Shopping Mall Math

Students participate in an activity in which they develop number sense in and around the shopping mall. They develop their skills in determining percents and estimating area.

To assess prior knowledge, begin by asking students to describe their experiences at malls. Tell them that these investigations will involve them in experiences that are a bit different from walking in the mall visiting stores, and spending money. Rather, these activities focus on space--space for parking and space for leasing shops in the mall.

The shopping mall is about as American as baseball and apple pie. Did you know that the United States has more shopping centers than movie theaters? Enclosed malls number more than cities, four-year colleges, or television stations.

Inform students that although some exceptions can be found, the International Council of Shopping Centers recommends that parking spaces be nine feet wide and twelve feet deep.

However, parking spaces for the handicapped must be fifteen feet by twenty feet. Parking regulations require that three out of every one hundred, or 3 percent, of the spaces in any parking lot must be set aside for physically challenges visitors (Kowinski, 1985).

Area

Write the word area on the chalkboard. Ask students what it means. Why are area measures usually given in square units, such as square inches, square feet, and so on?

Divide the class into groups of fours, and give each group some butcher paper and four twelve-inch rulers.

• Challenge each group to use its rulers to make on the butcher paper a shape with an area of one square foot. Encourage the discussion and demonstration of all responses.
• How do students know that the design measure one square foot?
• Why is the measure called a "square foot"?

  After confirming that each shape has the correct area, ask students to cut out their designs.

• Challenge students to use all their cutouts to create a shape onto the floor of the classroom. What is the area of their shape? How do they know?
• What would it mean to say that the area of a driveway is five hundred square feet?
• What might the driveway look like?

Parking Spaces

Using string or chalk and a measuring tape, measure and mark a nine-feet-by-twelve-feet parking space. Ask the groups to describe in any way they would like the area where a car would be parked, such as by paces, by people lying down in it, and so on.

Ask each group to share its description with the class. Use another string or chalk mark to "stretch" the parking space to meet the fifteen-feet-by-twenty-feet specifications of the space for the handicapped.

Ask the groups to describe how much larger this space is than a regular space. For example, students might respond, "I can lie down in the additional space."

Pose questions such as the following to students:

• Are the spaces for the handicapped twice the size of a regular space? Half as big?
• How do you know?
• How could we find out?

Discuss why such spaces are larger and why they are located closest to mall entrances.

Areas of Parking Spaces

Next ask each group to estimate the area of the handicapped-parking space. Younger students might pace off their parking space to determine an estimated area, others may describe the area as the estimated number of people who could lie down in the space, and some might use the square feet they made in the Area activity. Older students may use the formula for finding the area of a rectangle to estimate the square feet. Compare and contrast the strategies used as well as estimates.

• After discussing the estimates, ask each group to find the actual area of the parking space for the handicapped. Again, discuss the strategies and answers.
• Compare each group's estimates with the actual measure.
• Ask students to explain any differences.
• Challenge the groups to estimate the area of a regular space on the basis of the size of the space for the handicapped. Remind the groups that a regular space is six feet narrower and eight feet shorter than a handicapped space.

Introduction to Percents

Encourage students to discuss when they have seen percents in their everyday lives. If it is not offered, ask how many of them have received a grade of 80 percent, eaten 50 percent of a candy bar, or paid 6 percent sales tax. Ask the students what they think these numbers mean. After the discussion if it has not already been mentioned, tell the children that "per cent" means "of 100." Ask why they think "cent" might mean "hundred." Ask them to think of other words with "cent" in them and to explain what they man (e.g., cents in a dollar, century, centipede). Monetary discussion will inevitably occur at this point. What percent of a dollar is three pennies? How do they know? What does 50 percent of a candy bar mean? (If you could divide the candy bar into one hundred pieces, you would have fifty of them.) Provide a blank one hundred grid and ask students to shade in one block. Ask them to tell what percent of the paper is shaded (1 percent). Encourage them to explain their thinking. How many blocks of 100 would need to be shaded to represent 3 percent? One hundred percent? Fifty percent? How do they know?

Next, ask the students to look at a grid with 100 individual squares, or a 10 × 10 grid. For younger children, place the children in groups of ten, and use all ten of their 10 grids rather than require them to visualize a 1000 grid. How many individual squares would be needed to show 1 percent? Or 3 percent? Or 100 percent and 50 percent of this larger gird? (10, 30, 100, 500, respectively.) Encourage students to share their strategies. Some students may merely determine that the grid is 10 times larger, so the answers would be 10 times bigger; others might use their prior knowledge that 100 percent of anything is all of it and 50 percent is half. To find 1000 and 500, find a 10-times-larger patterns in those two answers, and use the patterns to determine the number of individual squares in 1 percent and 3 percent. Groups using the ten 100 grids will most likely count each time and finally realize that 1 percent of each of the 10 grids is the same as 1 percent of the total. Allow adequate time for this exploration, and have students compare and contrast their strategies.