Ohio Journal of School Mathematics: Number 68 (Fall 2013)

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https://kb.osu.edu/handle/1811/78127

Front Matter
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Shape Affects the Sound of a Drum: Modeling Area and Perimeter
Adabor, James K.; Foley, Gregory D. pp. 1-6
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Understanding Integer Addition and Subtraction Concepts Using Microsoft Word® Illustrations
De Los Santos, Estella pp. 8-14
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No 10-Element Subset of the First 100 Counting Numbers is Subset-Sum-Distinct
Harper, Brian pp. 16-18
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Investigating Non-linear Asymptotes and the Graphs of Rational Functions
Harrell, Marvin; Slavens, Dawn; Richardson, Connie pp. 19-25
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Getting Students Excited about Data Analysis
Mathews, Susann M.; Reed, Michelle; Angel, Nancy pp. 26-32
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Trigonometric Functions through Right Triangle Similarities
Moyer, Todd O. pp. 33-42
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Plotting the Effects of Industrialization: An Interdisciplinary Project
Vens, Kasey pp. 43-49
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Contest Corner: The 2013 State Tournament of Mathematics Results
Flick, Michael; Kuchey, Debbie pp. 50-52
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Mathematical Morsels: A Monthly Voyage of Problem Solving Goodness
Bolognese, Chris; Edwards, Michael Todd pp. 53-54
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Back Matter
pp. 55-56
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Now showing 1 - 11 of 11

Front Matter (Number 68, Fall 2013)
(Ohio Council of Teachers of Mathematics, 2013)
Shape Affects the Sound of a Drum: Modeling Area and Perimeter
(Ohio Council of Teachers of Mathematics, 2013) Adabor, James K.; Foley, Gregory D.
The sound of a drum is based on the wave equation from physics. The surface area of the drumhead and its fixed perimeter are key parameters. This paper uses area and perimeter to model and answer the question, Can a rectangular and a circular drum make the same sound?
Understanding Integer Addition and Subtraction Concepts Using Microsoft Word® Illustrations
(Ohio Council of Teachers of Mathematics, 2013) De Los Santos, Estella
Small colored disks of different colors have long been used to teach integer concepts to middle school children. Concrete drawings of the colored disks may be created using Microsoft Word®. This article contains illustrations of integer addition and subtraction problems that may be used in the middle school classroom. Using this mode of instruction, students understand the concepts, are motivated to create mathematical models for problems, and are able to submit their work electronically.
No 10-Element Subset of the First 100 Counting Numbers is Subset-Sum-Distinct
(Ohio Council of Teachers of Mathematics, 2013) Harper, Brian
The purpose of this article is to present a solution to an interesting problem suggested by Richard Little of Baldwin-Wallace College involving "subset-sum-distinctness." Paul Erdős introduced the notion of "subset-sum-distinctness;" however, the focus of this article is instead on the problem and solution rather than Erdős. A set of counting numbers is subset-sum-distinct if and only if there is a one-to-one correspondence between the power set and the set of subset sums. In this article, we establish that no 10-element subset of the first 100 counting numbers is subset-sum-distinct by demonstrating the impossibility of a bijection from the power set of a 10-element subset to the set of sums. In order to prove a bijection between the sets is not possible, it is clearly sufficient to prove that any mapping from the power set to the set of sums is not injective. Lastly, we list several results about subset-sum-distinct sets in instances in which one is trying to find k-element subsets of the first n counting numbers.
Investigating Non-linear Asymptotes and the Graphs of Rational Functions
(Ohio Council of Teachers of Mathematics, 2013) Harrell, Marvin; Slavens, Dawn; Richardson, Connie
When looking at rational functions and their associated asymptotes, we often only discuss vertical, horizontal, and oblique asymptotes with our students. Often students ask if there are other types of asymptotes. This calculator-based activity allows students to investigate this question. In this activity, students will investigate the end behaviors of rational functions and how they are directly related to the end behaviors of their associated quotient polynomials.
Getting Students Excited about Data Analysis
(Ohio Council of Teachers of Mathematics, 2013) Mathews, Susann M.; Reed, Michelle; Angel, Nancy
The Graphing Art Project encourages students to explore functions as they create art. Students write functions with domain and range restrictions that generate interesting pictures. The project is easily tailored for different levels of mathematical learners. Algebra 1 students create art using linear functions; precalculus students include conic sections, exponential, logarithmic, trigonometric functions and the greatest integer functions in their work. Students may write graphing calculator programs to reproduce and animate their art.
Trigonometric Functions through Right Triangle Similarities
(Ohio Council of Teachers of Mathematics, 2013) Moyer, Todd O.
This article presents an introduction to the trigonometric functions tangent, cosecant, secant, and cotangent. Students understand these functions as quotients of the sine and cosine functions only. However, applying right triangle geometry to a triangle constructed within the unit circle develops the remaining trigonometric functions as ratios of side lengths, fostering stronger student understanding.
Plotting the Effects of Industrialization: An Interdisciplinary Project
(Ohio Council of Teachers of Mathematics, 2013) Vens, Kasey
This interdisciplinary project combined a unit on basic data analysis with the social studies curriculum. Students created parallel box plots to compare and contrast a group of industrialized countries with a group of industrializing countries. Students analyzed twelve variables such as literacy rate, infant mortality, and GDP per capita in an effort to better understand the effects of industrialization. Due to the relevance of the data, students were able to have meaningful discussions of the differences in medians and interquartile ranges of the two groups.
Contest Corner: The 2013 State Tournament of Mathematics Results
(Ohio Council of Teachers of Mathematics, 2013) Flick, Michael; Kuchey, Debbie
The authors summarize results from the 2013 Ohio Council of Teachers of Mathematics (OCTM) Annual Contest. Sample problems from the contest are provided along with scores from top teams in Ohio.
Mathematical Morsels: A Monthly Voyage of Problem Solving Goodness
(Ohio Council of Teachers of Mathematics, 2013) Bolognese, Chris; Edwards, Michael Todd
Back Matter (Number 68, Fall 2013)
(Ohio Council of Teachers of Mathematics, 2013)

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