A Taste of What We're Doing Today

    Hi. You don't need to turn off your screen, just don't look at today's page.

    Please clear you desk. This is not a quiz.

    Open the envelope without discussion w/others.

    Figure out what's in the envelope and what to do with it, then, do it.

    When you and another have completed you task, discuss the task and its effectiveness.

Please do not continue yet.
  1. in the box
  2. still in the box, but near the edge of the box
  3. today's move out of the box
  4. what it takes to get out of the box
  5. out of the box in a different way
  6. even further from that box

Create One or More Web Pages for Today's Notes

    First, you will first be making one or more web pages. Don't worry, you need not know any HTML. You will need to know Select/ Copy/ Paste and then Save to edit quickly using Notepad.

    After editing in Notepad use [Alt] + [Tab], [Tab] to get to Internet Explorer. (This means: Press and continue to hold down [Alt]. Press [Tab] and press [Tab] again and again until the name of the program you wish to use is displayed. Release [Alt] and [Tab].)

    Once in Internet Explorer, use [f5] or the refresh page on the browser to revise your work so the browser displays your new work.

    Creating a web page is the best way to organize what you wish to keep, link, and note with today's work. It is also an excellent way to group links together for a specific lecture or course (see Algebra Notes and Trig Stuff).

    The work environment should be constructed first.

  1. Please create your work environment (probably on the thumb drive) and possibly create a file folder for today and a subfolder for images possibly called gif or media. You will do this individually, but we will wait as you do this.
  2. We will use some stuff from WORK ENVIRONMENT, but you need not open the page unless you wish to do so, We will look at the page together.

  3. Lecture, next.
  4. Examine the code below.
    <HEAD><TITLE>     </TITLE></HEAD>
    <BODY>                    </BODY>
    This is all it takes to create a blank web page.
  5. Notice below, a title has been added and how the green page below has recieved its color through a background color phrase in the first body tag: <BODY BGCOLOR="#CCFFCC">. Your will be adding color shortly.
    Notice that a page may be made as long as needed and it is easier to put the last body tag just before the last html tag.
    <HTML><HEAD><TITLE>Notes from May 31, 2018</TITLE></HEAD>
    <BODY BGCOLOR="#CCFFCC">               

  6. Below, a few more things have been added. You will see the code soon.
  1. If you wish to create a new web page, edit an old (source) page and save it under the new page name.
a. Use page 531text.htm as your source page.
b. Open page 531text.htm in your browser.
c. See the figure at the left. In your browser,
under the menu heading FILE, scroll down to "Edit with Notepad" and select it.
d. You are now in Notepad and have the code for
the page 531txt.htm before you.
e. Save the new file on the thumb drive as may3118.htm,
in your storage area. Use whatever name you wish as long as it ends in .htm making it a web page.
f. Make a few pages saved under different names to try
different color combinations and for more room to take notes.
g. Select a page to act as a primary notes page, probably
may3118.htm. Using your browser open this page and view your handy-work.

      Continue on to the next box only.
      Have fun. Good luck.

Add Color & Other Stuff to Your Page(s)
  1. Change the background color of your page to one you like.
    You might change the background color of the tables to see how they look with your page background. To do this you might wish to:
    Read how to add color
    Play with choosing a color with the color table page
    See how color names work
    Best of all, use VisiBone COLORLAB to choose a color
  2. Only if you have time, consider adding other stuff to you storage area. We will be working on adding and editing shortly. Your priority is putting colors you like on your page(s).
    Visit the Web Building Home Page for more info
    Exanine details on tables and their variety
    Definitely copy into storage the url of the "stuff I use the most" text file, OR,
            copy the file into your media folder
    Consider background info on links, jumps
    Please do not go past this box. Please do not go on to Start Note Taking & Storing. Thanks.

Start Note Taking & Storing
  • Edit may3118.htm.
  • Place an image in the web page.
  • Place a link in the web page.
  • Place a fancy (open-a-new-window & use image as locator before second link tag.
  • Consider formatting.
  • IMAGE STORAGE: 0 1 2 3 4

      No more web page stuff unless you have a question or need help. Now you can start making links to stuff or download it and a link it in your files. Everything on the site belongs to me. You are welcome to use it in your classroom. If you use it anywhere else, please cite the source.

Visit My Classroom
Hi. Welcome to my class.
We will be doing things with an asterisk. We will be skipping things with no asterisk.
Feel free to examine them if you wish.
The workshop is mostly a lecture with detours in which participants can work on the material presented.
math home

  • Please read this letter.
  • *"Everything with the tablet was really sick."
  • *How Sick

The Box

The Languages of the Math Classroom
© '98, '08, '09 Agnes Azzolino

Most Sophisticated and also the Most Basic

Most Sophisticated, Most Basic

VERBAL / Auditory WRITTEN / Symbolic     PICTORIAL / Visual     CONCRETE / Kinesthetic    
  formal spoken mathematics   written word   DIGITAL MANIPULATIVE     object
  informal spoken mathematics       written symbol   moving picture   model
  spoken symbol   semisymbolic   static picture   manipulative/token
  symbol speak   calculator symbol   numeral
  calculatoreze/computereze   graph
  web speak   nonverbal body language

Manipulative and Languages
  • *Features of the Languages of the Math Classroom
  • *manipulative use

Choose to Improve Instruction.
  • Choose a modality first.
            Visual, Auditory, Symbolic, or Kinesthetic
  • Introduce in the concrete.
  • Review in the abstract.
  • Sometimes use multiple modalities at the same time.
  • Strive for comfort in all modalities, not just your favorite.
  • Repeatition improves retention,
            especially in different modalities.

Vary the technique to achieve the above.
  • Use color rather than black and white.
  • Use active rather than passive.
  • Use pictures rather than just text.
  • Use spoken word rather than just text.
  • Use white space to improve clarity.
  • Larger is usually clearer than smaller.
  • Sometimes start with the big picture rather than the details.
  • Reference to earlier work improves comprehension.
  • Showmanship -- a performance -- improves retention.

Operations With Whole Numbers

  • *The Hundreds Board -- page and images
  • *The Hundreds Board -- Digital Manipulative and master page for multiples
  • page 40, 50 - Whole Number Addition and Subtraction and Multiplication and Division with multiples masters
  • *A Game for Two Players
  • *A Game for Two Players Digital Manipulative as 42.xls
  • *Prime Numbers Presented Logically as prime.xls
  • Recognition of Prime Numbers Exercise for Students in a Lab
  • slide rule
  • *slide.xls - slide rule digital manipulative
  • Someone's Powers of 10

Operations With Fractions

  • So, What's A Fraction?
  • *fract.xls -- Movable fraction bars from 1/1 to 1/15 on multiple sheets
  • Why "Invert and Multiply" When Dividing FRACTIONS
  • Multiple Strips & Fraction Bars
  • *strips.xls --DIGITAL MANIPULATIVE on a spreadsheet with multiple strips & fraction bars
  • Fraction Computation Stated in Symbolic Form (so you do not have to bother writing it out)
  • *Lessons in Dictionary
  • *Dictionary

Digital Manipulatives

“Tell me and I forget, teach me and I may remember, involve me and I learn.”
- Benjamin Franklin
  • Bing Your Students to a Lab or Just Enhance Your Lecture

Exploring Functions Through Manipulatives

  • Entire Book
  • Lecture Handout
  • *Please wait to do Graph by Placement
  • more graphing
  • *solving
  • *raw masters
  • absolute value dilator in hand
  • *Slopemeter w/movement
  • *"Math Exercises."
  • Math Exercises web page

Teacher Ed

  • nomogrf.xls -- Nomograph for whole, signed, fraction, decimal computation webpage
  • The Decimal Bakery
  • Napier's Bones spreadsheet webpage
  • *Area Formulas spreadsheet
  • Assessment Inventory -- A Journey with Self-Assessment as a Compass
  • *Math Tokens


  • Hypothesis Tests
  • *Spreadsheet to write Hypothesis Tests
  • Other Stuff


  • Name it with a title to make it more concrete and for better recall
    *2 mile race (visual with auditory and kinesthetic)
    *basic Veronica's bow tie
  • internet trig reasources at c33pg00.htm
  • *central angle, clockwise/counter-clockwise, coterminal, negative/positive angle measure
  • *Choose paper or spreadsheet
  • The Unit Circle
    *web, static, but with color
    *web, active
          The Animated Unit Circle. - animation w/text.
  • The Usual Way vs. The Active Way
    *sine/cosine only, web active
    *quadrantals notes the usual way
    *sine and cosine graphed
    *write on similar triangles
    tangent actively
  • Proofs
    *Pythagorean Identities -- graphically and by hand symbolically
    *Examine odd/even identities
  • Blank paper
        3 planes per page, gif
        3 planes per page, web
        *Other graph papers
  • *Review with Explorer
  • *Library of connect-the-dots puzzles/worksheets
  • *Assign students to build a cheat sheet and continue
  • *Curve shift with sine sine on a spreadsheet
  • *poly.xls
  • *Pass or Touch
  • *Who Has? Polynomial F(x)
  • *Other spreadsheets


  • *Take a derivative with a pencil
  • *Casa Omar answers
  • Other Connect-the-Dots

Operations With Decimals and Percents

  • *compute.xls
  • *compute areas and volumes with area.xls

Algebra Basics and
First Degree Equations and Inequalities in One Variable

  • *Invisible Ones
  • *Term Tiles & Tokens
  • *A Number, Zero, the Opposite, "Zero Out" to Simplify and Solve
  • Tough Topics to Teach
  • *Digital Manipulatives Spread Sheets:
        (for students, basic tiles only) tiles.xls
        (for students, basic + hot cells) create.xls
        (for teacher and to supplement students', all tiles, tokens, hot cells) hot.xls
        (for teacher) cubes.xls
  • Unit 17: Algebraic Multiplication
    *student work on a test

  • cubes.xls
  • The Square of the Difference of Two Numbers. [Textbook Presentation & Background]
    *** On the spreadsheet, use term tiles to compute the square of the difference of two numbers. [Just tile picture of tile product]
    *** With manipulatives try to assemble the cube of the difference of two numbers. [Just tile picture of tile product]
  • Source page [0n the "cube of the difference of two numbers"]
  • Appendix and Masters and Digital Manipulatives
  • "Who Has" Linear Expressions Game
  • Code, Semi-equations/semi-expressions

Systems of Linear Equations in Two Variables

  • Solve A Systems of Linear Equations by Term Tiles
  • *cramers.xls
  • Solve Systems of Equations Graphically answers

Courses or Foci
Operations With Whole Numbers
Operations With Fractions
Operations With Decimals and Percents
Algebra Basics
First Degree Equations and Inequalities in One Variable
Systems of Linear Equations in Two Variables
Exploring Functions Through Manipulatives
Teacher Ed
One Last Use of Technology

Focus of Presentation

    Think "out of the box" in a math classroom setting. Use 19 presentation & note taking styles in arithmetic, geometry, pre-algebra, & algebra. Examine Napier's Bones, slide rules, abacus & counting boards. Do some curve-shifting, inverse taking, trig, hypothesis testing, a little Calc I, and no Calc II, III, or Linear algebra.

  • Curriculum Redesign & Teacher Preparation
          - content presentation & note taking
  • Developmental Mathematics
          - arithmetic (fractions, decimals, whole numbers, vocabulary),
          geometry, prealgebra (integer addition & subtraction),
          algebra (polynomial computation, solving equations, inequalities, binomial expansion),
  • General Interest
          - games & manipulatives (digital & concrete), writing computational problems
  • Mathematics for General Education & History of Mathematics
          - Napier's Bones, slide rules, abacus & counting boards
  • STEM, Instructional Strategies & Technology
          - Precalc - Basic & Related Curve-Shifted functions & Inverses, Basic Trig,
                Unit circle, Identities
          - Statistics - hypothesis testing
          - Calc I - very little
          - Calc II, III, Linear algebra - nothing at all

Games and Manipulatives

  • Poly Who Has
    Pass or Touch     Use polyfx.htm to play.
    Sheet A of cards     Sheet B of cards     Sheet C of cards
  • Game for 2, 3, 4 Players
    Rules To Play Now     Digital Manipulative 42.xls  
    Instructions 42game.htm     42board.htm     42cards.htm
  • "Math Exercises" -- Kinesthetically Explore Functions: For Later       For Now
  • Con-Dots Home     Casa Omar Questions     Casa Omar Answers

  • Curve Shift, Find Inverse EF Manipulatives
  • (x-y)^3 boxes
  • unit circle puzzle

One Last Use of Technology

  • Review today's media files with Windows File Explorer.
  • Review Spring 2018 Precalc with Windows File Explorer.

[MC,i. Home, site home page] [Good Stuff -- free & valuable resources] [tutorials & resource material arranged by topic [this semester's schedule w/links] [master list of all MSH! dictionary words] math tokens math ed stuff [www home]

© 5/2018, A2