These work samples were drawn from two different classrooms although the
task given to the students was the same:
In each situation below, four friends want to “share 25” as
equally as possible. Show or explain how to “share 25” in each
situation.
1. 
Four friends shared 25 balloons as equally as possible. 
2. 
Four friends shared $25 as equally as possible. 
3. 
Four friends shared 25 cookies as equally as possible. 
These samples of student work
were produced under the following conditions: 
 alone 
in a group 
 in class 
as homework 
with teacher feedback 
with peer feedback 
timed 
opportunity for revision 
This five minute task was originally part of a field test for the
New Standards Reference Examination: Mathematics (Elementary). However,
these students were not timed.
Sample 2 was completed in Chinese and translated by the teacher and
the Chinese calibration team. 
Sample 1
The task is from Writing in Math Class,
pp. 7678. ©1995 by Math Solutions Publications. Used by permission.

These work samples illustrate standardsetting
performances for the following parts of the standards:

a 
Arithmetic
and Number Concepts: Add,
subtract, multiply, and divide whole numbers. 
c 
Arithmetic
and Number Concepts: Estimate,
approximate, round off, use landmark numbers,
or use exact numbers in calculations. 
d 
Arithmetic
and Number Concepts: Describe and compare quantities by using
simple fractions. 
e 
Arithmetic
and Number Concepts: Describe
and compare quantities by using simple decimals. 
a 
Mathematical
Skills and Tools: Add, subtract,
multiply, and divide whole numbers correctly. 
d 
Mathematical
Skills and Tools: Compute time and money. 

a
Arithmetic and Number Concepts: The
student adds, subtracts, multiplies, and divides whole numbers,
with and without calculators; that is: 
•

divides, i.e., puts things into
groups, shares equally…. 

• 
analyzes problem situations and
contexts in order to figure out when to add, subtract, multiply,
or divide. 
Both
students demonstrated conceptual understanding by applying arithmetic
skills as needed in a variety of situations. 

Sample 2

c
Arithmetic and Number Concepts: The student
estimates, approximates, rounds off, uses landmark numbers, or uses
exact numbers, as appropriate, in calculations.

Translation of Sample 2

Both students used rounding off and exact numbers appropriately
in each situation.
d
Arithmetic and Number Concepts: The student
describes and compares quantities by using concrete and real world
models of simple fractions; that is:
• finds simple parts of wholes….

e
Arithmetic and Number Concepts: The student
describes and compares quantities by using simple decimals; that is:
• adds, subtracts, multiplies, and divides money amounts….
a
Mathematical Skills and Tools: The student
adds, subtracts, multiplies, and divides whole numbers correctly….
d
Mathematical Skills and Tools: The student computes…money (in
dollars and cents).

