2nd Lesson McAllen e-PCMI July 19, 2007

Goal (8 th grade) For students to organize data, recognize, and predict patterns.

Texas TEKS (8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and nonexamples; and (B) validate his/her conclusions using mathematical properties and relationships.

Texas TEKS 8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem;

Previous Knowledge greatest common factor prime numbers odd & even numbers division organizing data in a table/list angle measures dimensions

Major Focus Recognizing patterns

Questioning How can you predict the number of hits and the pocket the ball will land in, for any dimensions of the pool table?

Guiding Questions How many times would you simulate the problem? What dimensions would you use? Do the dimensions 2,1 and 1,2 have the same outcome? (Does order matter?) How many patterns do you see?

Guiding Questions Do all the patterns matter? What rule can be used to predict the number of hits? What observations did you make about the number of hits that occur on tables of various sizes? How would you organize your data?

Anticipating Students Responses Students say if length is even pocket B, without sufficient examples. There is no pattern to predict the pocket. Add the dimensions without simplifying them to predict the hits. It’s impossible to organize data, too much info.

Facilitate Discussion What are the different ways to organize your data? Is there only one best way to organize data? What patterns seem to occur in the simulations? (hits/pockets) How or what dimension should you change?

McAllen Team Meiling Dang Steve Ferguson Raul Hinojosa Louis Shoe Armando Soto Dai Tolkov Dr Monty Taylor as table advisor