Precalc & Calc I Support Material Organized by the Course Outlines
and OpenStax Texts

Hi! Enter my classroom through https://www.mathnstuff.com/math/math.htm and consider the support material in precalc and calc I now organized day-by-day using the Middlesex math department course outlines and OpenStax "Algebra and Trigonometry" and "Analytic Geometry & Calculus I" textbooks.
Consider singing a derivative, taking a limit by approaching where one actually can approach, or by definition as one makes "h go to zero," hearing a slope of 2/3, seeing a sequence of a Reimann sum areas plot an antiderivative, view the derivative sine-cosine cycle graphically, connect a few dots and draw a picture, etc.
Consider using writing-to-learn and the VERBAL/Auditory, WRITTEN/Symbolic, PICTORIAL/Visual, CONCRETE/Kinesthetic Modalities and THE MOTHER TONGUE(S) to teach.
All material is free and downloadable.


The Languages of Math "Classroom(s)" © '98, '08, '09, '25 A², Agnes Azzolino

	MOTHER TONGUE & OTHER TONGUE(S) Most Sophisticated and also the Most Basic

	MOSTLY MATH TONGUES Most Sophisticated, Most Basic


VERBAL / Auditory	WRITTEN / Symbolic	PICTORIAL / Visual	ANIMATION / Video	CONCRETE / Kinesthetic
formal spoken mathematics	written word	DIGITAL MANIPULATIVE	viewer can not "touch"	object
informal spoken mathematics	written symbol	moving picture	perhaps a traditional video	model
spoken symbol	semisymbolic	static picture	learner replay possible	DIGITAL MANIPULATIVE
symbol speak	calculator symbol	numeral	may have a DIGITAL or concrete version
calculatoreze/computereze		graph	independent use possible
web speak		nonverbal body language	it may be written for young viewers
Languages of the Math Classroom Think Language or Modality

$calc.fa25$

Consider the support material in precalc and calc

Consider singing a derivative, Calc, M10/6, T10/7, c.1.htm
Taking a limit by approaching where one actually can approach,
Calc, T9/2, W9/3, c.1.htm (sheet 1 - approach by dragging)
Taking a limit by definition as one makes "h go to zero,"
Calc, c.1.htm (sheet 5 - limit as h goes) and squeeze (sheet 9) and delta-epsilon (sheet 7)
using limit sketchpad
Hearing a slope of 2/3,
Precalc, p.4.htm, M9/15, T9/16
hear a sample Listen to a slope of zero. Listen to a slope of one.
or go to p.4.htm, then, go down to the definition of slope,
then in the orange box go to "Slope in Sound & Picture"
Seeing a sequence of a Reimann sum areas plot an antiderivative,
Calc, T11/18, W11/19 c.21.htm - Riemann Sums (5.3)
or visit ReimannSums.gsp
View the sine-cosine derivative cycle graphically,
Calc, c.7.htm, W9/24, Th9/25,
Basic Differentiation Rules (2.3)
or visit DerSin.gsp

Connect-the-Dots

and draw a picture,

#1. Limits

# 4. Derivatives

# 8. Integration

# 9. Summation

"Oscar Had A Heap of Apples Connect-the-Dots"
27 mental computation questions like:
sin (A) of right triangle ABC.

It's ideal for trig or precalc.

questions

answers

easy print pdf

Using writing-to-learn and the VERBAL/Auditory, WRITTEN/Symbolic, PICTORIAL/Visual, CONCRETE/Kinesthetic Modalities and THE MOTHER TONGUE(S) to teach.
$calc.fa25$ Math Projects
SUMMARY PRESENTATIONS W9/17, Th9/18 pg. 5 W10/1, Th10/2 pg. 9

The Questionbooks -- Writing-to-Learn, "Critical Thinking Assignments"

Arithmetic
$QB, graded assignments$

Algebra
$QB$

Precalc

Calc I
$QB, graded assignments$

Status Quo Dowloads

Calc: TEXTBOOK Info; DownLoad or View the Text

Precalc: TEXTBOOK Info; Load or View the Text

MyOpenMath

FREE:

TI-83

Excel

Sketchpad

Parts of Each Day's Page

In the title: page name, dates
In the header, links to:
last class, math page, course name resource page,
semester course page w/support at bottom, next page
topic title, sections in text, problem pages
Above page content:
intro image
blue box message/summary w/me
including pink-box message link, "phone # in Canvas reminder"
In precalc, text book objectives
In all pages: links possibly needed to pages, spreadsheets, sketchpads
In the footer: class notes in image form uploaded for download preclass & post class

Features of Most Days

Yeah, NOTHING IS EVER "FINISHED."
Review of material of past courses and past classes
* Fake Quiz
Foreshadowing (sometimes), 3-Day Mention, review
* polar.gsp w/children f(x)= Asin(Bx - C) + D. Text 8.1,8.2,
Vocabulary on Page
* mine.htm
* in array: p.1.htm
* in paragraph: p.10.htm
vocabulary & computation built into page
* p.10.htm, M10/6, T10/7 , Exponential & Log Functions
Pages on a Specific Topic
* Inverse Functions & Their Derivatives -- Think "The Derivative of an Arc Function"
Function building tools
* Combinations of functions; Inverse functions. Text 3.4,3.7,
* compositeFx.poly.ratl.gsp
* inverse.gsp
Sine Law - Multiple Ways to Move
* Digital Manipulative with Sketchpad
* Digital Manipulative with Excel
* Concrete Manipulatives
Digital & Concrete Function Manipulatives
* parentFX -- function "manipulatives" -- curve shift to graph

Features of Some Days

Images -- Used & Used Again

* Graph papers 3 Regular Planes
3 Trig Planes

CALCULUS ON VIDEO

stat.gsp - From Calc to Stat to Calc

Page Intro & Purpose
During the Spring 2025 semester, I taught Calc I and Stat I. The calc had recent support material, and the stat had substantial support material but it was "older." To supplement the statistics, I took the calc material and used it in a video.
Within & Between in the "Center & Spread" Video
Beginning at 11:23 minutes into the video, and ending at 15:46 of the video, I used "The cumulative impact of the function from a to b" found in ReimannSums.gsp to teach the probability of a score being within x standard deviations of the mean or to compute p( a < z < b). See the Teachers' Guide at "Reimann Boxes & Sums, and Integration" and also Probability Notes for Calc I and also use fX.f'X.f''X.intX.gsp.

That spreadsheet and 5 minute video clip was the genesis of this page and the spreadsheet. Enjoy.

0 - toc, Table of Contents
1 - UNIFORM n=8
2 - Standard Normal & Normal
3 - between, within
4 - Stanine, drag a₀, b₃₂ 5 - interval between, within, confidence interval about mean, drag a
6 - cumulative PROBABILITY DISTR, type mu, sigma, a, b
7 - BACKUP p(a 8 - Reimann calc image - static
9 - Reimann calc image - movable
10 - Reimann calc by typing
11 - green dot plot anti
12 - HYPOTHESIS TEST mean = k (needs to be split)
13 - standard normal backup
14 - slide
15 - cumulative standard normal z table
16 - hold

Dowload inverse.gsp - Sketchpad of inverse functions

0 - vertical, horizontal line tests
1 - square root fx
2 - any function
3 - sqrt fx by parameters
4 - restricted domain on inverse

5 - arcsine
6 - arctangent
7 - f and inverse
8 - f, inverse, tangents

Dowload absement.gsp

0 - toc
1 - time, t
2 - displacement, distance, s(t)
3 - definition of derivative
4 - s(t), s'(t)
5 - s(t), s'(t), s''(t)
6 - emojis, f, f', f'', tangent line
7 - trace derivatives

8 - PARTITION & SUMS 4 boxes
9 - Reimann & Sums
10 - SUMS absement, input [a,b]
11 - absement, n=32
12 - absement plus c
13 - play absement plus c
14 -arcsine actual fx graphed
15 - arcsine mesh - useF(x) plot to plot arcsine

Hi!
Here's some stuff many would consider
unusual including: digital manipulatives,
sketchpads, spreadsheets, web pages, and,

web page

pdf of page

video of page

Precalc: 44:01 -- Curve shift/ translate many functions; 50:27 -- Determine if two angles are coterminal and; -- Define standard position; 51:32 -- Build a polynomial or rational function; 56:22 -- Assemble a Unit Circle jigsaw puzzle; 58:48 -- Add vectors
Calc I: 1:02 -- Take a limit by approaching and Take a derivative by definition; 1:09 -- Label a graph with function emojis< Mean Value Theorem, Rolle's Theorem; 1:22 -- Graph the sin(x) and its 1st, 2nd, 3rd, and 4th derivatives using trace; 1:26 -- Examine angle of elevation/depression and ladders with h(x), y(x), h(y), x(y), and h as variable, and h as a constant; 1:30 -- Compute an Antiderivative by Reimann Boxes