$[Words]$

Concepts & Computation
in Pre-Algebra & Early in Algebra I

Think composite, multiple, factor, linear, reciprocal, opposite, FOIL, solve, simplify, domain, graph.
Consider the focus of graphing in the 21st century.
Play "A Game for Two Players."
Use Term Tiles for "digitally concrete" computation.

Hi!

I wrote this talk to encourage the early use of the words and meaning of identity, opposite, and reciprocal functions in the teaching of algebra and prealgebra and to provide the support material to promote student success and faculty satisfaction on a job well done.
-- Agnes (A²) Azzolino

function name	symbol	meaning/performance/action

identity	x	no change, no sign change, no size change, exactly the same as the input, identically the same
opposite	-x	sign change, no size change, the additive inverse
reciprocal	1/x, x^-1	no sign change, size change, the multiplicative inverse -- if x>1, the reciprocal is smaller than x and positive -- if x=1, the reciprocal is x, 1, still positive -- if 0-- if x=0, the reciprocal infinite in size, is undefined -- if -1-- if x=-1, the reciprocal is x, -1, still negative -- if x<-1, the reciprocal is smaller in magnitude and negative
In short:
identity	no change
opposite	sign change
reciprocal	size change

MATH SPOKEN HERE!
- a richly illustrated arithmetic, algebra, precalc,
and calc dictionary & reference site

$[master list of all MSH! dictionary words]$ "Think composite, multiple, factor, linear, reciprocal, opposite, FOIL, solve, simplify, domain, graph," prime.

A Game for Two Players
Play "A Game for Two Players."

"Use Term Tiles for "digitally concrete" computation."

Exploring Functions through the Use of Manipulatives

The reciprocal functions is the best way to teach domain and range.
The best way to do that is with Exploring Functions.
For paper and pencil graphing, polka-dotting a curve ensures accuracy.

Asides

	Use the [[x]] to teach g(x) = af(bx-c)+d in precalc.

$Class Table$	Statistics resource.

$QB, graded assignments$ $QB$ $QB, graded assignments$	Writing-to-Learn, "Critical Thinking Assignments"

	Writing-to-Learn, Projects

$calc1$	Precalc & Calc material organized for students, and also organized by my department's course outline.

$spread sheet notes$	Anyone who writes tests involving computation