## Real Estate Tycoon

- Lesson

In this year-long project, students design, "build," and "sell" a
house; after which they simulate investment of the profits in the stock
market. Along the way, students make scale drawings, compute with
fractions and decimals in various contexts, and even solve simple
equations. This lesson plan was adapted from an article by David B.
Smith, which appeared in the September 2000 edition of *Mathematics Teaching in the Middle School*.

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.

### Drafting

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 the others.

Below is an example of an "award-winning" design.

### Real Estate

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 criteria:

- access to water
- zoning regulations
- taxes
- water and sewer requirements
- acreage
- 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 cost.

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.

*Investment*

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.

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 stock.

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.

### Reference

Smith, David B. "A Thematic Mathematics Project for Grade 7." Mathematics Teaching in the Middle School, Volume 5, Number 1 (September 2000): pp. 12-18.

- Drafting tools (T-square, drawing board, right triangles, compass)
- Graph paper
- Tag board
- Stock Market Activity Sheet
- Newspapers or other sources for information about stock market prices and local real estate values

**Teacher Reflection**

- Did any students show difficulty mastering basic drawing and measuring skills? If so, what did you do to overcome those difficulties?
- Did the project hold the students' interest throughout its duration? To what do you attribute the success if the project did hold the students' interest? If you feel the students were bored with the project, what could you have done differently?
- Did you involve members of the community, such as real estate agents, contractors, etc.? How did your students interact with these professionals? Is there anything you could have done to improve the interactions?

### Learning Objectives

Students will:

- 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.

### NCTM Standards and Expectations

- Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.

- Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

- Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations.

### Common Core State Standards – Mathematics

Grade 6, Expression/Equation

- CCSS.Math.Content.6.EE.A.3

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

- CCSS.Math.Content.6.EE.A.4

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

- CCSS.Math.Content.7.NS.A.3

Solve real-world and mathematical problems involving the four operations with rational numbers.

Grade 7, Expression/Equation

- CCSS.Math.Content.7.EE.A.2

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

- CCSS.Math.Content.7.EE.B.3

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

- CCSS.Math.Content.7.G.A.1

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

- CCSS.Math.Content.6.NS.A.1

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

- CCSS.Math.Practice.MP6

Attend to precision.