This 10-minute video lesson take the revolution around something other than one of the axes.

This 4-minute video lesson looks at the last part of the problem in part 7 (see previous video lesson).

This 9-minute video lesson uses the \shell method\ to rotate about the y-axis.

This 9-minute video lesson shows how to figure out the equation for the volume of a sphere.

After completing the associated lesson and its first associated activity, students are familiar with the 20 major bones in the human body knowing their locations and relative densities. When those bones break, lose their densities or are destroyed, we look to biomedical engineers to provide replacements. In this activity, student pairs are challenged to choose materials and create prototypes that could replace specific bones. They follow the steps of the engineering design process, researching, brainstorming, prototyping and testing to find bone replacement solutions. Specifically, they focus on identifying substances that when combined into a creative design might provide the same density (and thus strength and support) as their natural counterparts. After iterations to improve their designs, they present their bone alternative solutions to the rest of the class. They refer to the measured and calculated densities for fabricated human bones calculated in the previous activity, and conduct Internet research to learn the densities of given fabrication materials (or measure/calculate those densities if not found online).

This short video and interactive assessment activity is designed to teach second graders about capacity comparison problems with illustrations - word problems.

This short video and interactive assessment activity is designed to teach third graders an overview of capacity IIi (metric units).

This short video and interactive assessment activity is designed to teach second graders about capacity problems with illustrations - word problems.

Students observe Pascal's law, Archimedes' principle and the ideal gas law as a Cartesian diver moves within a closed system. The Cartesian diver is neutrally buoyant and begins to sink when an external pressure is applied to the closed system. A basic explanation and proof of this process is provided in this activity, and supplementary ideas for more extensive demonstrations and independent group activities are presented.

The purpose of this task is to use geometric and algebraic reasoning to model a real-life scenario. In particular, students are in several places (implicitly or explicitly) to reason as to when making approximations is reasonable and when to round, when to use equalities vs. inequalities, and the choice of units to work with (e.g., mm vs. cm).

This task is primarily about volume and surface area, although it also gives students an early look at converting between measurements in scale models and the real objects they correspond to.

This short video and interactive assessment activity is designed to teach second graders about making observations about capacity (metric units).

This short video and interactive assessment activity is designed to teach second graders about comparing the capacity by formula in quarts, pints and cups.

This short video and interactive assessment activity is designed to teach second graders about comparing gallons and quarts by pictures.

This short video and interactive assessment activity is designed to teach second graders about comparing gallons, pints, and quarts by formula.

This short video and interactive assessment activity is designed to teach second graders about comparing capacity with pictures (english units).

This short video and interactive assessment activity is designed to teach third graders an overview of conversion among units of measure.

This short video and interactive assessment activity is designed to teach third graders about comparing cups and pints by formula.

This short video and interactive assessment activity is designed to teach second graders about comparing cups and pints by pictures.

This short video and interactive assessment activity is designed to teach third graders about comparing cups and quarts by formula.