Young students often understand the world in terms of their immediate surroundings. Effectively teach beginning geometry principles, such as shapes, angles and distances, by assigning a project that asks students to draw a map of a familiar space, such as a classroom area, a room at home, or a section of the library, to approximate scale. They should identify shapes that form triangles and angles, such as a stapler, desk, chair, rug or chalkboard, and measure angles and distances between objects. The exercise will teach them to understand geometry in their immediate environment.
A more advanced project asks students to draw a map of their neighborhood, drawn to scale for an added challenge. Ask them to include their home, landmarks, trees, swings and other significant objects, and have them find isoscoles triangles in the map. Have them also measure the distance between their home and a neighbor's, and measure the angles that form when any three significant points on the map are connected.
For more advanced students, a political map that includes polities such as cities, states and countries alerts them to logistical geometric applications. Give them an automobile travel scenario from a major city to the closer of two similarly located destinations, which they will determine using lines and angles. Ask them to identify triangle angles that form when the capitol cities of three states are connected with lines.
A topographical map presents natural landmarks that form lines and angles significant in geometry. Instruct students to find roughly parallel topographical features, such as the three approximately parallel rivers of the Yunnan province in China, and measure the angles that form when a line connects them. Have students calculate the distance from a mountain peak to a city's center, or find the three deepest rivers in the world and calculate the angles formed when a line connect them.
A solar system map provides opportunities for identifying and measuring triangles, angles and lines. Exercises important for learning geometry with a map of the solar system include finding and measuring angles stars form in constellations, the distance between planets, and the diameter of the sun compared with the largest and smallest planets.