Post+1+-+Liz

** Rectangle: Area, Perimeter, Length, and Width **

[]

(1) In this activity, students are asked to maximize the area of a rectangle while keeping the perimeter constant at 20 units. The students are provided with a grid, and use their mouse to create rectangles. Through a process of trial and error, the students drag the boundaries to find the maximum area occurs when the shape is square. A second queston is raised, asking the students to form a conjecture about how to maximize the perimeter, keeping the area the same. This is slightly more challenging, as the perimeter could be made infinitely large while keeping the area constant. It is in this section where true critical thinking is employed. If I were to use this application in a classroom, I would provide the students with directions on a separate sheet of paper, as the answers are provided on the website. There is an additional link provided with just the JAVA applet, which is the link I would provide to the students.

(2a) The national standards used in this web activity are:
 * A.PS.1** Use a variety of problem solving strategies to understand new mathematical content.
 * A.PS.3** Observe and explain patterns to formulate generalizations and conjectures.
 * A.PS.6** Use a variety of strategies to extend solution methods to other problems.
 * A.RP.2** Use mathematical strategies to reach a conclusion and provide supportive arguments for a conjecture.
 * A.RP.10** Extend specific results to more general cases.
 * 7.A.6** Evaluate formulas for given input values.

(2b) The national technology standards used in this web activity are: Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students: **(a)** apply existing knowledge to generate new ideas, products, or processes. Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students: Students demonstrate a sound understanding of technology concepts, systems, and operations. Students:
 * 1. Creativity and Innovation **
 * 4. Critical Thinking, Problem Solving, and Decision Making **
 * (b)** plan and manage activities to develop a solution or complete a project.
 * (c)** collect and analyze data to identify solutions and/or make informed decisions.
 * 6. Technology Operations and Concepts **
 * (a)** understand and use technology systems.
 * (b)** select and use applications effectively and productively.

(3) Inquiry is an adventure in learning. It involves seeking the complex multiple outcomes to a present problem through active exploration of the surrounding world. It is more than simple research, review or study as these are means to pure facts; a simple answer to a simple problem. Inquiry differs from other types of investigation as it is more than a means to an end or the answer to a question. It allows the seeker the opportunity to use their mind to develop a concept or solution to a problem by using all available resources, including but not limited to observation, reasoning and critical thinking. Critical thinking allows the seeker the chance to think outside the box to develop one's own understanding of the unique issue. The student is required to do more than restate prior knowledge, it is necessary to process and internalize new information to use it to creatively problem solve. By the time the inquiry comes to an end, the seeker will have a larger understanding of the original problem as well as a set of skills to better problem solve in the future.
 * || Not Evident || Partial || Exemplary || Score ||
 * ^  || 1 || 2 || 3 ||^   ||
 * There is more than one correct answer || There is one correct answer. || Some answers are found, but there is an incomplete solution. || No restrictions on possible number of solutions. ||  ||
 * The task necessitates critical thinking to find the solutions || No use of critical thinking is evident || Some use of critical thinking is evident. || An obvious understanding of the task through critical thinking is evident. ||  ||
 * The task encourages the use of multiple forms of creative problem solving, i.e. reasoning, observation, experimentation, etc. || The task does not require the performer to use information in any other way than restating facts. || The task is mostly straightforward; the required task needs little new information to be used. || The performer of this task is required to manipulate new information in many ways to complete the task. ||  ||
 * The task strengthens or builds the knowledge of a specific problem or concept. || No new knowledge is attained through this task. || The task only asks for prior knowledge to be retold. || A full body of knowledge about the problem or concept is developed though this task. ||  ||
 * The requirements of the task aid in developing skills needed to better problem solve in the future || No new skills have been developed through this task. || The task encourages some new skills, but full potential cannot be reached. || The task allows the performer to fully develop a new set of problem solving skills. ||  ||

