In art class, fifth grade students constructed 20-pointed stars with Ms. Leckie. They used straws and string to construct the stars.
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Students first constructed an icosahedron, a solid with 20 faces that are all equilateral triangles. On each face of the icosahedron, they then attached a triangular pyramid to act as the points of the stars.
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Students in Ms. Shane's Math B class were then tasked with finding the following: the number of vertices, edges and faces of the geometric solid, as well as the surface area of the solid.
Students determined there were 32 vertices. |
There are 90 edges. |
There are 60 faces. |
These students drew 2-dimensional representations of the triangular pyramids that surrounded the icosahedron. They explained their reasoning in determining the number of vertices, edges and faces of the solid.
Students then figured out the surface area of the entire solid.
This student explains how she found the area of one of the faces. |
She then explains the computation for finding the surface area of the entire solid, 540 square inches.
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Students should also express the computation with parentheses, explaining what each part of the equation represents. |
Indicators:
3.6.3.1 develop and use formulas, using related formulas and models, to determine areas of polygons such as triangles, parallelograms, trapezoids, and circles.
2.6.3.3 make a model of a three dimensional figure from a two-dimensional drawing.
2.6.3.4 make a two-dimensional drawing of a three-dimensional figure.
3.7.3.2 use formulas to find the surface area and volume of basic three-dimensional figures, including prisms and cylinders.
3.7.3.1 use models to find and derive a formula for surface area and volume of prisms and cylinders.
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