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 4, students will:

 

A.     Geometric Properties

 1.         Identify and describe spatial relationships of two or more objects in space.

·        Direction, orientation, and perspectives (e.g., which object is on your left when you are standing here?)

·        Relative shapes and sizes

·        Shadows (projections) of everyday objects

 2.         Use properties of standard three-dimensional and two-dimensional shapes to identify, classify, and describe them.

·        Vertex, edge, face, side, angle

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

·        2D figures – square, rectangle, circle, triangle, quadrilateral, pentagon, hexagon, octagon

·        Inclusive relationships – squares are rectangles, cubes are rectangular prisms

 3.         Identify and describe relationships among two-dimensional shapes.

·        Congruence

·        Lines of symmetry

 4.         Understand and apply concepts involving lines, angles, and circles.

·        Point, line, line segment, endpoint

·        Parallel, perpendicular

·        Angles – acute, right, obtuse

·        Circles – diameter, radius, center

 5.         Recognize, describe, extend, and create space-filling patterns.

 

B.     Transforming Shapes

 1.         Use simple shapes to cover an area (tessellations).

 2.         Describe and use geometric transformations (slide, flip, turn).

 3.         Investigate the occurrence of geometry in nature and art.

 

C.     Coordinate Geometry

 1.         Locate and name points in the first quadrant on a coordinate grid.

 2.         Use coordinates to give or follow directions from one point to another on a map or grid.

 

D.    Units of Measurement

 1.         Understand that everyday objects have a variety of attributes, each of which can be measured in many ways.

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

·        Length – fractions of an inch (1/8, 1/4, 1/2), mile, decimeter, kilometer

·        Area – square inch, square centimeter

·        Volume – cubic inch, cubic centimeter

·        Weight – ounce

·        Capacity – fluid ounce, cup, gallon, milliliter

 3.         Develop and use personal referents to approximate standard units of measure (e.g., a common paper clip is about an inch long).

 4.         Incorporate estimation in measurement activities (e.g., estimate before measuring).

 5.         Solve problems involving elapsed time.

 

E.     Measuring Geometric Objects 

 1.         Determine the area of simple two-dimensional shapes on a square grid.

 2.         Distinguish between perimeter and area and use each appropriately in problem-solving situations.

 3.         Measure and compare the volume of three–dimensional objects using materials such as rice or cubes.

 

 

Link to Standard 4.2 Grade 3

 

Link to Standard 4.2 Grade 5

 

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