Students investigate the property dependence between liquid and solid interfaces and determine observable differences in how liquids react to different solid surfaces. They compare copper pennies and plastic "coins" as the two test surfaces. Using an eye dropper to deliver various fluids onto the surfaces, students determine the volume and mass of a liquid that can sit on the surface. They use rulers, scales, equations of volume and area, and other methods of approximation and observation, to make their own graphical interpretations of trends. They apply what they learned to design two super-surfaces (from provided surface treatment materials) that arecapable of holding the most liquid by volume and by mass. Cost of materials is a parameter in their design decisions.

This interactive Flash animation allows students to explore size estimation in one, two and three dimensions. Multiple levels of difficulty allow for progressive skill improvement. In the simplest level, users estimate the number of small line segments that can fit into a larger line segment. Intermediate and advanced levels offer feature games that explore area of rectangles and circles, and volume of spheres and cubes. Related lesson plans and student guides are available for middle school and high school classroom instruction. Editor's Note: When the linear dimensions of an object change by some factor, its area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube. This concept is the subject of entrenched misconception among many adults. This game-like simulation allows kids to use spatial reasoning, rather than formulas, to construct geometric sense of area and volume. This is part of a larger collection developed by the Physics Education Technology project (PhET).

From drinking fountains at playgrounds, water systems in homes, and working bathrooms at schools to hydraulic bridges and levee systems, fluid mechanics are an essential part of daily life. Fluid mechanics, the study of how forces are applied to fluids, is outlined in this unit as a sequence of two lessons and three corresponding activities. The first lesson provides a basic introduction to Pascal's law, Archimedes' principle and Bernoulli's principle and presents fundamental definitions, equations and problems to solve with students, as well as engineering applications. The second lesson provides a basic introduction to above-ground storage tanks, their pervasive use in the Houston Ship Channel, and different types of storage tank failure in major storms and hurricanes. The unit concludes with students applying what they have learned to determine the stability of individual above-ground storage tanks given specific storm conditions so they can analyze their stability in changing storm conditions, followed by a project to design their own storage tanks to address the issues of uplift, displacement and buckling in storm conditions.

To further their understanding of sound energy, students identify the different pitches and frequencies created by a vibrating ruler and a straw kazoo. They create high- and low-pitch sound waves.

This is a three act lesson in which students investigate the volume of 2 different cylinders made from the same size of paper. Students determine which would container would hold the greater volume of popcorn, or if the volume would be the same.

Working in teams, students learn the basics of fluid power design using the PFPD as their investigative platform. They investigate the similarities and differences between using pneumatic and hydraulic power in the PFPD. With the main components of the PFPD already assembled, student groups determine the correct way to connect the valves to the actuators using colored, plastic tubing. Once connected, they compete in timed challenges to test their abilities to separate material out of containers using the PFPDs. NOTE: No special pre-requisite knowledge is required for students to be successful in this activity.

Students will use the geometric formula for finding the surface area of a regular square pyramid.

This resource allows students to build conceptual relationships between two-dimensional shapes and three-dimensional figures by means of nets. Students cut different nets and identify and describe the corresponding figures. Students realize and understand why surface areas are measured in square units, and volume is measured in cubic units.

Students are presented with a challenge question that they must answer with scientific and mathematical reasoning. The challenge question is: "You have a large rock on a boat that is floating in a pond. You throw the rock overboard and it sinks to the bottom of the pond. Does the water level in the pond rise, drop or remain the same?" Students observe Archimedes' principle in action in this model recreation of the challenge question when a toy boat is placed in a container of water and a rock is placed on the floating boat. Students use terminology learned in the classroom as well as critical thinking skills to derive equations needed to answer this question.

Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

Students examine the existence of sound by listening to and seeing sound waves while conducting a set of simple activities as a class or in pairs at stations. Students describe sound in terms of its pitch, volume and frequency. They use this knowledge to discuss how engineers study sound waves to help people who cannot hear or talk.

Students should think of different ways the cylindrical containers can be set up in a rectangular box. Through the process, students should realize that although some setups may seem different, they result is a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations.

Students review what they know about the 20 major bones in the human body (names, shapes, functions, locations, as learned in the associated lesson) and the concept of density (mass per unit of volume). Then student pairs calculate the densities for different bones from a disarticulated human skeleton model of fabricated bones, making measurements via triple-beam balance (for mass) and water displacement (for volume). All groups share their results with the class in order to collectively determine the densities for every major bone in the body. This activity prepares students for the next activity, "Can It Support You? No Bones about It," during which they act as biomedical engineers and design artificial bones, which requires them to find materials of suitable density to perform as human body implants.

This simulation lets you see sound waves. Adjust the frequency or volume and you can see and hear how the wave changes. Move the listener around and hear what she hears.

This simulation lets you see sound waves. Adjust the frequency or volume and you can see and hear how the wave changes. Move the listener around and hear what she hears.

Students analyze and begin to design a pyramid. Working in engineering teams, they perform calculations to determine the area of the pyramid base, stone block volumes, and the number of blocks required for their pyramid base. They make a scaled drawing of the pyramid using graph paper.

In this activity, students will find surface area and volume of objects the teacher provides or students bring in.

This formula sheet my students to use for reference when calculating surface area and volume.

Students construct "a tetrahedron and describe the linear, area and volume using non-traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed." (from NCTM Illuminations)

This activity has the students calculate how many paperballs can fit into a trashcan.  There are many extensions that can be developed to use with this video.