Projecting School Enrollment

Matt Lohsl Leo Paveglio

Lora Rich Becky Tunnell

Class: Pre-Algebra, General Mathematics, Tech-prep

Materials: Calculators, graph paper, spreadsheet (optional)

Goals: 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.

Time Required: Two class periods for the project and one day for presentations

Background: Students should be able to read charts, graph, apply ratio and proportions. They might also use statistical measures.

Setting: As superintendent, you are in charge of the school district. It is your job to estimate the number of students who will be enrolled in your school district in the future.

Problem: Your school district needs to estimate enrollment for each grade. This estimate is very important since funding depends on how many students are in the school. The number of students is needed to determine how many teachers are required and to decide if the number of school buildings you have will be adequate in the future.

The school board needs to know what the school enrollment will be, both for the near term (three years) and for the long term (ten years.) Use the information in the table below to predict the enrollment in the high school for the next three years and make a prediction about the enrollment in ten years.

You are to report your findings to the board. Both an oral presentation and a written report are expected by the school board. Of course, they will be interested in knowing how you arrived at your estimates.

Enrollment History

 Grade

 Year 1 2 3 4 5 6 7 8 9 10 11 12 1 595 562 557 597 629 625 618 559 595 570 558 528 2 576 593 572 566 611 634 648 629 606 598 525 524 3 558 569 583 576 579 607 646 650 680 592 554 468 4 571 534 588 578 572 577 634 641 682 663 544 525

Sample Solution: Student solutions will vary with the assumptions made by the students and with their level of mathematical sophistication. There is no "correct" solution.

Table 1 is output from a spreadsheet. The Retention Rate is the ratio comparing the number of students who remained (as the group moves from one grade to the next) to the number of students who were in the group the preceding year and also includes transfer students. Hence the rate could be greater than 1. The Average Retention Rate is the mean of the retention rates for each grade level. Projections for the remaining years are the product of the average retention rate and the enrollment for the preceding year.

Evaluation: The written component should include a restatement of the problem, the assumptions used, an explanation of the method used to arrive at the estimate and a clear statement of the conclusion. After the oral presentations, ask the students to write an individual reflection on the problem - what would they change - is there another way to approach the problem - how well did the group function.

The oral component should include a summary of the process used and the findings. Visual aids (charts, overhead slides etc.) are encouraged. Since the "superintendent" is reporting to the school board an air of formality and "professionalism" could be encouraged.

Extensions: Enrollment information from your district could be used.

Students could compare the number of available classrooms and enrollment projections to determine if a building program is indicated.

Students can explore the reasons for changes in census as one group of students moves from one grade to the next (the drop from first grade to second grade, or ninth grade to tenth grade.)

Have students decide how to fairly allocate a limited the number of teachers based on the enrollment projections.

Teacher Notes: Since the groups are reporting to the "School Board", the students could dress

for the occasion. Invite the superintendent or building principal to sit in on the presentations.

Students may want to consider the age of the data. Perhaps they can develop a better model using the last two years. A model developed from the first three years could be tested against the fourth year.

Projecting School Enrollment

As superintendent, you are in charge of the school district. It is your job to estimate the number of students who will be enrolled in your school district in the future.

Your school district needs to estimate enrollment for each grade. This estimate is very important since funding depends on how many students are in the school. The number of students is needed to determine how many teachers are required and to decide if the number of school buildings you have will be adequate in the future.

The school board needs to know what the school enrollment will be, both for the near term (three years) and for the long term (ten years.) Use the information in the table below to predict the enrollment in the high school for the next three years and make a prediction about the enrollment in ten years.

You are to report your findings to the board. Both an oral presentation and a written report are expected by the school board. Of course, they will be interested in knowing how you arrived at your estimates.

Enrollment History

 Grade

 Year 1 2 3 4 5 6 7 8 9 10 11 12 1 595 562 557 597 629 625 618 559 595 570 558 528 2 576 593 572 566 611 634 648 629 606 598 525 524 3 558 569 583 576 579 607 646 650 680 592 554 468 4 571 534 588 578 572 577 634 641 682 663 544 525

SAMPLE SOLUTION: Table 1

 Grade Year 1 2 3 4 5 6 7 8 9 10 11 12 1 595 562 557 597 629 625 618 559 595 570 558 528 2 576 593 572 566 611 634 648 629 606 598 525 524 3 558 569 583 576 579 607 646 650 680 592 554 468 4 571 534 588 578 572 577 634 641 682 663 544 525 Retention Rate 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 0.996639 1.017794 1.016158 1.023451 1.007949 1.0368 1.017799 1.084079 1.005042 0.921053 0.939068 0.987847 0.983137 1.006993 1.022968 0.993453 1.018927 1.003086 1.081081 0.976898 0.926421 0.891429 0.956989 1.033392 0.991424 0.993056 0.996546 1.044481 0.99226 1.049231 0.975 0.918919 0.947653 Average Retention Rate 0.980492 1.011441 1.004858 1.013158 0.999316 1.033403 1.004382 1.071464 0.985647 0.922131 0.92605 5 559 540 590 585 571 596 636 686 672 611 503 6 0 548 529 578 573 559 584 623 672 658 599 7 0 0 537 518 566 561 548 572 610 658 645 8 0 0 0 526 507 554 550 537 560 598 645 9 0 0 0 0 515 497 543 539 526 549 586 10 0 0 0 0 0 504 487 532 528 515 538 11 0 0 0 0 0 0 494 477 521 517 504 12 0 0 0 0 0 0 0 484 467 510 506 13 0 0 0 0 0 0 0 0 474 457 500 14 0 0 0 0 0 0 0 0 0 464 448 15 0 0 0 0 0 0 0 0 0 0 454

Funded in part by the National Science Foundation and Indiana University 1995