This sample was completed in Spanish in a bilingual
classroom. The translation was provided by the teacher.
The teacher gave the students the following
Suppose you were given a string that is sixteen inches long. If
you cut or fold it in any two places, will it always make a triangle?
|This sample of student work
was produced under the following conditions:
||in a group
|- in class
|- with teacher feedback
||with peer feedback
||- opportunity for revision
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 pre-specified manipulative, or
go through a predetermined set of steps.
decided to use a trial-and-error approach, which later became more
systematic. The student also decided to use string, scissors, and
uses previously learned strategies,
skills, knowledge, and concepts to make decisions.
used knowledge about triangles and measurement to develop the approach.
uses strategies, such as using manipulatives
or drawing sketches, to model problems.
Problem Solving and Reasoning: Implementation.
The student makes the basic choices involved in planning and carrying
out a solution; that is, the student:
makes up and uses a variety
of strategies and approaches to solving problems and uses or learns
approaches that other people use, as appropriate.
used measurement strategies to solve the problem.
makes connections among concepts in
order to solve problems.
The student made connections between measurement and geometry concepts
to solve the problem.
solves problems in ways that make
sense and explains why these ways make sense, e.g., defends the
reasoning, explains the solution.
Problem Solving and Reasoning:
Conclusion. The student moves beyond a particular problem
by making connections, extensions, and/or generalizations;
for example, the student:
makes the solution into
a general rule that applies to other circumstances.
student went beyond the problem by finding a rule that would
work for making any triangle.
Mathematical Skills and Tools:
The student refers to geometric shapes and terms correctly with
concrete objects or drawings, including triangle,
The student shows mathematical ideas in a variety of ways,
including words, numbers,
Mathematical Communication: The student
explains solutions to problems clearly and logically, and
supports solutions with evidence, in both written and oral