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Web Resource—NCTM Illuminations

Grade Level
Grades 9-12
Creative Thinking
Students are asked to take concepts and apply them to real life situations. Inn doing so they use creative thinking skills often not tapped in the regular classroom. Analytical reasoning skills also come into play. In the investigations, the student takes on the role of mathematician and scientist in solving real life problems through the use of high level mathematics.
This site offers I-Math interactive activities for students. Pre-K through Grade 12 correlated to the NCTM Principles and Standards for School Mathematics. Each example consists of an interactive math applet with suggestions for student activities and a discussion of the mathematics and reflective questions for teachers. The math applet is also offered as a stand alone for the student to work on independently. The activities are written for all students at the specific grade bands, however there are extensions in many of the activities for greater challenge. It would also be appropriate to use the next high level grade band for activities that will meet the needs of your brightest students. You will need to be selective since not all investigations are appropriate for talented students.
The secondary section of Illuminations begins to tackle real life ideas. Car velocity, medicine dosage and sound waves are only a few of the ideas presented. These secondary investigations place a strong focus on student observation, reflection, and evaluation.
Appeal and User Friendliness
This site is very interactive and easy for both teachers and students to use. Students can do most activities independently although some investigations require pairs of students to conduct the experiments. Good reflective questions for teachers aid in assessing student understanding. The student applets also provide questions for students focusing on high-level analysis and evaluation.
Sample Problem
Put the Heart into Mathematics” is a rich exploration of the rates of change and accumulation in the context of measuring the amount of blood pumped by the heart. Although this problem is presented in a discrete format, it can be extended easily to a continuous perspective using Integral Calculus. In reflecting upon the investigation, students are asked to apply the methodology of what they learned to other real life contexts. This involves the higher order thinking skills of application, analysis, synthesis and evaluation.