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STANDARD 4.2 (GEOMETRY AND MEASUREMENT) ALL STUDENTS WILL DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES, RELATIONSHIPS, AND MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA.
Descriptive Statement: Spatial sense is an intuitive feel for shape and space. Geometry and measurement both involve describing the shapes we see all around us in art, nature, and the things we make. Spatial sense, geometric modeling, and measurement can help us to describe and interpret our physical environment and to solve problems.
Geometric Properties. This includes identifying, describing and classifying standard geometric objects, describing and comparing properties of geometric objects, making conjectures concerning them, and using reasoning and proof to verify or refute conjectures and theorems. Also included here are such concepts as symmetry, congruence, and similarity.
Transforming Shapes. Analyzing how various transformations affect geometric objects allows students to enhance their spatial sense. This includes combining shapes to form new ones and decomposing complex shapes into simpler ones. It includes the standard geometric transformations of translation (slide), reflection (flip), rotation (turn), and dilation (scaling). It also includes using tessellations and fractals to create geometric patterns.
Coordinate Geometry. Coordinate geometry provides an important connection between geometry and algebra. It facilitates the visualization of algebraic relationships, as well as an analytical understanding of geometry.
Units of Measurement. Measurement helps describe our world using numbers. An understanding of how we attach numbers to real-world phenomena, familiarity with common measurement units (e.g., inches, liters, and miles per hour), and a practical knowledge of measurement tools and techniques are critical for students' understanding of the world around them.
Measuring Geometric Objects. This area focuses on applying the knowledge and understandings of units of measurement in order to actually perform measurement. While students will eventually apply formulas, it is important that they develop and apply strategies that derive from their understanding of the attributes. In addition to measuring objects directly, students apply indirect measurement skills, using, for example, similar triangles and trigonometry.
Students of all ages should realize that geometry and measurement are all around them. Through study of these areas and their applications, they should come to better understand and appreciate the role of mathematics in their lives.
Cumulative Progress Indicators
Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will:
A. Geometric Properties 1. Understand and apply concepts involving lines and angles. · Notation for line, ray, angle, line segment · Properties of parallel, perpendicular, and intersecting lines · Sum of the measures of the interior angles of a triangle is 180° 2. Identify, describe, compare, and classify polygons and circles. · Triangles by angles and sides · Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi · Polygons by number of sides. · Equilateral, equiangular, regular · All points equidistant from a given point form a circle 4. Understand and apply the concepts of congruence and symmetry (line and rotational). 5. Compare properties of cylinders, prisms, cones, pyramids, and spheres. 6. Identify, describe, and draw the faces or shadows (projections) of three-dimensional geometric objects from different perspectives. 7. Identify a three-dimensional shape with given projections (top, front and side views). 8. Identify a three-dimensional shape with a given net (i.e., a flat pattern that folds into a 3D shape).
B. Transforming Shapes 1. Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.
C. Coordinate Geometry 1. Create geometric shapes with specified properties in the first quadrant on a coordinate grid.
D. Units of Measurement 1. Select and use appropriate units to measure angles, area, surface area, and volume. 2. Use a scale to find a distance on a map or a length on a scale drawing. 3. Convert measurement units within a system (e.g., 3 feet = ___ inches). 4. Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile). 5. Use measurements and estimates to describe and compare phenomena.
E. Measuring Geometric Objects 1. Use a protractor to measure angles. 2. Develop and apply strategies and formulas for finding perimeter and area. · Triangle, square, rectangle, parallelogram, and trapezoid · Circumference and area of a circle 3. Develop and apply strategies and formulas for finding the surface area and volume of rectangular prisms and cylinders. 4. Recognize that shapes with the same perimeter do not necessarily have the same area and vice versa. 5. Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one’s foot).
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