Summary
To 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 cubeshaped 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 seesaws and lever systems to create balanced mobiles.Engineering Connection
Students think like engineers as they design balanced mobiles composed of boxes.
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.
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Students review how to determine the surface area and volume of a rectangular prism, that all dimensions are equal in cubes so the volume of cubes are the length of any side raised to the third power, or cubed. This prepares them for two associated activities.
Educational Standards
Each TeachEngineering lesson or activity is correlated to one or more K12 science,
technology, engineering or math (STEM) educational standards.
All 100,000+ K12 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 K12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K12 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

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 )
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This Performance Expectation focuses on the following Three Dimensional Learning aspects of NGSS:Science & Engineering Practices Disciplinary Core Ideas Crosscutting Concepts Define a design problem that can be solved through the development of an object, tool, process or system and includes multiple criteria and constraints, including scientific knowledge that may limit possible solutions. Alignment agreement:
The more precisely a design task's criteria and constraints can be defined, the more likely it is that the designed solution will be successful. Specification of constraints includes consideration of scientific principles and other relevant knowledge that is likely to limit possible solutions. Alignment agreement:
All human activity draws on natural resources and has both short and longterm consequences, positive as well as negative, for the health of people and the natural environment. Alignment agreement:
The uses of technologies and any limitations on their use are driven by individual or societal needs, desires, and values; by the findings of scientific research; and by differences in such factors as climate, natural resources, and economic conditions.Alignment agreement:
Common Core State Standards  Math

Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation.
(Grade 6 )
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Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
(Grade 7 )
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International Technology and Engineering Educators Association  Technology

Design is a creative planning process that leads to useful products and systems.
(Grades 6  8 )
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Requirements for design are made up of criteria and constraints.
(Grades 6  8 )
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Apply a design process to solve problems in and beyond the laboratoryclassroom.
(Grades 6  8 )
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State Standards
North Carolina  Science

Explain the effects of balanced and unbalanced forces acting on an object (including friction, gravity and magnets).
(Grade
7 )
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Materials List
 boxes and leftover scraps from the New Boxes from Old activity
 ~20 36inch 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 singlehole 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
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 seesaws at a playground? What happens if a child (or an adult) on one end of the seesaw 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 seesaw.
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 seesaw. But, unlike the seesaw, 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
 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 1015 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.
 Observe students and troubleshoot with them to help them achieve success.
 Examine their finished mobiles using the provided rubric.
Worksheets and Attachments
Safety Issues
Advise students to use care when cutting the dowels with utility or other knife types. As an alternative, precut 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 problemsolving 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 finemotor 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.
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 cubeshaped 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.)
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.
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. Realworld 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.
Contributors
Mary R. Hebrank, project writer and consultantCopyright
© 2013 by Regents of the University of Colorado; original © 2004 Duke UniversitySupporting Program
Engineering KPhD Program, Pratt School of Engineering, Duke UniversityAcknowledgements
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 GK12 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 K12 science and math teachers.
Last modified: July 27, 2018
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