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The task
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.

Circumstances of performance
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. 76-78. ©1995 by Math Solutions Publications. Used by permission.

These work samples illustrate standard-setting
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.
What the work shows
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).