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

 

By the end of Grade 2, students will:

 

A.     Geometric Properties

 1.         Identify and describe spatial relationships among objects in space and their relative shapes and sizes.

·        Inside/outside, left/right, above/below, between

·        Smaller/larger/same size, wider/ narrower, longer/shorter

·        Congruence (i.e., same size and shape)

 2.         Use concrete objects, drawings, and computer graphics to identify, classify, and describe standard three-dimensional and two-dimensional shapes.

·        Vertex, edge, face, side

·        3D figures – cube, rectangular prism, sphere, cone, cylinder, and pyramid

·        2D figures – square, rectangle, circle, triangle

·        Relationships between three- and two-dimensional shapes (i.e., the face of a 3D shape is a 2D shape)

 3.         Describe, identify and create instances of line symmetry.

 4.         Recognize, describe, extend and create designs and patterns with geometric objects of different shapes and colors.

 

B.     Transforming Shapes

 1.         Use simple shapes to make designs, patterns, and pictures.

 2.         Combine and subdivide simple shapes to make other shapes.

 

C.     Coordinate Geometry

 1.         Give and follow directions for getting from one point to another on a map or grid.

 

D.    Units of Measurement

 1.         Directly compare and order objects according to measurable attributes.

·        Attributes – length, weight, capacity, time, temperature

 2.         Recognize the need for a uniform unit of measure.

 3.         Select and use appropriate standard and non-standard units of measure and standard measurement tools to solve real-life problems.

·        Length – inch, foot, yard, centimeter, meter

·        Weight – pound, gram, kilogram

·        Capacity – pint, quart, liter

·        Time – second, minute, hour, day, week, month, year

·        Temperature – degrees Celsius, degrees Fahrenheit

 4.         Estimate measures.

 

E.     Measuring Geometric Objects

 1.         Directly measure the perimeter of simple two-dimensional shapes.

 2.         Directly measure the area of simple two-dimensional shapes by covering them with squares.

 

 

 

Link to Standard 4.2 Grade 3

 

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