 Basic Tile & Token Set:
 Constants, Linears, Squares, Cubes
 x³, x², x, 1, and their backs/opposites
 front
back
 PRINT THESE SHEETS BACK TO BACK.

 Extended Tile & Token Set:
 Constants through Quartics
 After printing and cutting, punch a hole through the
quartic, x^{4} tokens so they are different from the cubic, x^{3} tokens
and so they do not suggest being solid.
 x^{4}, x³, x², x, 1, and their backs/opposites
 front
back
 PRINT THESE SHEETS BACK TO BACK.

 Additional Variable Tile & Token Set:
 Constants through Cubic
 y³, y², xy, y, 1, 5, 10 and their backs/opposites
 front
back
 PRINT THESE SHEETS BACK TO BACK.

x³ and a 1 cube 
x³ and a 1 cube  
x², x, y², y, and 1 
x², x, y², y, and 1
 y³ and y³   
x²y 
x²y  
xy² 
xy²  

Multiplying, Dividing, Factoring
 
 (x+y)³ = x³ + 3x²y + 3xy² + y³
 (xy)³ = x³  3x²y + 3xy²  y³
 (yx)³ = y³  3y²x + 3yx² x³

 (x+1)³ = x³ + 3x² + 3x + 1
 (x1)³ = x³  3x² + 3x 1
 (y+1)³ = y³ +3y² + 3y +1
 (y1)³ = y³  3y² + 3y 1

 Use these sheets to produce (x+y)³ and (xy)³ and (yx)³
 Print 1 copy of each x³, x³, and y³ (which also contains y³)

x³, 1
x³ 1
y³, y³
 Print 3 copies of each xy² and xy², x²y and x²y

x²y
x²y
xy²
xy²

 Use these sheets to produce
(x+1)³, (x1)³, (y1)³, and (y+1)³
 In addition to the cubes listed above, print 3 copies of each
 x², x, y², y, and 1

x², x, y², y, and 1

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
 Eliminates the use of an overhead projector or opaque projector and the transporting of
overhead tiles for anyone using Excel®, computer, and projector.
 Permits taking and storing notes on a lesson involving Term Tiles & Tokens.
 Permits the creation of tests, quizzes, worksheets, answer sheets using Term
Tiles graphics.
 Permits students to create and store Term Tiles pictures and text for homework
or projects.
 With restrictions, permits web based, or on site, Term Tile & Token staff developement.
 With restrictions, permits creation of texts, pamphlets, and papers by publishers, professionals, and parents.
 After introductory concrete use, eliminates the need for concrete tiles in a totally digital classroom since each student
could work on her / his own spread sheet.
 Joins other
digital spread sheets and
spread sheet resource materials available at
mathnstuff.com.
 Permits the user the full range of Term Tiles & Tokens
(the visual / auditory / symbolic / kinesthetic) modes, permitting one to speak
in pictorial, verbal, symbolic, and manipulative ways, permitting one to work with technology as well as
text and tile to compute and communicate mathematically.
