Hands-on Activity The Boxes Go Mobile:
Balancing Hanging Boxes with Levers

Learning Objectives

After this activity, students should be able to:

• Make a balanced mobile that displays their work and communicates with others their mathematical observations.
• Apply previous knowledge of lever systems to creative problem solving that involves spatial relationships.

Educational Standards

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.

NGSS: Next Generation Science Standards - Science

Common Core State Standards - Math

International Technology and Engineering Educators Association - Technology

State Standards

Materials List

• 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

Worksheets and Attachments

Introduction/Motivation

Today you will be making mobiles! (Show students a completed mobile that you made yourself. Looking at a 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!

Procedure

1. Give each student a copy of the Instructions for Students Handout and remind them to read all the instructions before beginning.
2. 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 construct a clear sketch with labels, including the dimensions, volume and surface area of each box. Ask students the Investigating Questions to aid the design process.
• Prototype: Students select a favorite idea and create a prototype from their sketches, using the materials provided.
• Test and evaluate solutions: Students test the mobile and investigate whether the design is balanced or not.
• Redesign: Students modify their designs to address further challenges that they encountered through testing.
• Communication: Students discuss their solutions with others, either in small groups or in front of the class.

3. Observe students and troubleshoot with them to help them achieve success.
4. Examine their finished mobiles using the provided rubric.

Assessment

Final Product Evaluation: Examination of the mobiles themselves serves as an assessment tool. Use the Mobile Scoring Rubric to evaluate each mobile and gauge student comprehension of the concepts.

Investigating Questions

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? (Answer: 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 lightweight portion of your mobile (such as the component showing the mathematical comparison of the two boxes) with this much heavier box? (Answer: If the dowel is long enough, a 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 need to add more weight to the lighter component. See the Troubleshooting Tips section for ideas.)

Safety Issues

Advise students to use care when cutting the dowels with utility or other knife types. As an alternative, pre-cut the dowels into a variety of lengths from which students may choose. Students with larger boxes need longer lengths of dowels, while students with small boxes can use shorter pieces.

Troubleshooting Tips

• Students may have difficulty balancing their mobile components, which is part of the problem-solving challenge. If their arrangements are such that it is impossible to balance some of components, they may need to change their designs. In some cases, they may be able to add a little bit of weight to a component. Slipping a few paper clips into one boxes may help, or adding a poster board border to either the mathematical comparisons or scrap components might make them heavier.
• Tying knots in thread requires considerable fine-motor ability so expect some students to need help with this. As an alternative, have students avoid it altogether by simply wrapping the thread around the dowel several times and then taping it in place. While this generally looks messy, it is effective. Students might get the idea to avoid tying thread by simply taping it to the tops of the boxes, but this method is not effective; once the mobile is hanging, it lifts up the tape, allowing the thread to slip away. Yet another alternative is to punch a hole into a corner of the box and tie the thread to it.

Activity Extensions

Now that students have designed mobiles that satisfy material and balance constraints using their knowledge about levers, discuss what kind of larger engineered structures use levers in their designs. Real-world examples include cranes, oil pump jacks, etc. Discuss how careful design of these engineered structures might help to reduce human injury or impact the environment.

Copyright

Contributors

Supporting Program

Acknowledgements

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.