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This Meta Media workshop presents information and activities for using the manipulative, Dr. Super's Triangles to teach pre-algebra,algebra and geometry in grades 6-12. The activities engage learners(teachers and students) in solving several puzzles, discovering measurement relationships, writing English sentences and algebraic expressions for those relationships, and applying that knowledge to find the area and perimeter of a complex geometric shape. In doing so, learners are experiencing directly ideas supporting four core goals (or standards) promoted by national and state standards documents such as the NCTM Curriculum and Evaluation Standards for School Mathematics (the Standards, 1989) and the Standards of Learning for Virginia Public Schools (SOLs, 1995).
Here are a few specific examples of how the unit addresses the four core NCTM standards for Grades 5-8. First, the standard is named.Then, a few of the more pertinent descriptors for the standard are given.Finally, a brief example is presented explaining how the standard's descriptors are addressed in the unit.
"In grades 5-8, the mathematics curriculum should include
numerous and varied experiences with problem solving as a method
of inquiry and application so that students can --
use problem-solving approaches to investigate and understand
mathematical content;develop and apply a variety of strategies to
solve problems, with emphasis on multi step and non routine
problems;verify and interpret results with respect to the
original problem situation;acquire confidence in using
mathematics meaningfully." (excerpt of statement, Standards,
page 75).
This standard is addressed when learners use Dr. Super's Triangles to solve a simple geometric shape puzzle and use the information learned to find the area and perimeter of a more complex geometric shape.
"In grades 5-8, the study of mathematics should include
opportunities to communicate so that students can --
model situations using oral, written, concrete, pictorial,
graphical,and algebraic methods;reflect on and clarify their own
thinking about mathematical ideas and situations;discuss
mathematical ideas and make conjectures and convincing
arguments;appreciate the value of mathematical notation and its
role in the development of mathematical ideas." (excerpt of
statement, Standards,page 78).
This standard is addressed when learners manipulate Dr. Super's Triangles to discover angle and side measurement relationships, write these relationships as English sentences and algebraic expressions, and state them orally.
"In grades 5-8, reasoning shall permeate the mathematics
curriculum so that students can --
recognize and apply deductive and inductive reasoning;understand
and apply reasoning processes, with special attention to spatial
reasoning and reasoning with proportions and graphs;make and
evaluate mathematical conjectures and arguments." (excerpt
of statement, Standards, page 81).
This standard is addressed when learners determine the side lengths for Dr. Super's triangles through a series of manipulative activities, explain how they arrived at their results, and justify their thinking to classmates.
" In grades 5-8, the mathematics curriculum should
include the investigation of mathematical connections so that
students can --
see mathematics as an integrated whole; explore problems and
describe results using graphical,numerical, physical, algebraic,
and verbal mathematical models or representations;use a
mathematical idea to further their understanding of other
mathematical ideas." (excerpt of statement, Standards, page
84).
This standard is addressed when learners use algebraic notation and procedures to find the area and perimeter of geometric shapes.
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