Spreadsheets in the Math Class

Computer technology is changing the ways we use mathematics; consequently, the content of mathematics programs and the methods by which mathematics is taught are changing. Students must continue to study appropriate mathematics, content, and they also must be able to recognize when and how to use computers effectively when doing mathematics ... Mathematics teacher should be able to appropriately use a variety of computer tools such as programming languages and spreadsheets in the mathematics classroom. For example, teacher should be able to identify topics for which expressing an algorithm as a computer program will deepen student insight, and they should be able to develop or modify programs to fit the needs of classes or individuals. Keeping pace with advances in technology will enable mathematics teachers to use the most efficient and effective tools available ...

- The Use of Computers in the Learning and Teaching of Mathematics, NCTM, 1987

The use of technology in instruction should further alter both the teaching and the learning of mathematics. Computer software can be used effectively for class demonstrations and independently by students to explore additional example, perform independent investigations, generate and summarize data as part of a project, or complete assignments. Calculators and computers with appropriate software transform the mathematics classroom into a laboratory much like the environment in many science classes, where students use technology to investigate, conjecture, and verify their findings. In this setting, the teacher encourages experimentation and provides opportunities for students to summarize ideas and establish connections with previously studied topics.

- Curriculum and Evaluation Standards for School Mathematics, NCTM, 1989

• a rectangular array of boxes in rows and columns
  
• columns are named by letters (A, B, C, etc.)
  
• rows are named by numbers (1, 2, 3, etc.)
  
• individual boxes in the array are known as cells
  
• typical spreadsheets programs allow more than 100 columns and 1000 rows. (More powerful programs allow several times this amount.)

• labels: non-numerical or text information, not processed by the spreadsheet when it does computations
  
• numbers: used in spreadsheets for computations and graphs
  
• formulas: direct the computer to do an operation on a cell or group of cells and to put the answer in the cell where the formula is entered.
  
• dates and times: for record-keeping purposes

• The spreadsheet is readily adaptable for problems that are iterative, recursive, or tabular in conceptual format and enables teacher and students to tinker with values of variables, constants, and step size and to explore the tempting "what if?" type of questions in the problem-solving process.

• The spreadsheet can enhance the user's insight into the development and use of algorithms and modeling for the solution of mathematical problems.

• The spreadsheet frees students from being hampered by laborious manipulation of numbers and allows them to concentrate on the mathematical problem itself. This permits the in-depth exploration of meaningful mathematical application without concern for the possible complex calculations needed to reveal the essence of the mathematics involved.

• The spreadsheet allows the students to see a progression of calculations on the screen as they are generated and permits students to change one variable at a time to see what effect that change has on the overall pattern of those calculations.

Below are several ideas and sources for real world data which could be analyzed and/or graphed using spreadsheets. Encourage your students to look for additional sources of data to analyze; ask them to bring examples to class.

1. Math
   • Estimations - then make actual calculations and/or graph;
     
   • Make predictions based on initial data gathered;
     
   • Statistical surveys from any subject area;
     
   • Metric (or English) measurements of the body, objects of various sizes, perimeters, areas;
     
   • Equations, functions, relations; and
     
   • Time needed to accomplish various tasks.

2. Science
   • Sizes of the planets, density, distance from Earth, atmospheric composition;
     
   • Temperature, humidity, rainfall over time, overcast-amount of sun-visibility;
     
   • Growth of plant or animal under different experimental conditions;
     
   • Distance, velocity, acceleration;
     
   • Falling objects, gravity, wind resistance; and
     
   • Animal population, growth and decline rates.

3. Health
   • Vitamins, minerals, or other composition comparisons;
     
   • Calories versus weight for various foods;
     
   • Fast food nutritional, saturated versus unsaturated fats; and
     
   • Heart rate over time, varying according to activity.

4. Social Studies
   • Size comparison for cities, states, or countries or their growth rates;
     
   • Size composition (farm land, mountains, lakes, etc.);
     
   • Population composition (cities, rural areas, small towns, etc.) or (percent literate versus decade) or ethnic backgrounds;
     
   • Economic growth (crops or mining or shipping or roads, (industrial, farming, services);
     
   • Buying power or cost of living comparisons versus different areas
     
   • Projected growth rates.

5. Language Arts
   • Number frequency in ciphering codes; and
     
   • Number of books read by different classes/students.

6. Physical Education
   • Scores versus time of specific track and field events; and
     
   • Number of push-ups, sit-ups, etc. one can do on a sequence of days.

1. Traditional graphing activities with pencil and paper, using a coordinate system with positive quadrant only.

2. Spreadsheet Battleship to practice naming cells on spreadsheets.

3. Enter data into a spreadsheet template created by the teacher and loaded onto each student's computer. The template would have row and column headings.

   Example: Select a group of rectangular objects in the classroom for which students can measure length and width. Set up a template listing the items to be measured as the row headings and 'length', width', and 'Area' as the column headings. Have the students measure the objects and record their data in the appropriate cells.

   Option A: You could use this as a discovery lesson for Area and have the formula for area already entered into the spreadsheet. As the students fill in their measurements, the area of the object will appear in the appropriate cell in the spreadsheet. Students could then examine the numbers to discover the relationship.

   Option B: Students could calculate the area for each object and enter the value into the appropriate cell.

   Option C: Students could be taught how to enter a formula, and enter the correct formula to calculate the area.

4. Enter data, labels, and formulas into a spreadsheet. Use the spreadsheets to draw bar charts, line charts, circle charts.

   Examples:
   

   1. Personal Data: Have students design a questionnaire with about 15 or so questions about their classmates which would have numeric answers. Discuss which type questions would be appropriate. Review and edit the questionnaire, prepare it for distribution, and then have students administer the questionnaire. Have students prepare a spreadsheet with appropriate headings and enter the data. Finally, when the data has been collected, entered, and analyzed, discuss the results with the group and ask questions which can be answered from the data, such as "What is the average number of hours students watch TV in a week?" Be sure to include questions from all levels, i.e. from basic questions requiring nothing more than reading a correct answer from the spreadsheet to higher level questions requiring thought, interpretation, and reasoning.

   2. Class Party Shopping Comparisons: Develop a shopping list for a class party consisting of about 20 items. Include the brand name and size of items. Have students go to local stores and collect prices of the items. Set up a spreadsheet to analyze the results, and decide which store has the best prices. You could follow up by actually having the party!

   3. Cheapest way to go on a trip: Students would collect information from a variety of sources on a variety of things: airlines, bus routes, rental cars, hotels, camp grounds, restaurants, etc. Start by discussing the options for travel, accommodation, meals, etc.

      Option A: Have students agree on the parameters for the trip and then determine the cost for the trip.

      Option B: Students could work as groups and compete to see which group could plan the most economical trip.

5. Mathematical Patterns:

   Spreadsheets are ideal to use as an exploration tool to investigate various patterns because of their ability to do quick calculations and to copy formulas to new locations using relative addresses rather than absolute addresses.

   Example: Give students a spreadsheet containing instructions and a number pattern. The students task is to continue the pattern for several more cells and then to reproduce the pattern by finding, entering, and replicating the appropriate formula. At a more advanced lesson, the students may be given the number system as a list on a chalkboard and students could be required to set up an appropriate spreadsheet from scratch with the correct formula to continue the pattern.

6. Discovering Properties:

   Example: Give students a spreadsheet with three columns of numbers (Columns A, B, C) and column headings: A*(B+C), A*B+C, A*C+B, A*B+A*C in columns D, E, F, G. Have students enter formulas which will calculate each of these, and then see that patterns they can discover.

7. Estimation:

   Example: Set up a spreadsheet with a column for the dividend, divisor, estimate of the quotient, and then a column for the product of the divisor and estimated quotient. Students can enter estimates for the quotient and then see how close their estimate was by examining the values in the product column.