a
Number and Operation Concepts: The student
consistently and accurately adds, subtracts, multiplies, and divides
rational numbers using appropriate methods…, i.e., rationals
written as decimals…or mixed fractions….
The student
realized that some computations would be redundant. That recognition
spared her some calculation. The student also recognized that the
opposite walls have equal sizes, thus avoiding some redundant computations.
(This paragraph is an example of how work is often more wordy than
it needs to be. A table would be a more effective means of communicating
the areas of wall and of woodwork.)
When rewriting
areas as decimals instead of mixed fractions, some of the numbers
(e.g., “241.86 square feet”) are more precise than is
necessary for this kind of project.
c
Number and Operation Concepts: The student
consistently and accurately applies and converts the different kinds
and forms of rational numbers.
e
Number and Operation Concepts: The student
interprets percent as part of 100 and as a means of comparing quantities
of…changing sizes.
f
Number and Operation Concepts: The student…reasons
proportionally to solve problems involving equivalent fractions
[or] equal ratios….
The computations
are not shown. However, it is apparent that, even though each unit
of the graph paper represents one halffoot, the student made conversions
(e.g., 4 in. =
foot =
of one halffoot) so that she could mark off the inches (fractions
of feet) with accuracy and according to scale.
d
Geometry and Measurement Concepts: The student
determines and understands length, area…; uses units [and]
square units…of measure correctly; computes areas of rectangles….
h
Geometry and Measurement Concepts: The student
chooses appropriate units of measure and converts with ease between
like units, e.g., inches and miles, within a customary or metric
system.
The conversions
between square inches, square feet, and square yards are correct
and significant.
j
Geometry and Number Concepts: The student
reasons proportionally with measurements…to make…scale
drawings.
a
Problem Solving and Mathematical Reasoning:
Formulation. The student:
• formulates and solves…meaningful
problems….
The student
planned to redecorate her room and created a realistic scenario
with a constraint of $700 and the added “twist” of being
able to keep 50% of the remainder, which impacts the decisions to
be made in ways that the $700 upper limit could not. Formulating
the problem of redecoration, imposing constraints not required by
the task, and determining the information needed in order to proceed
provide the evidence of .
• figures out what additional information
is needed.
b
Problem Solving and Mathematical Reasoning:
Implementation. The student….
• invokes problem solving strategies, such as…organizing
information….
• solves for unknown or undecided quantities
using…sound reasoning….
The decision
to purchase one gallon and one quart of paint is conceived and explained
well.
a
Mathematical Skills and Tools: The student
computes accurately with arithmetic operations on rational numbers.
d
Mathematical Skills and Tools: The student
measures length [and] area,…accurately.
h
Mathematical Skills and Tools: The student
uses…pencil and paper, measuring devices,…[and] calculators,…to
achieve solutions.

a
Mathematical Communication: The student uses
mathematical language and representations with appropriate accuracy,
including…diagrams.
b
Mathematical Communication: The student organizes
work, explains facets of a solution orally and in writing,…[and]
labels drawings…to make meaning clear to the audience.
This diagram
is very accurately drawn to scale and labeled well for clarity.
(This is one of several scale drawings the student prepared.)
This summary
of costs in an organized array is clearer than additional prose
would have been. Such a display would also have been appropriate
at other points in this report. The summary explains the total cost
of the renovation, and the subsequent diagrams show the configuration
of the redecorated room.
d
Putting Mathematics to Work: The student
conducts a management and planning project, in which the student:
• determines the needs of the event to be managed or planned,
e.g., cost, supply, scheduling.
• notes any constraints that will affect
the plan.
• determines a plan.
• uses concepts from any of Standards
1 to 4, depending on the nature of the project.
• considers the possibility of a more
efficient solution.
• prepares a presentation or report
that includes the question investigated, a detailed description
of how the project was carried out, and an explanation of the plan.
d
Writing: The student produces a narrative
procedure that:
• 
engages the reader by establishing
a context, creating a persona, and otherwise developing reader
interest; 
• 
provides a guide to action for a relatively
complicated procedure in order to anticipate a reader’s
needs; creates expectations through predictable structures,
e.g., headings; and provides smooth transitions between steps; 
• 
makes use of appropriate writing strategies
such as creating a visual hierarchy and using white space and
graphics as appropriate; 
• 
includes relevant information; 
• 
excludes extraneous information; 
• 
anticipates problems, mistakes, and
misunderstandings that might arise for the reader; 
• 
provides a sense of closure to the
writing. 
The work engages the reader by establishing a context: redecorating
a room on a budget.
The established
persona is maintained throughout the work.
The student anticipated the reader’s needs and used predictable
structures to fulfill those needs, such as headings (“Problem,”
“Solution”), a list of supplies needed, and a series of
scale drawings of the room to be redecorated.
The logical
transitions for the procedure give the writing a narrative quality.
However, the reference to design features are optional.
The proper use of several graphics helps to summarize the narrative.
The examples and explanations are clearly presented.
By writing clearly and concisely, the student ensured that the reader
would be able to follow even the somewhat complicated explanations.
The student
closed the work appropriately, summarizing the narrative in a few
brief sentences and filling in the last few pieces of information
the reader might require. Appropriate sales tax, although not explicitly
cited in the task, is correctly applied.
a
Conventions, Grammar, and Usage of the English
Language: The student demonstrates an understanding of the rules
of the English language in written and oral work, and selects the
structures and features of language appropriate to the purpose,
audience, and context of the work. The student demonstrates control
of:
• grammar;
• paragraph structure;
• punctuation;
• sentence construction;
• spelling;
• usage.
The student managed the conventions, grammar, and usage of English
so that they aid rather than interfere with reading. In this case,
management of conventions includes consistency in the use of numbers.
