Pascal's Triangle

URL: http://mathforum.org/workshops/usi/pascal/patterns_pascal.html

1007936

Here are three ways to explore the famous triangle: by finding patterns and relations within the triangle, solving a pizza toppings problem in Antonio’s Pizza Palace, or working with an interactive web unit. The set of three investigations could work well as one fair project.

Summary

Subject keyword(s)	Algebra, Combinations and permutations, Connections, Discrete mathematics, Education, Functions, Mathematics, Number and operations, Number patterns, Patterns and sequences, Probability, Process skills
Grade level	Middle School, High School, Vocational/Professional Development Education
Intended audience	Educator, Professional/Practitioner
Resource type	Instructional Material
Resource format	text, text/html
Rights	1994-2009 Drexel University. All rights reserved.

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Title	Middle School Portal: Math and Science Pathways (MSP2)
Link	http://msteacher2.org/
Description	The Middle School Portal 2: Math and Science Pathways (MSP2) supports middle grades educators with high-quality, standards-based resources and promotes collaboration and knowledge-sharing among its users. Educators use MSP2 to increase content knowledge in science, mathematics, and appropriate pedagogy for youth ages 10 to 15. MSP2 employs social networking and digital tools to foster dynamic experiences that promote creation, modification, and sharing of resources, facilitate professional development, and support the integration of technology into practice. MSP2 is a project of the Ohio State University College of Education and Human Ecology, National Middle School Association, and Education Development Center, Inc., and is funded by the National Science Foundation. The partners integrate resources, tools, and services across projects, and support multiple methods of resource discovery to meet the needs of this audience.
	Full description and distribution of resources

Content contained within the resource

     Exploring Pascal - Introduction || Student Center || Teachers' Place   1. Patterns, Relations, Functions, Algebra 2. Antonio's Pizza Palace 3. Student Worksheets Exploring Pascal's Triangle: Patterns, Relations, Functions, and AlgebraWorking with a partner, study the following array of numbers. What patterns do you see in the arrangement of the numbers? Describe each pattern using words and symbols.   As you look for patterns, try to answer the following questions: Can you predict the next row of numbers? Is there a pattern in the sums of the numbers in the rows? Do any numbers repeat? Can you find a pattern in the diagonal numbers? Share your discoveries with the group. See if you can find:     natural numbers          1, 2, 3, 4, ...   pentatope numbers        1, 5, 15, 35, 70, ...     powers of 2          2, 4, 8, 16, ...   Catalan numbers        1, 2, 5, 14, 42, ...     powers of 11         11, 121, 1331, 14641, ...   Fibonacci numbers        1, 1, 2, 3, 5, 8, ...     triangular numbers          1, 3, 6, 10, ...       binomial coefficients     tetrahedral numbers          1, 4, 10, 20, ...   probability & combinations     hexagonal numbers          1, 6, 15, 28, ...   Sierpinski triangle     Interactive Number Sets: The Geometer's Sketchpad If you have The Geometer's Sketchpad, you can download and experiment with an interactive version of Pascal's Triangle that will show some of the patterns (401K). You can also download sketches that illustrate Sierpinski's Triangle and Multiples of Threes (385K) and Hexagonal, Tetrahedral, and Pentatope Numbers (389K). If you don't have the Geometer's Sketchpad, you can download a demo version. If you are using Netscape 3.0, Internet Explorer 3.0 or a later version of these browsers you can view an interactive version of Pascal's Triangle that uses java script. Please be patient; this page takes a few moments to load.   Questions? Write to the workshop facilitators.                                                                                                                                                                                                                                 [Privacy Policy] [Terms of Use] Home || The Math Library || Quick Reference || Search || Help  © 1994-2012 Drexel University. All rights reserved. http://mathforum.org/ The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies. Math Forum * * * * 19 April 1998