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Pre-AP: Strategies in Mathematics - Developing Algebraic Thinking
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This one-day workshop is for mathematics teachers in grades 6 to 10. It provides teachers with hands-on activities and techniques to help students develop algebraic reasoning. A key feature of this workshop is the use of graphing calculators to help students visualize and explore algebra from graphic, numerical, and analytical perspectives as well as from traditional symbolic representations. Objectives for participants in this workshop include learning to develop techniques by using inquiry learning in teaching algebraic thinking, using patterns to find relationships, using tables in investigating relationships, and describing patterns using both recursive and closed relationships.
General Themes
- Using inquiry-learning techniques in teaching algebraic thinking
- Using patterns to find relationships
- Using tables to investigate relationships
- Using patterns to find relationships
- Describing patterns using both recursive and closed relationships
- Modeling and solving problems using graphs, tables, and equations
- Analyzing change using graphs and tables
- Acquiring the skills and facility needed to use graphing calculator technology in their classrooms
- Engaging in problem-solving situations that make use of graphing calculator technology as a tool for learning
- Developing and reflecting on ways in which to implement the use of graphing calculator technology
The workshop conforms to:
The workshop provides:
- Substantial content background for teachers
- Activities for students across grade levels
- Activities meant to illustrate good pedagogy (various instructional approaches, including cooperative learning)
- Activities that require communication to support observations and conclusions
- Opportunities for reflection
- Connections between activities
- Activities that use technology
Agenda
Activity 1: The Block Party
This activity involves problems where the outcomes form linear patterns. Working in groups, participants will analyze patterns, make tables of values, select variables, and interpret solutions to problems. Problems will be viewed numerically, graphically and symbolically. Graphing calculator skills to be developed include building a table of values on the home screen, entering data in lists, generating lists, plotting data, graphing equations, and using the table feature.
Break
Activity 2: Phone Rates
Participants will create a table of values, plot points, and graph lines to illustrate models for interpreting the long distance rate of two different phone companies. Making a table of values, plotting points, and graphing lines are used to make connections between the problem and multiple representations of the problem situation. A graphing calculator is used to find the point of intersection of the graph of two lines.
Activity 3: Get a Job
Exponential relationships are introduced by considering two possible ways of being paid for working a summer job for your uncle, one linear and one exponential. In a table for an exponential relationship, a constant amount is multiplied to the y-value for each constant increase in the x-value. Exponential patterns will ultimately increase or decrease very rapidly.
Lunch
Activity 4: Walk the Line
The CBRTM (Calculator-Based RangerTM) is a sonic motion detector. This device provides students with an interactive and visual means of exploring math and science concepts. With this unit and a TI graphing calculator students can collect, view, and analyze motion data. This activity will use the CBR to investigate linear functions involving time and distance.
Final break occurs in Activity 4.
Author
Mike Koehler teaches mathematics, including AP Calculus and AP Statistics, at Blue Valley North High School in Overland Park, Kansas. He has been an AP Calculus Exam Reader and a consultant for the Midwest region of the College Board. He is a national instructor for Texas Instruments' Teachers Teaching with Technology. He has instructed dozens of workshops on integrating technology in the teaching of mathematics throughout the United States and Puerto Rico and has given presentations at over 25 national conferences. He coauthored Exploring Statistics with the TI-83. He received the Presidential Award for Excellence in Mathematics and Science Teaching in 1993 and the Tandy Technology Outstanding Teacher Award in 1997. He served on the Commission on the Future of the Standards for the National Council of Teachers of Mathematics for Principals and Standards for School Mathematics, released in 2000, and most recently served on the board of directors of the National Council of Teachers of Mathematics from 2003 to 2005.
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