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 cm^{2}.


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© 2005, Agnes Azzolino
Permission is hereby granted to reprint & use this page
and linked pages for use in creating note sheets, tests, and worksheets for notforprofit purposes.
Permission IS NOT GRANTED WITHOUT REQUEST for use in
staffdevelopment, webuse, or items created for sale.

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 cm^{2}.

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)
 negativepositve board (0 on right)
 negativepositve board (0 on left)

 Term Tiles

#20,
#24
 term tiles  x^{2}, 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
 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
 DTWYP!
 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.


 www.mathnstuff.com/papers/oct105.htm
 © 2005, Agnes Azzolino

