- 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, x4 tokens so they are different from the cubic, x3 tokens
and so they do not suggest being solid.
- x4, 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
- (x-y)³ = x³ - 3x²y + 3xy² - y³
- (y-x)³ = y³ - 3y²x + 3yx² -x³
-
- (x+1)³ = x³ + 3x² + 3x + 1
- (x-1)³ = x³ - 3x² + 3x -1
- (y+1)³ = y³ +3y² + 3y +1
- (y-1)³ = y³ - 3y² + 3y -1
-
- Use these sheets to produce (x+y)³ and (x-y)³ and (y-x)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, (x-1)³, (y-1)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.
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