|
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. 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. |
|
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).
|
|
