student ideas.) To make it more balanced, the heavier person could move closer to the center point (the fulcrum), while the lighter person remains at the far end of the see-saw.
Take a look at this. (Show students two boxes of different weights suspended from the ends of one dowel.) See how these boxes are unbalanced in this mobile. Do you see how this is similar to the two children on the see-saw. But, unlike the see-saw, in our mobiles, the fulcrum can be moved along the dowel rod. It does not have to stay in the center. So, if we hang boxes or other items at either end of the dowel, the balance point can be somewhere besides the center of the dowel, and the hanging points of the components can be moved closer or farther away from the center of the dowel as well.
Now let's get started to make our mobiles!
- Give each student a copy of the Instructions for Students Handout and remind them to read all the instructions before beginning.
- Provide students materials as listed in the handout and remind students of the following design cycle:
- The challenge: Students need to identify the problem (create a mobile with the components described in the handout) while operating within physical constraints (balance boxes of different masses by changing their locations).
- Brainstorm: Give students 10-15 minutes to come up with possible ideas of how to create the mobile within the problem constraints. Students should construct a clear sketch with labels, including the dimensions, volume, and surface area of each box. Ask the students the Investigating Questions to aid their design process.
- Prototype: Students should select their favorite idea and create a prototype from their sketch using the materials provided.
- Test and evaluate solutions: Students should test their mobile and investigate whether their design is balanced or not.
- Redesign: Have students modify their designs to address further challenges that are encountered through testing.
- Communication: Have students discuss their solution with others either in small groups or in front of the class.
- Observe students and troubleshoot to help them achieve success.
- Examine their finished mobiles using the attached rubric.
Advise students to use care when cutting the dowels with utility or other types of knives. As an alternative, pre-cut the dowels into a variety of lengths and have students choose from them. Students with larger boxes will need longer lengths of dowels, while students with small boxes can use shorter pieces.
- Students may have difficulty balancing the components of their mobiles. If their arrangements are such that it is impossible to balance some of the components, they may have to change their design. In some cases, they may be able to add a little bit of weight to a component. Slipping a few paper clips into one of the boxes may help, or adding a border made of poster board to either the mathematical comparisons or scrap component might make these heavy enough.
- Tying knots in thread requires considerable fine-motor ability. Some students may need help with this. Students might also try to avoid it altogether, for example, by simply wrapping the thread around the dowel several times and then taping it in place. This generally looks messy, but is effective. Students may also avoid tying thread by simply taping it to the tops of the boxes; this method is not effective, however. The thread soon slips out from under the tape, which will lift up, once the mobile is hung. Instead, suggest students punch a hole into a corner of the box and tie the thread to it, despite the difficulties involved.
As students attempt to balance the various components of their mobiles. Ask questions to help with their problem solving, such as:
- Do these two boxes have the same weight? Which is heavier? How do you know? (The cube-shaped box, having less material, is lighter than the rectangular box.)
- What do you think needs to happen if you want to balance this light part of your mobile (such as the component showing the mathematical comparison of the two boxes) with this much heavier box? (If the dowel is long enough, the student may be able to place the fulcrum very close to the box and have the lighter component at the far, opposite end of the dowel; otherwise s/he may have to resort to adding more weight to the lighter component. See the Troubleshooting Tips section for ideas.)
The mobile itself serves as an assessment tool. Use the Mobile Scoring Rubric to evaluate each mobile and gauge student comprehension of the concepts.
- Students have now designed mobiles that satisfy material and balanced constraints using their knowledge about levers. Discuss what kind of larger engineered structures use levers in their design (some examples might include cranes, oil pump jacks, etc.).
- Discuss with students how might careful design of these engineered structures help reduce human injury or impact the environment.
ContributorsMary R. Hebrank, project writer and consultant
Copyright© 2013 by Regents of the University of Colorado; original © 2004 Duke University
Supporting ProgramEngineering K-PhD Program, Pratt School of Engineering, Duke University
This content was developed by the MUSIC (Math Understanding through Science Integrated with Curriculum) Program in the Pratt School of Engineering at Duke University under National Science Foundation GK-12 grant no. DGE 0338262. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.
This activity was originally published, in slightly modified form, by Duke University's Center for Inquiry Based Learning (CIBL). Please visit http://ciblearning.org/ for information about CIBL and other resources for K-12 science and math teachers.
Last modified: March 29, 2018