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Geometry
Geometry
Geometry is the study of space and shapes in space. The word geometry comes from the Greek and means measurement of the earth (geo = earth, metry = measurement). Mathematicians of ancient Greece developed fundamental concepts of geometry to answer basic questions about the earth and its relationship to the sun, the moon, and the planets: How big is the earth? How far away is the moon? How far away is the sun? The geometers of ancient Greece had to be able to visualize the earth and the heavenly bodies in space. They had to extract the relevant relationships from their mental pictures, and they had to analyze these pictures mathematically. The methods the ancient Greeks developed are still useful today for solving modern problems in construction, road building, medicine, and other disciplines.
Beckmann, Sybilla. Mathematics for Elementary Teachers with Activities (p. 451-452). Pearson Education. Kindle Edition.Standards for Mathematical Content in the CCSSM
In the domain of Geometry (Kindergarten through Grade 8), students learn to identify and describe shapes by their geometric properties and they learn about angles and about the concepts of parallel and perpendicular. By attending to shapes’ properties, students reason about relationships among categories of shapes, and they organize these categories into hierarchies. In later grades students reason about relationships among angles. They solve problems about angles and they give (informal) explanations for angle relationships, such as that the sum of the angles in a triangle is always 180°.
Standards for Mathematical Practice in the CCSSM
Opportunities to engage in all eight of the Standards for Mathematical Practice described in the Common Core State Standards occur throughout the study of shapes and their geometric attributes, although the following standards may be especially appropriate for emphasis:
• 4 Model with mathematics. Students engage in this practice when they view objects in the real world as approximated by ideal geometric shapes and when they make two-dimensional drawings to represent an aspect of a real-world situation and use geometric aspects of the drawing to analyze the situation.
• 5 Use appropriate tools strategically. Students engage in this practice when they use tools such as compasses, rulers, protractors, geometry software, or paper and scissors to make shapes and explore geometric properties. For example, students might make a rhombus by folding and cutting paper or by drawing it with a compass. In each case, they could argue that the resulting shape is a rhombus because of the way it was constructed.
• 7 Look for and make use of structure. Students engage in this practice when they correctly identify a shape based on its attributes rather than on its overall appearance, when they look for parallel lines to determine angle relationships, or when they draw an extra line into a figure so as to make use of known angle relationships. (From Common Core Standards for Mathematical Practice. Published by Common Core Standards Initiative.)
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