The teacher gave students the following instructions, and clarified
them through an extended discussion:
Plan and design your own “dream house” within certain
cost constraints. Here are the budget, cost, and building rules
you will have to work with.
• 
You will have $200,000 to spend altogether. 
• 
The land for the house costs $100,000. 
• 
Construction of “regular” rooms (traditional
rooms with no special requirements) costs $75 per square foot. 
• 
Construction of “special” rooms (requiring
special wiring, plumbing, or unusual materials) costs $150 per
square foot. 
• 
All houses must include a kitchen, bathroom, bedroom,
and living room. 
• 
Rooms and hallways must have reasonable areas. 
• 
The overall design must be convenient and practical
(e.g., provide easy access to rooms, allow for privacy, include
doors and hallways in practical locations, etc.). 
• 
The number of sides to your floor plan should
be limited, to avoid a sprawling, awkward design. 
To get started, you will: 
• 
Complete a rough draft of your floor plan by cutting
out the rooms from halfinch graph paper. 
• 
Record the calculations of the area and cost on
the cutout of the room. 
• 
Track your budget on a running budget sheet (“Budget
Update”). 
• 
Meet in a response group to see if your rough
draft is reasonable. 
To finish, you will: 
• 
Make a final draft of your floor plan without graph paper,
using a ruler and protractor, and following the scale exactly. 
• 
Draw a front and side view of your dream house based on your
floor plan. 



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 
Students completed this project over the course of four weeks. They worked
individually except when initially measuring the classroom as part of
a preproject activity (“Scale Model of Room 14”). They also
met once in small peer response groups, and once with an editing partner.
The teacher reviewed students’ progress on this project daily, and
created the “House Project Response Group Meeting Notes” and
the “Editing Checklist for House Description” in order to help
students complete the project.
The students had worked with two digit multiplication and the concept
of area prior to beginning the project. They were allowed to use calculators
to check calculations and for multiplication with multipliers of three
or more digits.
This work sample illustrates a standardsetting
performance for the following parts of the standards:

a 
Arithmetic
and Number Concepts: Add, subtract, multiply, and divide whole
numbers. 
b 
Geometry and
Measurement Concepts: Visualize and represent two dimensional
views of simple rectangular three dimensional shapes. 
g 
Geometry and
Measurement Concepts: Use basic ways of estimating and measuring
the size of figures and objects in the real world. 
k 
Geometry and
Measurement Concepts: Use scales in maps and scale drawings. 
c 
Statistics
and Probability Concepts: Make statements and draw simple conclusions
based on data. 
a 
Mathematical
Skills and Tools: Add, subtract, multiply, and divide whole
numbers correctly. 
c 
Mathematical
Skills and Tools: Measure length, area, and perimeter accurately. 
h 
Mathematical
Skills and Tools: Use measuring devices. 
a 
Mathematical
Communication: Use appropriate mathematical terms, vocabulary,
and language. 
b 
Mathematical
Communication: Show mathematical ideas in a variety of ways. 
d 
Mathematical
Communication: Consider purpose and audience when communicating
about mathematics. 
c 
Putting Mathematics
to Work: Design a physical structure. 

a
Arithmetic and Number Concepts: The student
adds, subtracts, multiplies…whole numbers with and without
calculators; that is:
• adds, i.e., joins things together, increases.
The student
added costs of rooms to determine the amount remaining in the budget.
• subtracts, i.e., takes away, compares,
finds the difference.
The student
subtracted to determine the amount of the budget remaining.
• multiplies, i.e., uses repeated addition,
counts by multiples….
The student
multiplied the area of rooms by cost per square foot to determine
the total cost of each room.
b
Geometry and Measurement Concepts: The student
visualizes and represents two dimensional views of simple rectangular
three dimensional shapes….
The student
visualized and represented the two dimensional house floor plan
in side and front views, i.e., as if in three dimensions.


g
Geometry and Measurement Concepts: The student
uses basic ways of estimating and measuring the size of figures and
objects in the real world, including length, width, perimeter, and
area.
The student
measured the length and width of the classroom in order to determine
area.
k
Geometry and Measurement Concepts: The student
uses…scales…for rectangular scale drawings based on work
with concrete models and graph paper.
The student used halfinch square graph paper to create a scale
model of a room (
inch = 1 foot).



c
Statistics and Probability Concepts: The
student makes statements and draws simple conclusions based on data;
that is, reads data in line plots….
The student
interpreted line plot data in order to make decisions about reasonable
areas of rooms in the floor plan.
a
Mathematical Skills and Tools: The student
adds, subtracts, multiplies…whole numbers correctly.


There is evidence of accurate calculations in these parts of the
work and throughout.
c
Mathematical Skills and Tools: The student
measures length, area,…perimeter…accurately in…the
customary…system.


These
parts of the work provide evidence of accurate calculations that
are supported by the calculations shown in the rough and final drafts.
h
Mathematical Skills and Tools: The student…uses
measuring devices graded appropriately for given situations, such
as rulers (customary to the 1/8
inch…), graph paper (customary to the inch or halfinch…)….
The student used a ruler and graph paper to measure lengths of sides
of rooms.
a
Mathematical Communication: The student uses
appropriate mathematical terms, vocabulary, and language, based
on prior conceptual work.



The student
used appropriate mathematical vocabulary to describe the process
involved in completing the project, e.g., “area,” “unit,”
”reasonable.”
b
Mathematical Communication: The student
shows mathematical ideas in a variety of ways, including words,
numbers…graphs…tables….
d
Mathematical Communication: The student
considers purpose and audience when communicating about mathematics.
The
student communicated the purpose and explained



the process for completing the project clearly
enough for the project to be understood by an otherwise uninformed
peer.
c
Putting Mathematics to Work: The student
conducts a project to design a physical structure, in which the
student:
• decides on a structure to design, the size and budget constraints,
and the scale of design.
The student
made the important decisions in planning the dream house.
• makes a first draft of the design, and revises and improves
the design in response to input from peers and teachers.
The student made revisions to the rough draft floor plan and to
the rough draft description on the basis of feedback from peers
and the teacher.



• makes a final draft and report of
the design, drawn and written so that another person could make
the structure….
There are several spelling and grammatical errors in the rough
draft work. Only the final draft description and floor plan were
edited for spelling and grammar. A few errors remain in the final
draft work; however, the errors do not detract from its accuracy
or clarity (e.g., “mutiply” for “multiply”).









