Gold Seal Lesson:
Quality Control

Subject:

Mathematics

Grade:

5-8

ICLE Standards:

Statistics: Systematically collect, organize and describe data. Make inferences and convincing arguments that are based on data analysis.

Probability: Appreciate the power of using a probability model in a real world setting.

Problem Solving: Acquire confidence in using mathematics meaningfully.

Performance Task:

Note to the teacher: This project is written as a team activity. It may, however, be adapted for use by individual students. You are part of a manufacturing team. You have noticed that in your work cell, Line A, there have been a number of parts produced lately that do not meet your customers' quality standards. Your team has decided to work through the situation by simulating the production line and analyzing the present situation.

You will simulate the problem by using M&M candies. Each member of your team is given a bag of M&M candies containing the various colors. The candies represent different classifications of parts produced in your work cell as outlined below:

• Blue: length is out of tolerance

• Red: part is acceptable

• Green: part is acceptable

• Orange: part is slightly discolored

• Yellow: part is not square

• Brown: part is acceptable

Each member of your group is to make a frequency table for each of the different classifications indicated above. Combine your tables into one frequency table for the entire team and construct a histogram showing your data. Compute the team mean, median and mode for each of the classifications. State whether or not you have a normal distribution. Following a production run, what is the probability of reaching into the Line A parts bin and selecting each of the following based upon your data?

1. a part which is slightly discolored

2. a part whose length is out of tolerance

3. an acceptable part

4. a part which is slightly discolored

5. a part which is not square 

Based on your group's data, how many parts in a batch of 500 would you expect to be:

1. slightly discolored

2. out of tolerance

3. not square

4. acceptable 

Write a brief report discussing your simulation and explaining your results. What inferences, if any, can you make. Include a statement expressing the role probability and statistics play in ensuring quality in a manufacturing environment.

Knowledge / Skills:

Understand the best procedures for statistical data collection, organization, and display.  (m5)

Understand the characteristics of measures of central tendency (i.e., mean, median, and mode).  (m15)

Understand the characteristic differences between theoretical and empirical probability (e.g., the theoretic probability of rolling a six an a die is 1/6; empirical probability is derived from repeated experimentation or accumulated statistics).  (m20)

Determine the probability of single and compound events using the basic premise that the probability of an event is equal to the number of ways it can occur divided by the total number of outcomes.  (m25)

Use expository writing skills in subjects other than English language arts.  (ela58)

Rubric:

4 Points  =  The student works cooperatively with team members to simulate a workplace problem. The student's calculations show a thorough understanding of the principles of statistics and probability. Her/his written responses demonstrate that s/he is able to transfer knowledge of statistics and probability to a work situation.

3 Points  =  The student collaborates to some extent with his/her team, but does not fully engage in the simulation. Data presentation is not complete and some calculations are incorrect, but the student shows a basic understanding of statistics and probability. His/her written response demonstrate a limited transfer of the knowledge of statistics and probability to a work situation.

2 Points  =  The student is passive in team collaboration. S/he depends fully on teammates in the simulation. Several errors occur in calculations or they are not understood by the student. Her/his written response shows that s/he has little knowledge of the principles of statistics and probability and that h/she cannot transfer any knowledge to a work situation.

1 Point  =  The student does not participate as a team member. His/her calculations are incomplete and/or contain many errors. The student's written response demonstrates little, if any, knowledge of statistics and probability. No attempt is made to transfer any knowledge to a work situation

Keywords:

GEOMETRY
EXPOSITION STATISTICS
DATA ANALYSIS
DATA COLLECTION
GRAPHS
INFERENCE
NORMAL DISTRIBUTION
PROBABILITY
DATA DISPLAY
CENTRAL TENDENCY
SAMPLING
SIMULATIONS
TABLES

Grades:

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [X] - 6 [X] - 7 [X] - 8 [X] - 9 [] - 10 [] - 11 [] - 12 []

ICLE Application:

D

© 2000 International Center for Leadership in Education
1587 Route 146 - Rexford - NY - 12148
518.399.2776 Fax: 518.399.7607
95