Malls and shopping areas are places where students can engage in a wide variety of mathematics. The following are activities that students can consider when they are at the mall. Since all of our malls are different, answers will vary from location to location. What makes up a mall? Malls have lots of different types of shops, so you can approach this question in a number of ways. 1. Obtain or create a list of all the different shops in the mall. (You may want to choose a medium-sized mall or shopping area. That gives you the range and sizes of shops. If it is a very large mall you may want to divide the mall up into regions and give groups of students a region.) 2. Organize the various shops and businesses into different categories that are appropriate for your mall. Some possible categories include: department stores, clothing stores, shoe stores, record stores, software stores, book stores, food shops, toy stores, sporting goods stores, etc. You may need to make up categories to describe your mall. Work to make categories broad enough so that they generally contain more than one store or business. Also, try to account for everything that is at the mall. (The people who manage your mall may be able to supply you with a list of the shops alphabetically or by location. This way your students can role play being the owners of the mall and making the decisions about the categories and where each shop fits.) 3. From the total number of shops and businesses in the mall, calculate the percentage of total businesses in each category. 4. Create a bar chart or circle graph that represents the number and percentage of businesses in each category. 5. Analyze your data and graphs, and write a statement that describes the number of shops and businesses in the mall. Can you use this information to make any conjectures about the people that use the mall? Another way to look at what makes up the mall is to consider the area that each of the different categories account for in the mall. 6. Many malls have maps that offer a scale drawing of the mall. Take some measurements and calculate what scale was used to make the drawing. 7. Using the list of shops and categories developed in Question 2 and your scale drawing, calculate the amount and percentage of mall floor space accounted for by each category. 8. What percentage of the mall floor space is not accounted for by the shops and businesses? What is this space used for? 9. Create a bar chart or circle graph that represents the amount and percentage of floor space for each category. 10. Analyze your data and graphs, and write a statement that describes how floor space is used in the mall. Can you use this information to make any conjectures about the mall? 11. What can you say about malls from your analysis of numbers of shops and floor space? Mathematics is everywhere! The following questions relate to things you might see in the world around you in a city or in a park. Keep your eyes open. Mathematics and Bricks Bricks are useful and durable building blocks. They also offer an opportunity to explore mathematics. 1. As you travel around, watch for different shapes of bricks. Most bricks are what shape? 2. Why do you think bricks are this shape? 3. If you keep your eyes open, you will probably be able to find bricks that are not rectangles. Side walks and patios are good places to look. What shapes are the bricks? Do they still tessellate? 4. See if you can find a place where rings of bricks are laid in a circular pattern. Good places to look are around statues and fountains. How does the number of bricks in each ring change as the rings get larger? Try to come up with a rule to describe the pattern. A Mathematical Look at Fountains and Pools 5. Once you find a fountain or pool, try to figure out how much water it contains. Using what you know about calculating volumes and measurement skills, estimate how many cubic feet of water are in the pool or fountain. 6. One cubic foot of water contains 7.48 gallons of water. That is a lot of water! Calculate how many gallons of water it takes to fill the fountain or pool. 7. How much does the water in the pool weigh? Water is a pretty heavy liquid, which explains why most people float in water instead of sink. It turns out that 1 gallon of water weighs approximately 8.57 pounds. How much does the water in the pool or fountain weigh? Shadows and Heights With the help of a couple of meter sticks or yardsticks, you can figure out the height of some tall objects like a tree or flagpole. There is a direct relationship between the height of an object and the length of its shadow. This relationship is the same for all things if the measurements are taken at the same time of day, which means the sun is in the same spot. 8. Find something tall so that you can measure its height. It should be something like a tree or flagpole that casts a shadow and that you can actually measure from its base. A fountain would be more difficult since you don't want to be at the base of the fountain. 9. On flat ground, place one measuring stick point straight up. Measure the length of the shadow. 10. Figure out what number you would need to multiply the length of the shadow by to generate the length of the measuring stick. Call this number the shadow factor. 11. Measure the length of the shadow of the tree or flagpole. Multiply the length of the shadow by the shadow factor you calculated in Question 10. This will give you a good estimate of the height of the tree or flagpole. 12. Note that the shadow factor changes as the sun moves. When is the shadow factor very small? 13. When is the shadow factor very large? 14. Can the shadow factor ever equal 1? If so, when?
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