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This lesson focuses on how materials behave differently as their surface area increases.

Learners display their findings after a study of surface area and volume. They build a mobile to show a commercially available box and a constructed cubical box of the same volume.

In this math lesson, learners use a variety of manipulatives to explore spatial relationships of squares and their transformations.

This activity explores the main algorithms that are used as the basis for searching on computers, using different variations on the game of battleships.

In this activity, learners create a mind and math puzzle that requires a three-dimensional solution.

Groups of learners are provided with a generic car base and an egg. Their mission: design a device/enclosure to protect the egg on or in the car as it rolls down a ramp with increasing slopes.

In this activity, learners get hands-on experience with ratios and scaling while making their own jewelry out of recycled plastic containers.

In this team design challenge (page 19-24 of PDF), learners "land" a model Lunar Rover in a model Landing Pod (both previously built in activities #3 and #4 in PDF).

In this activity (on pages 41-47 of PDF), learners explore tesselating geometric patterns (repeated shapes, similar to the art of M.C. Escher).

In this math lesson, learners use the setting of a flower-making fundraiser to explore a variety of patterns. Learners examine the patterns in a flower design made of triangles surrounding a square.

In this math lesson, learners identify, describe, and construct the five regular polyhedra.

In this activity, learners build a paper stellated rhombic dodecahedron, a three-dimensional 12-pointed star.

In this activity, learners discover how NASA engineers develop experimental aircraft.

In this team design challenge (page 2-10 of PDF), learners design and build a model of a Lunar Transport Rover that will carry equipment and people on the surface of the Moon.

In this activity, learners explore scale by using building cubes to see how changing the length, width, and height of a three-dimensional object affects its surface area and its volume.

In this activity, learners will predict the size of a giant scale model of a comb or other rectangular object, then make one. If you tripled the size of a dollar bill, could you sit on it?

In this calculus activity, learners use a classic problem of geometrical probability to find an important mathematical constant (pi).

How does a green roof, or roof covered by plants, affect the temperature of the inside and outside of a building? Learners design and build houses to find out the answer.

In this activity, learners will measure the length of a shadow and use the distance from the equator to calculate the circumference of the earth.

In this math lesson, learners estimate distances between landmarks and use a map and scales to determine the actual distances.