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The task
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 half-inch graph paper.
Record the calculations of the area and cost on the cut-out 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.

Circumstances of performance
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 pre-project 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 standard-setting 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.

What the work shows
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 half-inch 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 half-inch…)….
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”).