## Shops at the Mall

Students participate in an activity in which they develop number sense in and around the shopping mall. They solve problems involving percent and scale drawings.

Begin by generating a class list of stores typically found in a shopping center or mall. Challenge students to group stores into general categories, such as women's clothing, food service, and so on. Ask students which types of stores seem to be most prevalent and least prevalent at a mall.

Discuss the word *lease*. What does it mean? (For rent or
hire.) Why are leases important to shopping center or mall operators?
The International Council of Shopping Centers recommends that malls
allocate a certain percent of the total square footage of lease-able
retail space using the following guidelines:

- women's clothing: 25%
- men's clothing: 10%
- food: 15%
- service (salons, etc.): 5%
- shoes: 10%
- jewelry: 3%
- family items: 7%
- gifts: 17%

Note that the International Council only recommends space allotments and does not recommend specific allocations for all 100 percent of the space within a mall. Ask students why they think this is.

To review the concept of percents, it may be helpful to distribute a 10 × 10 grid to each student.

Students can then shade each of the above types of stores on the grid to show how much space should be allotted for each type of store.

Encourage students to conduct some research at the mall or shopping center closest to where they live. For a homework assignment, ask them to list all the stores in the mall and to place each into one of the International Council's categories listed above. Alternatively, students can find this information on individual shopping mall websites. Draw the students' attention to the fact that the recommendations were made in 1985. Ask students, "How have malls changed since then?" What problems might those changes pose for students in their task?

When all lists have been compiled, ask students to share their data and justify the placement of specific stores within each category. Where did they place stores such as clothing stores? A bank? A pharmacy? A video store? Ask them to find the total number of stores at the mall, the number of stores in each category, and the percent of each type of store listed. How does the local mall's space allocation compare with the International Council's recommendations?

Tell students that they can lease space within a new mall. Distribute the Shops at the Mall Activity Sheet to each student.

Shops at the Mall Activity Sheet

After students have completed the first two items, encourage them to share their results and strategies. Some may use proportional reasoning, calculate with fractions, or use calculators.

Organize students into groups of two or three for the final activity.

Distribute centimeter graph paper to each group to use when creating the scale drawing of the mall. Before beginning the activity, discuss the criteria for mall design in item 3 on the activity sheet. After all drawings are complete, encourage each group to share its plan along with a justification for each element. The plans can be compared with, and contrasted against, the criteria provided as well as the International Council's recommendations.

- 10 × 10 Grid or Centimeter Graph Paper
- Shops at the Mall Activity Sheet
- Calculators (optional)

**Extensions**

- Ask the class how to determine which stores are the most popular or which stores sell the most merchandise. Allow them to develop a plan for collecting data that could help answer their question. Ask the class to consider surveying store managers or mall shoppers or observing mall traffic.
- Students may want to investigate where they spend most of their time or money at the mall.
Encourage students to identify possible ways to collect information that would answer their questions, design a study that controls for the variable identified, and collect and analyze the data collected. They might want to include students in the local middle school so that they can compare the spending habits of upper elementary student with these of middle school students.

- The cost of leasing space might be of interest to students. How is the cost determined? How do factors such as rent and placement in the mall affect the store manager's decision to locate in a mall? Invite the manager of your local shopping mall to help student explore these issues.
- A related but different question involves profit.
Do stores that sell the most merchandise make the most money? Do they have the greatest profit?

Explain the differences between a store's costs, sales, and profit. Are these items related to size? Do the biggest stores necessarily enjoy the greatest profit? Again, the manager of a local shopping mall may be helpful.

### Parking at the Mall

### Learning Objectives

Students will:

- Estimate using percent.
- Compute using percent.
- Create a scale drawing.
- Solve problems involving percent and scale drawings.

### NCTM Standards and Expectations

- Work flexibly with fractions, decimals, and percents to solve problems.

- Understand and use ratios and proportions to represent quantitative relationship.

- Solve problems involving scale factors, using ratio and proportion.

### Common Core State Standards – Mathematics

Grade 7, Ratio & Proportion

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

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

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, 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.