Open Educational Resources - Math

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  OER Ancient Egyptian Numerals and Arithmetic Activity

  Cynthia Huffman Ph.D.

  Many people are fascinated with ancient Egypt. The amazing, unique culture influenced many other civilizations and cultures. If you study the history of math, you will see how this influence included mathematics. Ancient Egypt also lasted an incredibly long time – over 3000 years. According to Egyptologist Bob Brier, “No civilization lasted so long, contributed so much, or repeatedly amazed as did ancient Egypt.”

  In this Open Educational Resource activity, students will have the opportunity to learn about ancient Egyptian numerals and basic arithmetic. For motivation, the setting is a scribal school with each student using a clipboard, paper, and fine point black marker to simulate a board, papyrus, and brush with ink. The activity can also be completed on its own without the scribal school setting.

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  OER Curve Fitting Applied to Easter Island Stone Foundations

  Cynthia Huffman Ph.D.

  In this activity, curve fitting is applied to drone pictures of ruins of stone foundations of the traditional houses (hare paenga) on the island of Rapa Nui. The free mathematics application GeoGebra (geogebra.org) is used, but the activity can be adapted to other technology, such as Desmos (desmos.com). The activity can be used as a teacher demonstration or completed by students, individually or in small groups, with access to computers.

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  OER Ellipses and traditional Rapanui houses on Easter Island

  Cynthia Huffman Ph.D.

  This worksheet activity is appropriate for secondary students in a class studying conic sections or students in a college algebra class. The first part of the activity gives an algebraic review of ellipses with exercises while the second part finds the equation of an ellipse corresponding to a Rapanui boat house foundation.

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  OER Indoor Ellipse Multicultural (Easter Island) Activity

  Cynthia Huffman Ph.D.

  This activity would fit in with a secondary or college algebra class studying conic sections, in particular ellipses, and gives students a multicultural hands-on application of the definition of an ellipse, while tracing out a scale model of the foundation of a hare paenga (boat house) from prehistoric Easter Island (Rapa Nui)..

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  OER Outdoor Ellipse Multicultural (Easter Island) Activity

  Cynthia Huffman Ph.D.

  This activity would fit in with a secondary or college algebra class studying conic sections, in particular ellipses, and gives students a multicultural hands-on application of the definition of an ellipse, while tracing out a full-scale model of the foundation of a hare paenga (boat house) from prehistoric Easter Island (Rapa Nui)..

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  Place Value in Primary Sources OER Activity

  Cynthia Huffman Ph.D.

  An activity for student to examine the use of place-value in the Hindu-Arabic numeration system from a historical viewpoint by looking at primary sources. Includes the key.

  (Revised May 2021)

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  Ada Byron Lovelace Activity

  Cynthia J. Huffman Ph.D.

  This activity was originally created for a Women in Mathematics course to provide students with a small taste of some basic mathematics connected to the work of Lady Ada Byron Lovelace. The activity is based on her work related to the Difference Engine of Charles Babbage, and has students investigate differences of sequences. The activity could also be used in other courses, such as a general education mathematics course, a course for pre-service elementary teachers, or a history of mathematics course.

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  A Historical Activity Adding Irrational Numbers

  Cynthia J. Huffman Ph.D.

  In this activity, students will follow and then analyze work by mathematician and fencing master Ludolph Van Ceulen (1540-1610) on adding similar radical numbers, like . His method is quite different from the method currently in use in the secondary school curriculum and College Algebra, in that he does not first simplify the square root expressions before adding them. This activity could be used with high school or College Algebra students after they have learned the current method, in order to reinforce their understanding of radicals. The activity would also be appropriate to use with pre-service mathematics teachers or in a history of math class or in a math circle. It demonstrates that there may be more than one algorithm or technique for performing arithmetic operations, and that mathematics, including arithmetic, develops and evolves over time.

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  A Real World Example of Solving a Quadratic Equation in Movie CGI

  Cynthia J. Huffman Ph.D.

  It is important to expose students to the beauty and usefulness of mathematics. Since computer graphics are familiar to most students due to video games and movies, they make a great source for motivating topics in mathematics. This activity shows students an application of solving quadratic equations to computing the line of sight to spherical objects in computer graphics.

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  CGI (Computer Generated Imagery) Matrix Multiplication Activity

  Cynthia J. Huffman Ph.D.

  Many students are motivated by real world applications of mathematics, and most students are familiar with the term CGI from watching movies and playing video games. This particular activity ties matrix multiplication to CGI (Computer Generated Imagery). It has been used successfully with high school students in an Algebra II course who had just learned how to do matrix multiplication, middle school and high school students (some of whom were seeing matrix multiplication for the first time) attending a special Math Day on a university campus, and with College Algebra students (during a unit about matrices).

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  Constructing a Square an Ancient Indian Way Activity

  Cynthia J. Huffman Ph.D.

  In this activity students use string to model one of the ways that was used in ancient India for constructing a square. The construction was used in building a temporary fire altar. The activity is based on a translation by Sen and Bag of the Baudhāyana-śulba-sūtra.

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  Constructing a Square Indian Fire Altar Activity

  Cynthia J. Huffman Ph.D.

  In this activity, we will model constructing a square fire altar with a method similar to one used by people in ancient India. The fire altars, which were made of bricks, had various shapes. Instructions for building the altars were in Vedic texts called Śulba-sūtras. We will follow instructions for constructing a square gārhapatya fire altar from the Baudhāyana-śulba-sūtra, which was written during the Middle Vedic period, about 800-500 BC.

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  Emilie du Chatelet Activity

  Cynthia J. Huffman Ph.D.

  This activity was originally created for a Women in Mathematics course to provide students with a small taste of some basic mathematics connected to work of Émilie du Châtelet. The activity has the students use some algebra to look at rates of change (velocity and acceleration) of a paraboloid apparatus. It could also be used in other courses, such as history of math, high school or college algebra, and calculus.

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  Emmy Noether and Modular Arithmetic Activity

  Cynthia J. Huffman Ph.D.

  This activity was originally created for a Women in Mathematics course to provide students, who may not have had an abstract algebra class, with a small taste of some basic mathematics connected to the work of Emmy Noether. The activity has the students perform some basic modular (clock) arithmetic and then investigate real world applications of modular arithmetic to ISBN and UPC codes. It could also be used in other courses, such as a general education mathematics course.

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  Euler Construction Activity

  Cynthia J. Huffman Ph.D.

  Original sources of mathematics provide many opportunities for students to both do mathematics and to improve their problem solving skills. It is also interesting to explore original sources in new ways with the use of technology. In this activity, students can gain experience with dynamic geometry software and enhance their geometric intuition by working through a construction given by Euler in 1783.

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  Ingrid Daubechies Wavelet Activity (Function Transformations)

  Cynthia J. Huffman Ph.D.

  This activity was originally created for a Women in Mathematics course to provide the students with a small taste of some basic mathematics connected to the work of Ingrid Daubechies on wavelets. The activity could also be used in a high school algebra or college algebra course to motivate transformations of functions, in particular, translation (shifting) and scaling. The functions used are a basic quadratic x², the exponential function e^x , and the sine function, but other functions could be used to fit the level of the students.

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  Maria Agnesi Activity

  Cynthia J. Huffman Ph.D.

  This activity was originally created for a Women in Mathematics course to provide students with a small taste of some basic mathematics connected to the work of Maria Agnesi. The activity has the students look at some of her work in algebra and calculus (optional). It could also be used in other courses, such as history of math, a general education mathematics course, high school or college algebra, and calculus.

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  Maryam Mirzakhani Riemann Surface Activity

  Cynthia J. Huffman Ph.D.

  This activity was originally created for a Women in Mathematics course to provide students (who may not yet have taken much upper level mathematics) with a small taste of some basic mathematics connected to the work of Maryam Mirzakhani. In this activity, students investigate some Riemann surfaces and one non-example. The activity could also be used in other courses, such as a general education mathematics course, a course for pre-service elementary teachers, or a history of mathematics course.

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  OER Women in Math course

  Cynthia J. Huffman Ph.D.

  This Women in Math course takes a look at 11 notable women mathematicians through readings, quizzes, discussion boards, and activities related to the mathematical contributions of the women. Several of the activities are original and can be found separately at Pittsburg State University Digital Commons (https://digitalcommons.pittstate.edu/ - search by author for Huffman, Cynthia).

  Course URL

  The OER Women in Math course can be accessed at https://pittstate.instructure.com/courses/1081791 .

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  Place Value in Primary Sources Activity

  Cynthia J. Huffman Ph.D.

  An activity for student to examine the use of place-value in the Hindu-Arabic numeration system from a historical viewpoint by looking at primary sources.

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  Problem Solving Practice with Problems from Fibonacci's "Liber Abbaci"

  Cynthia J. Huffman Ph.D.

  In this activity, problem solving skills are practiced using two well-known problems from Fibonacci's world-changing book "Liber Abbaci". Students are also asked to reflect on the differences and similarities between their solutions and those of Fibonacci. The two problems are the famous rabbit problem which led to what is now know as the Fibonacci sequence and the 30 birds for 30 denarii problem, which is not as well-known to the general public.

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  Sophie Germain Activity

  Cynthia J. Huffman Ph.D.

  This activity was originally created for a Women in Mathematics course to provide students, who may not have had an abstract algebra class, with a small taste of some basic mathematics connected to the work of Sophie Germain on Fermat’s Last Theorem. The activity has the students find all primes less than 100 using the Sieve of Eratosthenes and then determine which of those are Germain primes. The activity could also be used in other courses, such as a general education mathematics course or a history of mathematics course.

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  The Game of Ur: An Exercise in Strategic Thinking and Problem Solving and A Fun Math Club Activity

  Cynthia J. Huffman Ph.D.

  In this Open Educational Resource activity, students learn a little about the history of the Royal Game of Ur, the first board game, and get to practice critical thinking and problem solving by playing the game. Instructions are given along with a template for the game and game pieces and tetrahedral die.

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  What is the Shape of a traditional Rapanui house on Easter Island? A Multicultural Mathematical Activity Involving Ellipses

  Cynthia J. Huffman Ph.D.

  The Rapanui people of the island Rapa Nui, also known as Easter Island, at one time had a system of “writing” called Rongorongo. Unfortunately, the ability to read Rongorongo has since been lost. So currently archaeology and oral tradition are the only available sources for information about the early people of the island. Oral tradition states that the houses originally had upside down canoes for their roofs, and thus they are called hare paenga, or in English, boat-houses. In the literature, these boat-houses are said to be elliptical in shape. In this activity, we will investigate the shape of archaeological remains of foundations of the boat-houses to try and determine if they are indeed in the shape of an ellipse.