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Name of NGM Educator:

William Trapp, Business Math, Cheney Technical High School

Name of Host Company:

Pratt & Whitney, United Technologies, Inc.

Grade Level:

12th grade

Student Work Types:

Type One:

As a review, put up slide of a part and data sets representing specific measurements of a dimension of the part. Using calculators, show class how to calculate mean and standard deviation manually. Explain that standard deviation is a measure of how widely data varies.

Students will practice on other small data sets from teacher-generated worksheet.

Type 2

Remind class of standard deviation calculations we did the previous day. Tell them that standard deviation is one way to compare one data set to another. Ask if they’d like to do these big data sets manually like we did before? Tell them they’re in luck, help is available to do the hard calculations electronically. We can use a TI-83 or use a program like Excel to help. Using data set on board show class the process to create a list in their calculators. Explain that this is the hardest part. Once done with the list, demonstrate how easy it is to calculate mean and standard deviation. Explain these are key components that industry uses to get their manufacturing processes under control. Students will practice on other large data sets displayed on board using TI-83 and Excel (if computers are available).

Type 3

Using a data set from the previous day’s work and reasonable upper and lower design limits, lead the class through the first calculation. Do this for Cpl and then Cpu. Explain that the real measure we’re looking for is the Cpk which is the lower value of the two we just computed. List Cpk. Explain that this is as hard as it gets. Refer back to original slide of calculation. Ask class which of the inputs they as designers have control over. (LSL, USL). Explain how important it is to a company that they work for not to make the tolerance tighter than needed. This is called overdesign. Ask class for opinions as to what problems overdesign can create. List the answers. Ask they determine how much quality is required in a design? (Customer’s requirements, mating parts, etc.) Using data sets presented on smartboard, have students calculate Cpu and Cpk for various LSL’s and USL’s. Have then watch how numbers improve. Also impress upon them the effects that USL and LSL have on the calculation. Process control is not just a manufacturing problem. It should always be a team effort to come up with the easiest design to make which meets customer’s needs.

Type 4

Remind class of the Cpl, Cpu and Cpk calculations. Tell them these numbers can be directly related to the number of bad products a company makes over time. Using several data sets with same mean and decreasing variance, have students calculate mean and standard deviation for each. Ask volunteers for answers and list them on the board. Using slide form above, compare these values to the slide to see what levels of rejections each Cpk would yield. Now have class go through the calculations again but this time relaxing the LSL and USL numbers to see what effect a design change can have. Relate the new Cpk’s back to the rejection slide to see the difference.

Type 5

Put up slide of Dr. Deming and Taichi Ohno. Explain Deming’s role in the U.S. during World War II and in Japan after the role. Explain how Toyota was in rough shape but embraced Deming’s teaching (especially Ohno). Go through highlights of the TPS especially Deming’s 14 points and the 7 wastes. Tell them that this has become the model companies all over the world are striving for. List some of the benefits to a company that derive from lean manufacturing. Ask for opinions from class how these can come from the procedures listed above. List the responses. Explain this that this isn’t the way things used to be done in most companies. Go through a brief scenario about an “unenlightened� company. (lots of inventory to make up for slow processes and parts that might be ruined, things designed with no regard as to how the company can possibly make them, managers telling workers what to do when most times it is the worker on the floor who knows best how to do a job, running machinery until it breaks, a messy unsafe manufacturing area, office processes that made it difficult for customers to place an order or find out even basic information, no programs for workers to improve their knowledge, etc.). Assign extra credit report to students who would like to find out more about Dr. Deming, or Toyota , etc.

Type 6

Present catapult to class (it can be made by the class if time allows). Explain its operation and how several settings can be changed. Tell class were going to make teams and launch the ball 25 times recording carefully how far it goes. : Each team uses catapult to launch the ball 25 times and records how far it goes. Uses Excel, they will create a spreadsheet and calculate mean and standard deviation. Using formulae, etc. they can also use the spreadsheet to calculate Cpl, Cpu and Cpk given reasonable design limits by the instructor. Based on different settings of the catapult, teams will record their findings on the board. We can use these to decide how well the process is in control. Once data is compared, ask students for ideas about how we would go about improving the process to make it more consistent.Watch for techniques when launching ball, measuring distance and recording data. Also check to make sure calculations seem to make sense. Listen for responses about improving the process. Review entire process improvement process. Explain there is lots more to this and that there are books to read or websites that provide more information if they want to learn more.

Task Abstract: After a review of the basics of statistics (mean and standard deviation calculations) students will learn about how Cpk is used to bring processes under control.

Task Objectives: Students will be able to calculate mean and standard deviation for increasingly large data sets, will learn how the relate to Cpl, Cpu and Cpk calculations, will calculate different Cpk’s by varying the tolerances and relate these numbers to the number of rejects being produced.

Esssential Understandings/Questions: The math behind these concepts is not that difficult. Once lists are made, using modern tools mean and standard deviation calculations are not difficult. These figures along with tolerances are directly related to the numbers of bad parts a company will produce.

Task Description: Students will progress from basic statistics to large data lists using calculators or spreadsheet applications. They will relate their findings to processes in the manufacturing world and get rough estimates of the scrap produced by uncontrolled and controlled processes.

Resources Required: A Smartboard, TI-83 calculators, computers with Excel and data sets derived from actual examples from my internship. Also a simple catapult to generate data with variation.

Prior Learning Required: Basic statistics from earlier algebra courses. Familiarity using TI-83 and Excel.

Work will be produced during class time set aside during PLTW sessions for integrating math.

There will be plenty of opportunity for group (team) and individual work

The visual aids such as Smartboard slides, Excel spreadsheets and the catapult should help special needs students and those whose learning styles favor visual or tactile stimulation.

Educator Comments: I am hoping that working with data from real world applications will motivate student learning. I think some of this will “sneak up� on some of the students and they’ll be doing fairly complicated computations before they realize it. I also want to impress on them that this is how successful companies are actually doing things right now and that some of this knowledge will make them more valuable when they are looking for careers.