|
|
|
|
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 8, students will:
A. Geometric Properties 1. Understand and apply concepts involving lines, angles, and planes. · Complementary and supplementary angles · Bisectors and perpendicular bisectors · Parallel, perpendicular, and intersecting planes · Intersection of plane with cube, cylinder, cone, and sphere 2. Understand and apply the Pythagorean theorem. 3. Understand and apply properties of polygons. · Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi · Regular polygons · Sum of measures of interior angles of a polygon · Which polygons can be used alone to generate a tessellation and why 4. Understand and apply the concept of similarity. · Using proportions to find missing measures · Scale drawings · Models of 3D objects 5. Use logic and reasoning to make and support conjectures about geometric objects.
B. Transforming Shapes 1. Understand and apply transformations. · Finding the image, given the pre-image, and vice-versa · Sequence of transformations needed to map one figure onto another · Reflections, rotations, and translations result in images congruent to the pre-image · Dilations (stretching/shrinking) result in images similar to the pre-image 2. Use iterative procedures to generate geometric patterns. · Fractals (e.g., the Koch Snowflake) · Construction of initial stages · Patterns in successive stages (e.g., number of triangles in each stage of Sierpinski’s Triangle)
C. Coordinate Geometry 1. Use coordinates in four quadrants to represent geometric concepts. 2. Use a coordinate grid to model and quantify transformations (e.g., translate right 4 units).
D. Units of Measurement 1. Solve problems requiring calculations that involve different units of measurement within a measurement system (e.g., 4’3” plus 7’10” equals 12’1”). 3. Recognize that the degree of precision needed in calculations depends on how the results will be used and the instruments used to generate the measurements. 5. Recognize that all measurements of continuous quantities are approximations. 6. Solve problems that involve compound measurement units, such as speed (miles per hour), air pressure (pounds per square inch), and population density (persons per square mile).
E. Measuring Geometric Objects 1. Develop and apply strategies for finding perimeter and area. · Geometric figures made by combining triangles, rectangles and circles or parts of circles · Estimation of area using grids of various sizes · Impact of a dilation on the perimeter and area of a 2-dimensional figure 2. Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height). · Volume - prism, cone, pyramid · Surface area - prism (triangular or rectangular base), pyramid (triangular or rectangular base) · Impact of a dilation on the surface area and volume of a three-dimensional figure 4. Use formulas to find the volume and surface area of a sphere.
Link to Standard 4.2 High School
|
|
