Geometry and Measurement and Algebra: Describing three-dimensional shapes and analyzing their properties, including volume and surface area.

Work on three-dimensional shapes begins with hands-on play, either virtual or with actual materials. Using these resources, students can investigate the properties of solids and go on to consider the rules that determine volume and surface area.

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2D to 3D morphing : flat 2D shapes rise up to make 3D forms http://pbskids.org/cyberchase/games/23dgeometry/index.html

As students follow the directions on the printable pages, they construct a pyramid, a cube, and an octahedron. They can fold the flat, two-dimensional polygons and see them rise up to form three-dimensional polyhedra. Each page is decorated with colorful images of the Cyberchase team so that one image appears on each face of the constructed three-dimensional objects. MSP full record

Geometric Solids and Their Properties http://illuminations.nctm.org/LessonDetail.aspx?id=U122

Using an applet, students investigate several polyhedra. They can revolve each shape, color each face, and mark each edge or vertex. They can even see the figure without the faces colored in — a skeletal view of the "bones" forming the shape. The lesson leads to Euler’s formula, connecting the number of edges, vertices, and faces, and ends with creating nets to form polyhedra. An excellent introduction to three-dimensional figures! (From Illuminations — MSP full record)

Cubes http://illuminations.nctm.org/ActivityDetail.aspx?ID=6

Students fill a box with cubes. This can be done online or using actual materials, depending on what’s available in your classroom. The number of cubes needed to fill the entire box is defined as the “volume” of the box. Students are challenged to determine a rule for finding the volume of a box when they know its width, depth, and height. (From Illuminations — MSP full record)

How high? : measurement (grades 6-8) http://nlvm.usu.edu/en/nav/frames_asid_275_g_3_t_4.html

With this virtual manipulative, students pour a liquid from one container to a container of the same shape, but of a different size. There are four shapes to choose from: rectangular prism, cylinder, cone, and pyramid. The left container is partially filled with liquid and the base dimensions are given. The student uses a slider to estimate how high the liquid will rise when poured into the second container. After clicking a button that initiates pouring, the student can compare the estimate with the results. Opens up interesting discussion on volume! MSP full record

Surface area and volume http://www.shodor.org/interactivate/activities/sa_volume/index.html

This applet enables students to form and rotate both rectangular and triangular prisms. They can set the dimensions (width, depth, and height), observing how each change in dimension affects the shape of the prism as well as its volume and surface area. This is a quick way to collect data for a discussion of the relationship between surface area and volume. Users can rotate the figure and call for its front, side, or back view — very interesting with a triangular prism! MSP full record

Keeping cool : when should you buy block ice or crushed ice? http://www.figurethis.org/challenges/c62/challenge.htm

Which would melt faster: a large block of ice or the same block cut into three cubes? The prime consideration is surface area. The solution demonstrates how to calculate the surface area of the cubes as well as the area of the large block of ice. Related problems involve finding surface area and volume for irregular shapes and examining the relationship between surface area and volume in various situations. MSP full record

Drip drops : how much water do you waste? http://www.figurethis.org/challenges/c56/challenge.htm

In this activity, students are given a situation in which a leaky faucet is dripping at the rate of one drop every two seconds. They are asked to decide if the water lost in one week would fill a drinking glass, a sink, or a bathtub. The answer page shows students how to convert the drops to gallons using an equation or a table. Related questions ask students to consider how much water is lost in one year by a single leaky faucet and by two million leaky faucets. Real applications of work on volume! MSP full record

Popcorn : if you like popcorn, which one would you buy? http://www.figurethis.org/challenges/c03/challenge.htm

This challenge directs the student to use popcorn to compare the volumes of tall and short cylinders formed with 8- by 11-inch sheets of paper. The importance of being able to make visual estimates and find volumes is pointed out. MSP full record

Platonic Solids (Grades 6-8) http://nlvm.usu.edu/en/nav/frames_asid_128_g_3_t_3.html?open=instructions

Students examine in detail the five Platonic solids — their shapes, vertices, edges, and regular polygonal faces. With the virtual manipulative, they can rotate each solid, viewing it from every angle, change its size, then use the transparent mode to see only the skeletal structure of the polyhedron. (From National Library of Virtual Manipulatives — MSP full record)

Scaling the pyramids http://www.pbs.org/wgbh/nova/pyramid/geometry/index.html

These activities engage students through their fascination with the sheer size of the Great Pyramid. In one hands-on activity, students use a template to construct a scale model of the Great Pyramid. In another, students are given the actual dimensions for two other pyramids and challenged to create their own models. MSP full record

NCTM. (2006). Curriculum Focal Points for Kindergarten Through Grade 8 Mathematics: A Quest for Coherence. Reston, VA: Author

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Copyright March 2008 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.