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.

Students must calculate the volume of a cone in this real world task.

The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. The purpose of this first task is to see the relationship between the side-lengths of a cube and its volume.

The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. In this iteration, we do away with the lines that delineate individual unit cubes (which makes it more abstract) and generalize from cubes to rectangular prisms.

The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. Here, we are given the volume and are asked to find the height.

The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. This problem is based on ArchimedesŐ Principle that the volume of an immersed object is equivalent to the volume of the displaced water.

Watch your solution change color as you mix chemicals with water. Then check molarity with the concentration meter. What are all the ways you can change the concentration of your solution? Switch solutes to compare different chemicals and find out how concentrated you can go before you hit saturation!

Students conduct Internet research to investigate the purpose and current functioning status of some of the largest dams throughout the world. They investigate the success or failure of eight dams and complete a worksheet. While researching the dams, they also gain an understanding of the scale of these structures by recording and comparing their reservoir capacities. Students come to understand that dams, like all engineered structures, have a finite lifespan and require ongoing maintenance and evaluation for their usefulness.

You Pour, I Choose presents students with a real-world application of which cylindrical container holds more soda. Students will find the volume of soda in two different sized cylinders.

Why do objects like wood float in water? Does it depend on size? Create a custom object to explore the effects of mass and volume on density. Can you discover the relationship? Use the scale to measure the mass of an object, then hold the object under water to measure its volume. Can you identify all the mystery objects?

Why do objects like wood float in water? Does it depend on size? Create a custom object to explore the effects of mass and volume on density. Can you discover the relationship? Use the scale to measure the mass of an object, then hold the object under water to measure its volume. Can you identify all the mystery objects?

In this first part of a two-part lab activity, students use triple balance beams and graduated cylinders to take measurements and calculate the densities of several common, irregularly shaped objects with the purpose to resolve confusion about mass and density. After this activity, conduct the associated Density Column Lab - Part 2 activity before presenting the associated Density & Miscibility lesson for discussion about concepts that explain what students have observed.

Concluding a two-part lab activity, students use triple balance beams and graduated cylinders to take measurements and calculate densities of several household liquids and compare them to the densities of irregularly shaped objects (as determined in Part 1). Then they create density columns with the three liquids and four solid items to test their calculations and predictions of the different densities. Once their density columns are complete, students determine the effect of adding detergent to the columns. After this activity, present the associated Density & Miscibility lesson for a discussion about why the column layers do not mix.

Middle School Students love these two things together--squeezing things that are squishy, and eating candy!This is a lab using Playdough and Tootsie Rolls, in which students will measure the volume, mass, and the density of both substances.  Students should gain a deeper meaning of what the physical property of density is after completing this lab.  They should be able to explain WHY one substance is more dense or less dense than another.

The purpose of the task is to analyze a plausible real-life scenario using a geometric model. The task requires knowledge of volume formulas for cylinders and cones, some geometric reasoning involving similar triangles, and pays attention to reasonable approximations and maintaining reasonable levels of accuracy throughout.

This six-day lesson provides students with an introduction to the importance of energy in their lives and the need to consider how and why we consume the energy we do. The lesson includes activities to engage students in general energy issues, including playing an award-winning Energy Choices board game, and an optional graphing activity that provides experience with MS Excel graphing and perspectives on how we use energy and how much energy we use.

Students learn that buoyancy is responsible for making boats, hot air balloons and weather balloons float. They calculate whether or not a boat or balloon will float, and calculate the volume needed to make a balloon or boat of a certain mass float. Conduct the first day of the associated activity before conducting this lesson.

Explore size estimation in one, two and three dimensions! Multiple levels of difficulty allow for progressive skill improvement.

This lesson unit is intended to help teachers assess how well students are able to solve problems involving area and volume, and in particular, to help you identify and assist students who have difficulties with the following: computing perimeters, areas and volumes using formulas; and finding the relationships between perimeters, areas, and volumes of shapes after scaling.