1999 Curriculum Abstracts

"Discrete mathematics and computer science,"

Exploring Pascal's Triangle and Other Recursive Patterns - Carole Bersani, Washington Elementary

The purpose of this unit is to develop students' critical thinking skills and problem solving strategies by teaching them to recognize and create patterns. A familiarity with patterns will allow students to gain a deeper understanding of attributes and relationships between numbers. These patterns will build a base for understanding fractions, algebra, geometry, and calculus. The patterns will be developmentally introduced starting with actions, shapes, and pictures, and ending with numbers. Class discussion will be a large component in order for the students to understand how others think. Mathematical discussions are beneficial because students see that there is quite often more than one way to solve a problem. I intend to discuss why Pascal's Triangle is an effective tool as one of the focuses for this unit. Additionally, there will be an emphasis on integrating children's literature within the unit. Lastly, students will be writing in math journals at the completion of each lesson. There will be three specific lesson plans designed for a third, fourth, or fifth grade classroom. The time required for completing this unit is two weeks, depending on the ability level of the students.

In addition to focusing on patterns, I have suggested a few extensions in the area of Number Theory and Discrete Mathematics: specifically combinations of numbers. I recommend having a poster of Pascal's Triangle as well as providing multiple copies of the triangle for each student to use. Pascal's Triangle is an excellent choice for a unit on recursive patterns because there is such a wide variety of patterns including, but not limited to primes, Fibonacci's Sequence, factorials, polygonal numbers, and Serpinski's Right Triangle. The extensions are not presented with as much detail as the actual lesson plans for the simple reason that they are not the focus of the unit. At the end of the unit is a comprehensive bibliography, including children's literature, teacher resources, and Internet sites.

"Discrete mathematics and computer science,"

	Exploring Pascal's Triangle and Other Recursive Patterns - Carole Bersani, Washington Elementary

	The purpose of this unit is to develop students' critical thinking skills and problem solving strategies by teaching them to recognize and create patterns. A familiarity with patterns will allow students to gain a deeper understanding of attributes and relationships between numbers. These patterns will build a base for understanding fractions, algebra, geometry, and calculus. The patterns will be developmentally introduced starting with actions, shapes, and pictures, and ending with numbers. Class discussion will be a large component in order for the students to understand how others think. Mathematical discussions are beneficial because students see that there is quite often more than one way to solve a problem. I intend to discuss why Pascal's Triangle is an effective tool as one of the focuses for this unit. Additionally, there will be an emphasis on integrating children's literature within the unit. Lastly, students will be writing in math journals at the completion of each lesson. There will be three specific lesson plans designed for a third, fourth, or fifth grade classroom. The time required for completing this unit is two weeks, depending on the ability level of the students. In addition to focusing on patterns, I have suggested a few extensions in the area of Number Theory and Discrete Mathematics: specifically combinations of numbers. I recommend having a poster of Pascal's Triangle as well as providing multiple copies of the triangle for each student to use. Pascal's Triangle is an excellent choice for a unit on recursive patterns because there is such a wide variety of patterns including, but not limited to primes, Fibonacci's Sequence, factorials, polygonal numbers, and Serpinski's Right Triangle. The extensions are not presented with as much detail as the actual lesson plans for the simple reason that they are not the focus of the unit. At the end of the unit is a comprehensive bibliography, including children's literature, teacher resources, and Internet sites.