Learning Resources ler 4331 manual Euler’s Formula, Intervention Strategies

Euler’s Formula

Euler’s Formula is named after Swiss mathematician Leonard Euler. In the mid-eighteenth century, Euler discovered that for any polyhedron, F + V = E + 2. In the formula, F represents the number of faces, V represents the number of vertex points, and E represents the number of edges. For example, a cube has 6 faces, 8 vertex points, and 12 edges.

F + V = E + 2 6 + 8 = 12 + 2

Have the students use their data from the preceding chart to discover Euler’s Formula. Euler’s Formula is true for the first nine solids listed in the table.

Intervention Strategies

Scaffolded Instruction: Before providing formulas to students, instead provide the definitions of perimeter and area, and opportunities to solve problems that allow students to gain data leading to the use of a formula. Begin with two-dimensional shapes before advancing to three-dimensional solids.

Directed Orientation: Use different household items that resemble a cube, cone, sphere, cylinder, pyramid, or prism. Have students sort the items by different attributes you provide. Then, introduce the formal shapes and have students match the shapes to the corresponding household items.

Free Exploration: Have students fill the solids with rice or water to explore properties of volume. Encourage students to make estimations and compare which shapes are able to hold more or less than the others.

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