Projecting School Enrollment
Matt Lohsl Leo Paveglio
Lora Rich Becky Tunnell
Class: PreAlgebra, General Mathematics, Techprep
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 
12 
23 
34 
45 
56 
67 
78 
89 
910 
1011 
1112 


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