Examine some of the complexities and complications inherent in the development of a micro engine. This video focuses on how MIT researchers have to consider proportions comparing volume and surface area when factoring heat loss, taking math out of the classroom and into real world problem solving.

Use spatial reasoning skills to calculate the volume when given a 3D figure. [1:49]

Official homepage of Robert Boyle (1627-1691 CE). The site is very comprehensive in its information about Boyle. The site has links to a bibliography, his works, correspondence, etc.

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.

Revealing multiple ways to find volume using a Rubik's cube. This video focuses on modeling volume and explaining why two different volume equations will give you the same answer.

This video lesson [3:38] demonstrates how to use scale factor to calculate the volume of similar figures. Students can check their understanding with an assessment.

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.

This site provides great practice on the concept of volume. Students can first learn about the topic by watching a step by step instruction video that also points out areas of concern. Finally, students can practice their knowledge by taking a quiz.

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.

This short video and interactive assessment activity is designed to teach third graders about selecting capacity by comparison.

This short video and interactive assessment activity is designed to teach fifth graders about converting capacities using illustrations (english units).

Students explore the volume of three-dimensional shapes, connecting it to the operations of multiplication and addition, as well as classify two-dimensional shapes hierarchically.

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.

This short video and interactive assessment activity is designed to teach fifth graders about single-unit, multi-step problems - word problems.

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.

Learn about sound waves, which move vibrations from one place to another through liquids, gases and solids, with this interactive lesson.

Choosing how to present your talk is an important aspect of preparing for public speaking. Use these tips to decide the most effective method.

As if they are engineers, students are tasked to design solar-powered model vehicles that are speedy and compact in order to make recommendations to a local car sales company. Teams familiarize themselves with the materials by building solar-panel model car prototypes, following kit instructions, which they test for speed. After making design improvements, they test again. Then they take measurements and calculate the volume of each team’s vehicle. They rank all teams’ vehicles by speed and by size. After data analyses, reflection and team discussion, students write recommendations to the car company about the vehicle they think is best for consumers. Youngsters experience key portions of the engineering design process and learn the importance of testing and collaborating in order to make better products. Pre/post-quizzes and numerous worksheets and handouts are provided.

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 Cyberchase media gallery, the Cybersquad must try to follow a recipe exactly to create a mixture that will help cure their friend Slider. At first, the squad must find a way to ensure standard measures of the ingredients. When this proves only partially effective, they must determine how to make the mixture five times stronger.