1 
Colorcoded
circular pieces 
Name
pieces 


Compare
sizes 


Observe
that as size decrease, number to make whole increases 


Observe
equivalence 
2 
Colorcoded
rectangular pieces 
Name
pieces 


Compare
sizes 


Observe
that as size decrease, number to make whole increases 


Observe
equivalence 
3 
Colorcoded
circular and rectangular pieces 
Observe
similarities and differences between circular and rectangular
pieces 


Translate
between circular and rectangular pieces 
4 
Colorcoded
circular and rectangular pieces 
Attach
unit fraction names (onefourth, onefifth) to parts of whole 


Work
with equivalent sets of fractions 
5 
Paper
folding with circles and rectangles 
Attach
fraction names to shaded parts of folded regions 


Learn
names for unit and proper fractions 


Associate
names with colorcoded parts and with shaded parts of folded
regions 


Note
similarities and differences 
6 
Cuisenaire
rods 
Attach
fraction names to display of rods 


Note
fractions as sums of unit fractions 


Compare
display with colored pieces and paper folding 


Investigate
realworld problems 
7 
All
materials from Lessons 1 to 6 
Review,
using all four embodiments 


Identify
proper fractions orally, in written form, symbolically, and
pictorially 


Translate
from one mode to another 
8 
Chips 
Review
division as partitioning (18 ÷3 = 6 represents 18 chips,
3 groups, 6 in each group) 


Represent
fractions by covering equalsized groups of chips 


Associate
fractions with amount covered (3 of 4 groups covered is 3/4) 
9 
All
materials from Lessons 1 to 7 
Translate
to any mode, using any embodiment, a fraction represented
with physical objects, orally, or with a written symbol 
10 
Colorcoded
pieces

Represent
improper fractions using pieces 

Paper
folding
Chips 
Translate
between improper and mixed number notation orally and in writing



Translate
representation to paper folding 


Translate
representation to chips 
11 
Number
line 
Associate
whole number, fraction, and mixed numbers with points on the
number line 


Convert
improper fraction to whole or mixed numbers 


Determine
equivalence 


Add
fractions with same denominators 
12 
All
materials from Lessons 1 to 11 
Using
pieces, chips, rods, or pictures of parts of a unit, construct
the unit 
13 
Chips
Paper folding 
Represent
a model for multiplication of fractions 


Generalize
to algorithm with product of numerators and product of denominators 
