The Stepping Stones

40 modeling projects have been written and tested by high school teachers under the direction of university mathematics and education professors. You can download them from here, or you may order them by regular mail on 3.5" disks as Microsoft Word files. These projects are best suited for students who are new to mathematical modeling. You should customize them to fit your needs.



Project Description/Goals of Project HTML link Downloadable Word file
Balanced Diet The mathematics that is covered in this project involves basic addition, reasoning skills to identify combinations of high/low values, possible ratios, gathering data from a table of values, and creating double bar graphs. The students will work on this project with at least one other person; therefore their group skills can be exercised, and each person will be able to practice their communication skills both in the oral presentation and the required write-up. The students should also gain a better understanding of nutrition. This project will reinforce the five food groups, and students will be able to see a connection between mathematics and health. View it Get it
Brahma Tower Develop skills in problem solving, pattern recognition, and formula design. View it Get it
Bungee Barbie & Kamikaze Ken Students will work in teams, gather and graph data, fit a line to data or determine equations using data, make predictions from the model and gain an appreciation for simulations. View it Get it
Buying Time After gathering information on preferences, examine the different methods for determining a winner - Plurality, Borda Count, Run-Off, Sequential Run-Off, and Condorcet. To enable students to become familiar with oral and written presentations in Discrete Math. View it Get it
Bytes In a Box The student will be able to stack boxes with minimal wasted space using concepts of area and volume. The student will write a work order with drawing for storing the largest number of computer systems per storage unit. View it Get it
Cafeteria Seating Arrangement Problem To give students practice on area, problem-solving, and mathematical modeling write-ups and presentations. View it Get it
Doin' The Can-can
  • To determine the minimum surface area of a can with a given volume
  • To find an economical way to package 12 of these cans
 View it Get it
Carefully Constructed Cones Students will make a judgement as to what shape of cone will hold the maximum number of gumballs. View it Get it
The College Fund Savings Problem This project should show the student the power of compound interest. It will allow the student to set up a table to model the answer and suggest patterns for a geometric sequence and series. View it Get it
Cover Up To develop formulas, to apply reasoning/logic skills, and to use discriminating skills. View it Get it
Decimals To Fractions: How Many Times At Bat? Exploration and discovery of algorithms View it Get it
Family Budget Developing group work skills, model revision skills, decision making based on budget, facility with percentages, and arithmetic skills View it Get it
 geometrical Gardening To examine perimeter and volume in a usable situation and give students an opportunity to see connections between concepts and "Real-World" situations. View it Get it
Gerry-who!?! In groups, students will apportion the imaginary state of Computia into congressional districts. View it Get it
Flu For All Enhance student understanding of probability and sample taking. Students will also sharpen problem solving skills. This could be used to introduce probability or after it has been taught. View it Get it
Hexagonal Patterns Develop an appreciation for geometric patterns in nature, combine random events with geometric topics, recognize patterns. View it Get it
Homeowners Insurance To enable students to see how ability with compound interest can assist them in making important financial decisions. View it Get it
Life Insurance And Investment Counseling Life inurance options View it Get it
A Line Is a Line, Or Is It? This project offers students the opportunity to explore the use of simulation to model a probability situation. View it Get it
Maximize Parking Develop measurement skills, interpret scale drawings, apply area and perimeter calculations, develop problem-solving skills and the ability to interact in a group. View it Get it
Maximum Viewing Angle A major goal of this project is for students to gain greater insight into the theory of placement with desired advantages. This is an opportunity for students to make connections between the concepts and constructs of calculus and the real world application of them. Background: Students should be well versed in trigonometry, inverse trig. functions, trig. formulas, derivative forms, and extrema theory. View it Get it
Olympic Track Times To enhance the students' understanding of linear graphs. To estimate a line of best fit. To use linear graphs as a method of predicting future or past events. To decide if a linear model is the best/only model available. View it Get it
Counting Pennies To give students practice on measuring skills, graphing, using proportions, organizing data, and modeling problem solving skills. View it Get it
Pass The Pigs Develop a winning strategy for Pass the Pigs. View it Get it
Student Portrait Apply the concepts of Mean, Median, and Mode in real life situations. View it Get it
Quality Control Chart "qcees" Enhance student's understanding of statistical sampling, mean and range; demonstrate the practical applications of statistics in quality control; reinforce calculator and graphing capabilities; and develop skills in generating and interpreting quality control charts. View it Get it
Rate The Racers Students will form a better understanding of the equation distance=rate*time while experimenting, solving for different variables in the equation, and making predictions from data collected about a specific car. View it Get it
Recycling Estimating the volume of recycling at your school View it Get it
Repaving The School Parking Lot This project will reinforce the use of area and volume to help estimate the amount of asphalt present in the parking lot. The use of formula manipulations will be emphasized in the calculation of mass from the density and volume. The project will also encourage teamwork in problem-solving and presenting/explaining solutions to other students. View it Get it
Projecting School Enrollment The student will use historic data to estimate the future needs of a school district. The estimates will be reported in both written and oral presentations. View it Get it
Shortest Distance Problem To introduce the students to mathematical modeling problems, write-ups, and presentations through a simple distance problem. View it Get it
Telephone Cables To apply the relationships between circles and triangles, and the right triangle relationships (especially the Pythagorean Theorem) to "real-world" situations. View it Get it
Television Ratings To examine the reliability of survey techniques using small samples to predict population trends. To enable students to become familiar with oral and written presentations in statistics. View it Get it
Geometry Racing To apply geometric ideas of circumference, radius, and length to design a sixlane, 1000 meter running track. View it Get it
Talkin' Trash Students should learn to fit a linear equation to data, use the equation to predict future outcomes and compare these to Monroe County's actual predictions. View it Get it
Christmas Tree Farm To apply triangle relations. To apply area formulas. To make logical plans. To use Algebraic skills in making future plans. View it Get it
Should I Buy a Washer And Dryer? This project will reinforce the concepts of simple interest and the total cost of purchasing and using an item weighed against the continuation of an alternative (e.g., renting). Estimation and critical thinking skills will be enhanced as students work to determine the total cost of buying and using a washer and dryer for five years or going to a laundromat for the same time period. The project will stress teamwork in problem-solving and presenting and explaining solutions to other students. View it Get it
Wheeling Deals Use linear graphs to interpret data, research and interpret expenses to fit income constraints, and make decisions as a group View it Get it
What Will It Cost? To: 1) reinforce graphing techniques (linear, step-function, quadratic, power, exponential); 2) support interpretations of graphs; 3) expand experience in curve-fitting (determining curve of best fit); and 4) strengthen ability to predict future behavior from graphs. View it Get it

Stepping Stones Home Modelling Projects Modelling the Modelling Process Participants Other Resources