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IMGALTTAG Volume VI: The Unreasonable Effectiveness of Math


Pondering Fibonacci

Vivienne Bartman
Robert L. Vann K - 8

In the flash and glitter of the everyday world students are becoming bored and resistant to recently successful lessons. The teachers of today must create animated, hands-on activities to keep the majority of the students actively engaged. In a child’s eye math is a very mundane and unnecessary part of their lives. Little do they understand that without a thorough knowledge of mathematics their adult life will be miserable.

This unit is designed for the middle school math student but could be adapted to any age group. The unit has been created to investigate the Fibonacci Sequence throughout the year. The catch is that the students must develop a keen sense of patterns to be able to identify Fibonacci in often surprising ways. The unit will end with a class created book of Fibonacci Sightings.


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Fractals and Proportional Reasoning
Jane H. Fraser
Pittsburgh Classical Academy

The concept of proportionality is a difficult one for middle school students to grasp. Whether they are not cognitively mature enough to understand proportion, or if the material presented is not “real” enough for them, is open to debate. Fractals, in all their glorious complexity, are an excellent vehicle for exploring proportions at the middle school level.


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Patterns in Nature:  The Logarithmic Spiral and Parabolic Trajectories
Jeff Laurenson
Brashear High School

This unit is intended to be used in an Elementary Functions class, with 11th and 12th graders. The unit has two parts. In the first part, students will identify and quantify the mathematical relationship found in a spiraling whelk shell. In the second part, students will identify and quantify the mathematical relationship found in each trajectory of a bouncing golf ball, and then model the decreasing maximum height of each bounce using exponential decay as a function of time and as a function of the bounce number. They will determine the percent lost per second, and the percent lost per bounce, and then consider which of these two models is more appropriate.


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How Math fits in Chemistry
Maria Orton
David B. Oliver High School

This unit is meant to be implemented into a high school chemistry course in order to supplement the unit on light and atomic emission spectra. The unit may be helpful for students in grades 10 – 12 in a regular education or inclusion classroom. The atomic emission spectra for each element are unique and can be used as a means of identification. This unit can be tied into the exchange of energy in a chemical reaction, and reaffirm that every element and compound has its own unique set of properties. This will also show that there is an energy transfer when atoms get excited, and show the wave-particle duality of light. This unit is to show the uncanny application of math in science. The objective is to allow students to calculate the energy of an electron during transformation. Students should be able to prove the mathematical equation for this transformation from experimental data showing how math and science really do coincide.


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Why Pi? And Other Math Mysteries
Sarah J. Ricketts
Robert L. Vann School

Did we create mathematics to explain science, or did we design our study of science to fit the descriptive language we already knew? Why is it that math works so well in relation to the natural sciences? While these questions have puzzled mathematicians and scientists alike for generations, many people take the relationship for granted and never really give much thought to the origins of mathematics or science as separate entities.

This unit will provide 7th and 8th grade students with an opportunity to explore the history and evolution of mathematics in relation to the natural sciences. By design, it will be available as a complete course (10-11 lessons) to be taught at the Pittsburgh Gifted Center, but could be modified for various abilities and classroom dynamics. The unit can also be used in pieces in conjunction with the Connected Mathematics curriculum (pull activities/lessons where appropriate.) It will be a broad overview and introduction to the history of some of the most poignant math concepts, but will focus on those concepts that have major applications in science.


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Looking for Patterns in Math and Nature
Alice Rysdon
Rogers CAPA Middle School

This unit was designed to be taught to 7th and 8th grade algebra students and 8th grade pre-algebra students. These students tend to be engaged in the learning process, but at times feel that math is dry and difficult to learn. I developed this unit to help students learn pre-algebra and algebra better and to increase their enjoyment of these subjects. Our Connected Math curriculum emphasizes patterns, however I think that patterns should be more strongly emphasized. Instead of talking about patterns here or there in the curriculum, I want to introduce patterns as a theme in math for the year. If students can develop the habit of looking for patterns every time we start a new unit or a new idea is taught, the students will benefit greatly. Many math ideas are based on patterns. Patterns were used by mathematicians to develop rules for negative numbers and rules for complex numbers. Patterns of graphs for different situations and equations are reflected in the graphs, equations and situations; students when they see the patterns can understand the math better.


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Chatham University
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IMGALTTAG Pittsburgh Teachers Institute
Jointly sponsored by Carnegie Mellon University, Chatham University and the Pittsburgh Public Schools.
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