Polyhedra

A polyhedron is a three-dimensional figure with flat faces, straight edges, and sharp vertices. The word "polyhedron" comes from the Greek words "poly," meaning "many," and "hedra," meaning "faces." There are different types of polyhedra based on the number and shape of their faces, such as cubes, pyramids, prisms, and more.

Characteristics of Polyhedra

1. Faces: The flat surfaces of a polyhedron.

2. Edges: The line segments where the faces of a polyhedron meet.

3. Vertices: The points where the edges of a polyhedron meet.

Types of Polyhedra

1. Cube: A polyhedron with six square faces, 12 edges, and 8 vertices.

2. Pyramid: A polyhedron with a polygonal base and triangular faces that meet at a common vertex.

3. Prism: A polyhedron with two parallel and congruent faces called bases, and rectangular faces connecting the corresponding sides of the bases.

4. Platonic Solids: A group of five polyhedra (tetrahedron, cube, octahedron, dodecahedron, icosahedron) with identical faces, edges, and angles.

Euler's Formula

Euler's formula states that for any polyhedron, the number of faces (F), edges (E), and vertices (V) are related by the equation: F + V - E = 2. This formula holds true for all convex polyhedra, regardless of their shape or size.

Conclusion

Polyhedra are important geometric figures with various applications in mathematics, engineering, and everyday life. Understanding the characteristics and types of polyhedra can help in solving problems related to spatial reasoning, surface area, volume, and more.

◂Math Worksheets and Study Guides Third Grade. Measurement

Measuring Line Segments

Vocabulary/Answer key

Measurement

Vocabulary/Answer key

Measurement

The resources above cover the following skills:

Measurement (NCTM)

Understand measurable attributes of objects and the units, systems, and processes of measurement.

Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute.

Understand that measurements are approximations and how differences in units affect precision.

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.

Connections to the Grade 3 Focal Points (NCTM)

Measurement: Students in grade 3 strengthen their understanding of fractions as they confront problems in linear measurement that call for more precision than the whole unit allowed them in their work in grade 2. They develop their facility in measuring with fractional parts of linear units. Students develop measurement concepts and skills through experiences in analyzing attributes and properties of two-dimensional objects. They form an understanding of perimeter as a measurable attribute and select appropriate units, strategies, and tools to solve problems involving perimeter.