The teacher asked students to complete
a large scale mathematics project chosen from among five kinds.
This student chose to do a “Pure Mathematics Investigation.”
The teacher gave the student the written instructions illustrated
here.
This sample of student work
was produced under the following conditions: 
 alone 
in a group 
in class 
 as homework 
 with teacher feedback 
 with peer feedback 
timed 
 opportunity for revision 


In this classroom students were using the New Standards
Elementary Mathematics Portfolio. The teacher intended students to be able
to use their chosen projects to fulfill the requirements for the project
exhibit in the portfolio.

a
Problem Solving and Reasoning: Formulation.
Given the basic statement of a problem situation, the student:
• makes the important decisions about the approach, materials,
and strategies to use, i.e., does not merely fill in a given chart,
use a prespecified manipulative, or go through a predetermined
set of steps.
The student
made all decisions regarding how to proceed with this entirely unformulated
project.
g
Mathematical Skills and Tools: The student
reads, creates, and represents data on charts, tables, diagrams….



b
Mathematical Communication: The student shows
mathematical ideas in a variety of ways, including words, numbers,
symbols,…charts, tables, diagrams….


c
Mathematical Communication: The student
explains solutions to problems clearly and logically, and supports
solutions with evidence, in both oral and written work.
The student
used a narrative description and tables to illustrate the nature
of the “problem” (or, in this case, “trick”).
d
Mathematical Communication: The student considers
purpose and audience when communicating about mathematics.
The student
clearly explained the nature of the project as well as how it would
be conveyed to the classroom audience.
e
Putting Mathematics to Work: The student
conducts a pure mathematics investigation, in which the student:
• decides on the area of mathematics to investigate, e.g.,
numbers, shapes, patterns.
• describes a question or concept
to investigate.
• decides on representations
that will be used, e.g., numbers, symbols, diagrams, shapes, or
physical models.
• carries out the investigation.
• writes a report that includes
any generalizations drawn from the investigation, and acknowledges
assistance received from parents, peers, and teachers.
The three errors in counting the letters (32, 13, and 30) and the
spelling mistake (“ect” instead of “etc”) do
not detract from the project.

