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).
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