Lessons via PowerPoint
Lessons using Clickers and PowerPoint
Virtual Manipulatives using GeoGebra to Highlight Co-variation of Quantities and Invariant Relationships
Invariant product for this
There were a large number of election ballots to be counted manually in a city in 1980. The major of the city expected a team of 25 people to take approximately 8.4 hours to count all the ballots. Let p represents the number of people in the team and h represent the number of hours it took the team to count all the ballots. Write an equation and draw a graph to show the relationship between h and p.
Invariant ratio for this
Two different candles, P and Q, lighted at the same time were burning at different, but constant, rates. When candle P had burned 16 mm, candle Q had burned 10 mm. Let p represent the number of millimeters candle P has burned when candle Q had burned q mm. Write an equation and draw a graph to show the relationship between p and q.
Invariant difference for
this two-identical-candles problem:
Two identical candles, A and B, lighted at different times were burning at the same constant rate. When candle A had burned 20 mm, candle B had burned 12 mm. Let a represent the number of millimeters candle A has burned when candle B had burned b mm. Write an equation and draw a graph to show the relationship between a and b.
Invariant sum for this
A candle is burning at a constant rate. When it has burned 30 mm, its height is 75 mm. Let h represent the candle’s height when it has burned x mm. Write an equation and draw a graph to show the relationship between h and x.
A Java Applet for the Two-Candle Problem
· A collection of Java applets to illustrate how a graph represents the co-variation between the height of a burning candle and time.
List of Mathematics and Mathematics Education Courses
MATH 2303: Mathematics for Preservice EC-4 & 4-8 Teachers (1. Number Systems, Arithmetic Operations)
Fall 2006, Spring 2007
MATH 2304: Mathematics for Preservice 4-8 Teachers (2. Shapes & Measurement)
MATH 3305: Mathematics for Preservice EC-4 Teachers (3. Fractions, Ratios & Proportions, Measurement, Algebra)
MATH 3308: Mathematics for Preservice 4-8 Teachers (3. Rational Numbers, Ratios & Proportions, Algebra)
Spring 2007, Fall 2007, Spring 2008, Fall 2008
MATH 3309: Mathematics for Preservice 4-8 Teachers: Generalists (Co-variations & Functions)
Fall 2010, Spring 2011, Fall 2011, Spring 2012
MATH 4302: Mathematics for Preservice 4-8 Teachers: Math Specialists (Capstone Course)
Spring 2010, Spring 2011, Spring 2012
MATH 5360: Introduction to Research in Mathematics Education I
Fall 2008, Fall 2009, Fall 2011
MATH 5360: Introduction to Research in Mathematics Education II
MATH 5370: Seminar for Mathematics Teachers in M.Ed. Program (Quantitative Reasoning)
Spring 2008, Summer 2008, Spring 2009
MATH 5370: Seminar for Mathematics Teachers in M.Ed. Program (Algebraic Reasoning)
MATH 5396: Graduate Research
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Updated on Feb 17, 2012