MATYCNJ Fall Meeting, Brookdale CC, 10/1/05 

© 2005, Agnes Azzolino

9:15 - 10:15 AM, SLC 105
Making the Writing of Expressions and Equations More Concrete by Using Term Tiles and Code.
See a slightly different way of completing these:
Write the expression/equation.
1. What is left when you decrease a number by 2?
2. What is left when you decrease 2 by a number?
3. A bank contains $2.45 in nickels, dimes and quarters ...
4. Find the maximum volume of a rectangular box with a square base at least 1 cm by 1 cm if its surface area is 600 cm2.


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Please answer the following questions.
1.     You are new to a country, do not know the language, must remain in the country for many months, and must remain on your own.
      How do you manage? learn the language?

Answers questions so as to achieve the most partial credit.
2.Compute the change from a fifty dollar bill for the purchase of 3 notebooks at $2.90 each and 2 CDs at $14.50 each.
3.Three consecutive integers are involved. The sum of the first, triple the middle, and four times the largest is 131. Find the integers.
4. Find the maximum volume of a rectangular box with a square base at least 1 cm by 1 cm if its surface area is 600 cm2.
5. Compute the area of the figure.

The Math Class Languages
Please discuss your answers with your partners.
Discuss This With Your Partner, DTWYP,
  • Teaches students to confer with others in order to gain knowledge.
  • Permits student who are stronger to assist the weaker and feel better about their own expertise.
  • Permits the weaker to be in command of their own education by seeking help.
  • Permits students to communicate mathematics in the mother tongue, in other tongue(s), in formal spoken mathematics and in informal spoken mathematics

Term Tiles & Hundreds Board

100s Boards
Signed Numbers on the Hundreds Board
traditional 100s board
0 to 99 board (0 on left)
negative-positve board (0 on right)
negative-positve board (0 on left)
Term Tiles
#20, #24
term tiles - x2, x, 1: front (required) ,
back (optional)

Examples of Abstract Communication:

Code, Semiequation and Semiexpression
      answers to #2, #3, #5, above,
Using Code to Write Expressions & Equations
      code guidelines
Notes from an Algebra I Course: 80/text/day0.htm
Lessons, Algebra QB, Precalc QB, Calc QB Classes QB QB, graded assignments QB, graded assignments
Quick graphs

Closing Remarks
  • Discuss This With Your Partner is the most valuable strategy!
  • Introduce in the Most Concrete
    in the Mother Tongue when possible
    at the earliest opportunity
    repeat the message in summary or with a picture
    then, later, formally introduce the topic

  • Debrief in the Most Abstract
    Visualize, Verbalize, thenWrite
    in the Mother Tongue after Formal Mathematics

  • Regularly Require Translation from One Language to Another
    Use tiles and words and symbols alone and together

  • Good Stories Are Worth Retelling.
  • Retell your mathematical stories in as many languages as possible.

Classes [Words] math ed stuff spread sheet notes [Good Stuff Page]

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© 2005, Agnes Azzolino