Summary
Students are introduced to the important concept of density with a focus is on the more easily understood densities of solids. Students use different methods to determine the densities of solid objects, including water displacement to determine volumes of irregularlyshaped objects. By comparing densities of various solids to the density of water, and by considering the behavior of different solids when placed in water, students conclude that ordinarily, objects with densities greater than water sink, while those with densities less than water float. Then they explore the principle of buoyancy, and through further experimentation arrive at Archimedes' principle—that a floating object displaces a mass of water equal to its own mass. Students may be surprised to discover that a floating object displaces more water than a sinking object of the same volume.Engineering Connection
Density is a scientific property that is important in many materials engineering applications. In this unit, students experience engineering by designing boats to float with various amounts of weight.
More Curriculum Like This
Students use modeling clay, a material that is denser than water and thus ordinarily sinks in water, to discover the principle of buoyancy. They begin by designing and building boats out of clay that will float in water, and then refine their designs so that their boats will carry as great a load (m...
Students explore material properties in handson and visually evident ways via the Archimedes' principle. First, they design and conduct an experiment to calculate densities of various materials and present their findings to the class. Using this equation, they calculate the numerical solution for a...
Students are introduced to the important concept of density. Students devise methods to determine the densities of solid objects, including the method of water displacement to determine volumes of irregularlyshaped objects.
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

Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object.
(Grades 6  8)
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This standard focuses on the following Three Dimensional Learning aspects of NGSS:Science & Engineering Practices Disciplinary Core Ideas Crosscutting Concepts Plan an investigation individually and collaboratively, and in the design: identify independent and dependent variables and controls, what tools are needed to do the gathering, how measurements will be recorded, and how many data are needed to support a claim.Science knowledge is based upon logical and conceptual connections between evidence and explanations. The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion.All positions of objects and the directions of forces and motions must be described in an arbitrarily chosen reference frame and arbitrarily chosen units of size. In order to share information with other people, these choices must also be shared. Explanations of stability and change in natural or designed systems can be constructed by examining the changes over time and forces at different scales. 
Ask questions that can be investigated within the scope of the classroom, outdoor environment, and museums and other public facilities with available resources and, when appropriate, frame a hypothesis based on observations and scientific principles.
(Grades 6  8)
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Common Core State Standards  Math

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
(Grades 9  12)
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Unit Overview
In the first lesson, Floaters and Sinkers, students gain an intuitive understanding of density by comparing objects of equal volumes but different masses. They use different methods to determine the densities of solid objects, including water displacement to determine volumes of irregularlyshaped objects. By comparing densities of various solids to the density of water and considering the behavior of different solids when placed in water, students conclude that objects with densities greater than water usually sink while those with densities less than water float. Through the associated activity, Determining Densities, students learn to determine densities of objects and depict their results graphically (mass vs. volume). They use two different methods to determine the densities of a variety of materials and objects, some of simple geometric shapes (direct measurement of volume) and others irregularlyshaped (water displacement). Results reveal that objects with densities less than water (floaters) lie above the graph's diagonal line while those with densities greater than water (sinkers) lie below the diagonal.
Next, students complete the Clay Boats activity, which challenges them to design and build boats from modeling clay (a material that normally sinks in water) that are able to carry as much weight as possible. After discussing their observations and conclusions, students complete the Buoyant Boats activity, in which they conduct a simple experiment to see how the water level changes in a beaker when a lump of clay sinks in the water and when the same lump of clay is shaped into a bowl that floats. The surprising observation is that the floating clay displaces more water than the sinking clay. Comparing the mass of water that is displaced when the clay floats to the mass of the clay itself reveals that they are about the same. These activities prepare students to receive the content material of the second lesson, What Floats Your Boat?, giving them a full understanding of the principle of buoyancy and Archimedes' principle.
Unit Schedule
 Day 13: Floaters and Sinkers lesson
 Day 45: Determining Densities activity
 Day 68: What Floats Your Boat? lesson
 Day 9: Clay Boats activity
 Day 10: Buoyant Boats activity
Assessment
 Provide students with a table of densities of common materials. Ask them to identify the materials with the highest and lowest densities. Ask them to give an example of a material that floats in water, and a material that sinks in water. Also, ask them what the density of water is.
 Provide students with a list of several objects, their masses and their volumes. Ask students to calculate the density for each object, and check that they include units in their answers.
 Ask students to each write a paragraph that explains why a hollow wooden cube and a solid wooden cube, both made of the same type of wood and having the same dimensions, do not float in quite the same way. Suggest they include diagrams in their explanations if it helps.
 Ask students to each write a paragraph that explains why a lump of clay sinks in water, while the same volume of clay, when shaped like a shallow bowl, floats in water. Similarly, ask students why a bar of steel sinks in water, but ships made of steel do not. Suggest that they include diagrams if it helps with their explanations.
 Ask students to predict the weight of water that would be displaced by an empty canoe weighing 120 pounds. Assume the canoe is afloat. Also, ask if the amount of water displaced by the same canoe would increase or decrease if the canoe tipped over, filled with water, and sank.
Contributors
Mary R. Hebrank, project writer and consultant, Duke UniversityCopyright
© 2013 by Regents of the University of Colorado; original © 2004 Duke UniversitySupporting Program
Engineering KPh.D. 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.
The lessons and activities in this curricular unit were originally published, in slightly modified form, by Duke University's Center for Inquiry Based Learning (CIBL). Visit http://ciblearning.org/ for information about CIBL and other resources for K12 science and math teachers.
Last modified: January 10, 2019
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