$[Words]$

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. page pdf

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."
Lab 1 - Sheet 1 - Select, Copy, Paste & Sheet 3 - A Game for Two Players Lab 2 - Term Tiles & hyrogliphics

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

represent
simplify
multiply
solve
Term Tiles Handout

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.
Exploring Functions Handout AMTNJ.2024.gsp

Asides

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

	Wipebook Contest https://wipebook.com/30iba4

	Make your own QR code for free at https://www.qrcode-monkey.com

$Class Table$	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

Comments on Inverses
The identity, opposite, and reciprocal functions are their own inverses.

It is useful to keep the phrases for inverses as similar as possible.

function name	symbol	its inverse function

identity	x	the identity function is its own inverse
opposite	-x	the opposite function is its own inverse
reciprocal	1/x, x^-1	the reciprocal function is its own inverse
squaring	x²	√x, the square root function A square root is a number. Square root of x means the number whose square is x.
exponentiate, raise to a power	b^x	log_b(x), the log, base b, of x A log is an exponent. Log, base b, of x means the exponent to which b must be raised to get x.
sine function	sin(x)	sin^-1(x), or arcsin(x), the arcsine of x An arcsine is an angle. Arcsine of x means the angle whose sine is x.

Closing Remarks & Requests

Play is a valuable way to learn.

Manipulatives are valuable tools for teaching and thinking and learning.

	Think and use the words, not just the symbol:
	identity	no change
	opposite	sign change
	reciprocal	size change

$[MC,i. Home, site home page]$

[Good Stuff -- free & valuable resources]

$[master list of all MSH! dictionary words]$

$math games toc$

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

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