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