Number Systems and Number Patterns

The first part of this section, Number Systems, examines the number systems devised by different cultures. Students should become aware that all peoples invented systems of counting as needed for trade, tax collection, and other activities. Scroll down to the second part, Number Patterns, to find activities that are, perhaps surprisingly, based on Pascal’s triangle.

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Number Systems

Mayan Math Activity http://nsdl.exploratorium.edu/nsdl/showRecord.do?id=10914

The Maya developed a sophisticated number system that they used to record possessions, dates, and astronomical observations. How is that system like ours, and how it is different? In this activity, students decode Mayan numerals as they are written in a document known as the Dresden Codex. The activity can be downloaded and printed. MSP full record

Egyptian Mathematics: Numbers http://www.eyelid.co.uk/numbers.htm

This web site has a brief introduction to the ancient Egyptian way of writing numerals. It includes graphics of what the hieroglyphics looked like, problems written using Egyptian numerals, and a downloadable worksheet creator, which is also available as a CD. MSP full record

History Topics: Babylonian Mathematics http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Babylonians.html

This web site contains an overview of Babylonian mathematics, with links to in-depth analyses of some topics. All students will be interested in the Babylonian numerals and their sexigesimal (versus our decimal) system. Older students who have studied the Pythagorean theorem will be surprised that knowledge of this theorem, so thoroughly linked to Greek mathematics, appears in a Babylonian clay tablet written between 1900 B.C. and 1600 B.C. MSP full record

History Topics: Chinese Numerals http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Chinese_numerals.html

Chinese number symbols from ancient times (14th century BC) are shown here, along with ideas on why particular symbols were chosen to represent certain numbers. A second set of symbols appeared after the abacus came into use. A great opportunity for discussion on the evolution of place value notation! (From MacTutor History of Mathematics Archive - MSP full record )

Indian Numerals http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Indian_numerals.html

This article begins with a quote from the mathematician Pierre-Simon Laplace: "The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India." Theories of how the Indians developed this method are described in detail, including the evolution of the numerals themselves and the invention of the decimal place value system we use today. (From MacTutor History of Mathematics Archive - MSP full record )

Links to Information on Number Systems http://mathforum.org/alejandre/numerals.html

If you are looking for more resources about different numbering systems, you will find them here. The site includes links to Arabic, Chinese, Mayan, Roman, Greek, Egyptian, and Babylonian numbering system resources. MSP full record

A Creative Encounter of the Numerical Kind http://studenthome.nku.edu/~webquest/gabbard/index.htm

In this WebQuest, students help an imaginary civilization develop a number system. They work in teams to explore place value, counting, and different number systems. After this preparation, they create and name a set of original number symbols for a base four number system and explain it in a formal presentation. MSP full record

Number Patterns in Pascal’s Triangle

Sierpinski Meets Pascal http://math.rice.edu/~lanius/fractals/pasc.html

This activity opens with students constructing Pascal’s triangle on a special grid. It continues with their creating a pattern in Pascal’s triangle as they shade in all the triangles except the odd-numbered ones. A surprise connection to the Sierpinski fractal results! (From Cynthia Lanius’ Fractal Unit - MSP full record)

Coloring Multiples in Pascal's Triangle http://www.shodor.org/interactivate/activities/pascal1/index.html

Teachers can assign this applet and discussion materials to small groups to help students identify multiples of numbers. As each multiple of the selected number is correctly identified, it changes color. The patterns created in this way are both surprising and satisfying. Since the triangle can be increased to as many as 15 rows, finding all the multiples can become quite a challenge! MSP full record

Which Way? Oh, Which Way Do I Go? http://www.figurethis.org/challenges/c06/challenge.htm

In this math challenge, the student looks for different ways to go from his home to the video store. The challenge page contains links to hints, the solution, and other similar investigations. The solution describes and illustrates how a number pattern is embedded in the question. The connection to Pascal’s triangle is shown under the "Did You Know?" link. MSP full record

Pascal's Triangle: Number Patterns http://mathforum.org/workshops/usi/pascal/pascal_intro.html

How to construct the triangle, notes on its history, and a link to several patterns to explore — triangular numbers, Fibonacci numbers, hexagonal numbers, and so forth — are found here. Among these patterns, you will find a concise but clear explanation of the connection between Pascal’s triangle and the coefficients of a binomial expansion An unexpected pattern for your algebra students!

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Copyright January 2008 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.