The project can be divided into three units to correspond with
three marking periods (fall, winter, and spring). The first part,
Drafting, includes a basic introduction to mechanical drawing skills,
design format, and function. The curriculum objectives are to review
operations with fractions, practice measurement skills, introduce the
multiplication property of equality, and apply each of these skills and
concepts to designing a floor plan for a one-story summer cottage. The
second part, Real Estate, introduces terms and practices through an
elaborate simulation. Students are asked to select a cottage design
from the first part, purchase a building site, build a cottage using
current building costs, and try to sell this property for a profit. The
objectives for this unit are to review operations with decimals and
percents and apply those skills to determine brokers' fees and closing
costs. In the third part, Investment, student teams invest the profits
from their property sales in the stock market. This last part targets
the relationship between fractions and decimals and demonstrates the
value of memorizing conversions from basic fractional units, such as
fourths, thirds, and eighths, to the corresponding decimals.
To set the stage for success, the class should understand basic
measurement skills, multiplication with fractions, and the
multiplication property of equality. Using these skills, students
should able to measure distances accurately with a ruler and convert
inches to feet using a scale of ¼ inch = 1 foot. Students should then
be introduced to drafting tools, including the T-square, drawing board,
right triangles, and compass, and should have practice in drawing a
rectangle, an L-shape, a T-shape, and design symbols.
After completing these exercises, students are told they will be designing their
cottages according to the following guidelines:
- The maximum building size is 24 ft. × 36 ft.
- The scale for the drawing must be ¼ inch = 1 foot or 1/8 inch = 1 foot.
- The maximum number of rooms is five.
The need for these parameters is essential, as middle school
students often have no concept of appropriate room dimensions and,
consequently, exhibit little understanding of form and function.
The primary objective at this stage is to create a functional
living space. First, ask students to cut out graph-paper models of
appropriately sized rooms and to piece them together in functional
patterns. For example, a bedroom, sun room, kitchen, and family room can
be arranged to demonstrate a variety of walking patterns, light
exposures, and proximity. In addition, once the pattern is selected,
room dimensions can be altered slightly to lower building costs.
The figure below shows two functional patterns that may be created.
When the rough drafts are complete with room assignments and symbols
for doors and windows, students can begin their final drawings using
mechanical drawing tools. Students should choose one of two scales,
¼ inch = 1 foot or 1/8 inch = 1 foot, on the basis of the size of their
designs. Remind students to draw pale lines with a pencil first, in
case they make a mistake and need to erase.
Once corrections are complete, the designs should be given
numbers and placed on tables around the room for viewing. The names of
the designers should be covered. Each student is given a ballot and
asked to record the number of the drawing that best demonstrates the
qualities of functional living space, solar efficiency, and creativity.
Once the winning design is chosen, review what distinguishes it from
Below is an example of an "award-winning" design.
Photograph by David Smith; all rights reserved.
The goal at this stage is to purchase an appropriate building
site for the award-winning design. Ask students to define a region for
the search, using local newspaper or real estate information. Then, as
a class, list
the advantages and disadvantages of each property using the following
- access to water
- zoning regulations
- water and sewer requirements
- total cost
- soil composition
- resale value with proposed building
Once a location is selected, the next step is to determine building
costs per square foot and calculate closing costs. A contractor or real
estate agent may be helpful with this step. A real estate agent may
also help with the next step.
After the class has "built" its cottage on the selected site,
conduct a market comparison and fill out a listing agreement to sell
the home. Determining a sales price may be challenging because the
market comparisons present as many differences as similarities.
Students should be reminded to ask for a higher price than they think
they can get, but not so high as to discourage potential buyers from
even looking at the property.
Next, discuss the commission for the real estate agent, which
is usually six percent of the sales price. Students should calculate
the commission for a variety of sales prices to get a sense of this
During the next class meeting, the class agents can conduct a
mock sale with fictional buyers. Once the sale is agreed upon, students
can calculate the profits by subtracting the agent's commission and
original purchase price from the final sale price.
After a review of the conversions from fractions to decimals and
an overview of investment terms and principles, students should discuss
guidelines for investing their profits in the stock market. The class
can be divided into teams of two, and each team receives the profit
from the sale of the cottage to invest over an eight-week period. Their
initial assignment should be to survey peers, parents, and neighbors
about wise investment opportunities.
Each team is required to buy two blue-chip stocks and
two stocks from NASDAQ. Students keep track of their investments weekly
with the Stock Market Activity Sheet.
Stock Market Activity Sheet
At the end of four weeks, give teams the opportunity to sell
unsatisfactory stock and reinvest their money. Students will probably
begin to follow the market daily and make conjectures about why stock
values rose and fell. Students may memorize decimal conversions and use
calculators almost exclusively to determine the total value of their
At the end of eight weeks, students should calculate their
profits and losses and submit their activity sheets. The teams can be
graded on the following criteria:
- completion of worksheets
- efforts to show work clearly in well-organized steps
- accuracy of calculations
- cooperation and focus during work periods
The following are two examples of student work from this project.
- Work flexibly with fractions, decimals, and percents to solve problems.
- Solve problems involving scale factors.
- Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations.
- Recognize and apply mathematics in contexts outside mathematics.
Common Core State Standards – Mathematics
Grade 6, Expression/Equation
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Grade 6, Expression/Equation
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
Grade 7, The Number System
Solve real-world and mathematical problems involving the four operations with rational numbers.
Grade 7, Expression/Equation
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that ''increase by 5%'' is the same as ''multiply by 1.05.''
Grade 7, Expression/Equation
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Grade 7, Geometry
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Grade 6, The Number System
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Common Core State Standards – Practice
Attend to precision.