Kimberly Gasaway
Concept Analysis – Objective One EDCI 675
Fall 2008
Concept Analysis – Objective One
Target Concept: Quadrilaterals
Audience: Fourth grade
I. Outline of the taxonomy for which quadrilaterals is a part:
Closed Plane Figures
Circles
Polygons
Triangles
Isosceles
Scalene
Equilateral
Quadrilaterals
s
Parallelogram Rectangle
Square Trapezoid Other *
Kite Rhombus *Pentagon; Hexagon; Octagon; Decagon; Heptagon; Nonagon II. Defining the concept of Quadrilaterals in terms of its attributes.
A Quadrilateral is a four-sided, closed polygon. It consists of four line segments and four interior
angles. The sum of the angles of a quadrilateral is 360 degrees.
III. Specifying the defining attributes and some of the variable attributes of Quadrilaterals.
The following attributes which apply to all Quadrilaterals are:
1. Closed polygon
2. Consists of only four line segments
3. Contains only four interior angles of which the sum of those angles is 360 degrees
Variable attributes: size, length of line segments, degree of each interior angle, parallel sides,
orientation within a plane
Kimberly Gasaway
Concept Analysis – Objective One EDCI 675
Fall 2008
IV. Indicating illustrative Examples and Non-Examples of Quadrilaterals.
1. Being a closed polygon
• Example:
•
Non-example:
•
Rationale: Even though a figure can be constructed using four line segments, the line
segments much be arranged in such a way that it forms a completely closed shape.
2. Consists of four line segments
• Examples:
3.
•
Non-examples:
•
Rationale: Even though a figure can be a closed polygon, it must consist of exactly four
line segments. A circle contains no line segments, therefore, it cannot be a Quadrilateral.
Contains only four interior angles of which the sum of those angles is 360 degrees
• Example:
If each interior angle measures 90 degrees, then 90 degrees
times four angles is equal to 360 degrees. (90x4=360)
•
•
Non-examples:
The sum of the three interior angles equals 180 degrees.
The sum of the six interior angles of this hexagon equals 360
degrees. (6x60=360) Quadrilaterals can only contain four
interior angles.
Rationale: Even though a polygon can have an interior angle measurement of 360
degrees, the polygon must only have four interior angles.
V. Identifying illustrative principles in which Quadrilaterals is incorporated.
1. All Quadrilaterals are similar in that they are composed of four line segments that connect to
form a closed polygon.
2. Quadrilaterals can contain one pair, two pairs, or no pairs of parallel line segments.
3. All Quadrilaterals consist of four interior angles whose sum measurement is 360 degrees.
4. Quadrilaterals may contain one, more than one, or no 90 degree angles.
Kimberly Gasaway
Concept Analysis – Objective One EDCI 675
Fall 2008
VI. Formulating illustrative problem-solving exercises involving the use of Quadrilaterals.
1.
Students will participate in an interactive activity utilizing a teacher-created template in which
the students will click on and drag a shape to the appropriate column indicating whether it is a
quadrilateral or a polygon. This activity assesses the ability of the students to differentiate
between a true quadrilateral and a polygon. (Classification skill which will address the need for
remediation if necessary.)
Polygons
2.
Quadrilaterals
Given a ruler and a protractor, the students will draw on paper an example of each type of
quadrilateral. The students will label the measurement for each side and angle of the
quadrilateral. The student will write an explanation for each quadrilateral drawn detailing its
justification for being a quadrilateral. (Application of learned concepts for assessment purposes.)
3. The students will record on paper as many real life objects as they can that represent a
quadrilateral and give examples of where these objects can be found. (Transfer of knowledge to
real world application.) As an extension of this activity, the students can take pictures of
quadrilaterals in their community with a camera and create a Power Point Presentation to share
with their classmates. Other forms of presentations will also be encouraged.
4. Additional resources and manipulative activities can be found at the following Internet site:
http://www.teachers.ash.org.au/jeather/maths/dictionary.html
A Math’s Dictionary for Kids
VII. Developing a vocabulary associated with Quadrilaterals and its defining attributes.
Vocabulary: plane, figure, closed, polygon, regular, irregular, quadrilateral, parallel lines, angles,
degrees