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(Download as Microsoft Word documents: Homework Lottery, Cover Page, Page 1, Page 2, Page 3, Page 4, Dice Graph, Dice Graph 2)

Title of Project:    

 

Homework Lottery

 

 

Team Members:

·

Richard Bull         

Upattinas School

 

·

Heather Godine

Central York High School

 

·

Rick Keshner

Palmyra Area High School

 

·

Roni Topp

Brashear High School

 

Grade Level and/or Course:

 

·

10-12

·

Algebra II/Trigonometry

 

Concepts Used:

 

·

Exponential Decay

·

Probability

·

Exponential Regression

PA Standard(s) Addressed:

 

·

2.6.11.C

Determine the regression equation of best fit (e.g. linear, quadratic, exponential)

·

2.7.11.C

Draw and justify a conclusion regarding the validity of a probability or statistical argument.

·

2.8.11.A

Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically.

·

2.8.11.N

Solve linear, quadratic, and exponential equations both symbolically and graphically.

NCTM Standard(s) Addressed:

 

·

Judge the reasonable ness of numerical computations and their results. (393)

·

Draw reasonable conclusions about a situation being modeled. (395)

·

Apply and adapt a variety of appropriate strategies to solve problem. (402)

·

Select, apply, and translate among mathematical representations to solve problems. (402)

Introduction / Applications:

 

Miss Schernie Broeder wants to reward her class of twenty-four students for their hard work. She will assign each student a six-sided die where one side is marked with a letter to distinguish each student’s die from another. All twenty-four dice will be placed into a large box. Once each day over a ten-day period, Miss Broeder will shake the box and look at the dice. Each student’s die that faces letter side up will be permitted to submit only half of the homework assignment for the remainder of the ten-day period. (Note: Since Miss Broeder created the reward system, she will also decide which problems constitute half of the homework assignment.) When a student’s die faces letter side up, that student will remove it from the box. Miss Broeder poses these questions to her class:

 

 

 

Questions

 

·

Would you prefer that everyone in the class has exactly two nights of no homework or would you prefer to try this method?

·

Is it likely that all students will be responsible for only half of the homework by the end of the ten-day period? (Or will some students need a Schroeder [oops – shoulder] to cry on?)

 

Model:

 

Students will use simulations, averaging, and exponential regression to examine this homework situation.

 

 

 

Resource and Materials (estimated cost):

 

·

Student Handouts (Cover page, page 1, page 2, page 3, page 4)

·

Six boxes with lids (shoe boxes would work well).

·

Six sets of 24 dice ($48.00).

·

Small letter labels ($3.00)

 

Procedures & Activities:

·

In six groups of four, students read the problem and make conjectures regarding results.

·

Groups model the problem with 24 standard dice.

·

Groups complete four trials, removing all dice that fall with a six facing up and recording the number of dice remaining after each shake.

·

Groups use the four trials to calculate the average number of dice remaining on each shake.

·

Groups calculate the average number of dice removed on each shake.

·

Groups plot the average number of dice remaining and the average number of dice removed on separate coordinate axes.

·

Groups use technology to develop an exponential regression for the number of dice remaining.

·

Teacher uses technology to develop a class average and an exponential regression for class results of the number of dice remaining.

·

Teacher uses technology to compare group and class results with theoretical solution.

·

Class discussion regarding how original conjectures relate to theoretical solution.

 

Answers: (Solution 1, Solution 2)

 

1.

For one roll of a single die, what is the chance that it will land letter side up?  1/6

2.

For one roll of a single die, what is the chance that it will NOT land letter side up? 5/6

3.

On average, how many students will still be doing all of the homework after 10 shakes of the box? Explain your answer. (ANSWERS WILL VARY)

4.

On average, how many students will only be doing half of the homework after 10 shakes of the box? Explain your answer. (ANSWERS WILL VARY)

 

 

Sample Answer:

        Trials

 

 

Shakes

Trial #1

Number Completing All  HW

Trial #2

Number Completing All  HW

Trial #3

Number Completing All  HW

Trial #4

Number Completing All  HW

AVERAGE

Number Completing

All  HW

AVERAGE

Number Completing

Half  HW

0

24

24

24

24

24

0

1

22

22

19

18

20.25

3.75

2

18

20

18

13

17.25

6.75

3

16

18

13

11

14.5

9.5

4

11

17

12

10

12.5

11.5

5

7

14

10

9

10

14

6

6

11

10

9

9

15

7

6

7

10

7

7.5

16.5

8

5

4

9

5

5.75

18.25

9

3

4

9

4

5

19

10

2

4

6

4

4

20

 

 

Sample Graph:

 

Exponential Regression Equation:                    f(x) = 24(5/6)^x

 

 

 

Number of Days

Number of Students 

Who Still Have to Complete All  of the Homework

 

 

Sample Graph:

 

 

 

 

Number of Days

Number of Students 

who Only Have to Complete Half of  the Homework

 

 

 

 

Accommodations / Adaptations:     

ESL:

 

Provide reading assistance as needed.

 

Special Ed:

 

Allow students to complete only the data collection, or only the averaging, as applicable to their individual needs. Allow special needs students to work with regular education students.

 

Enrichment:

 

Find a regression equation for students who only have to complete half of the homework.

 

 

 

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