Sunday, November 27, 2011

Driving and Texting


Goal: Is Car and Driver correct? Learn the difference in the stopping distance of a car when driving while texting vs. not texting.

Drivers today have many distractions that can keep them from applying braking as soon as possible. One of the biggest distractions while driving is texting. Many times drivers believe that a quick, short text is doable while driving. In this lab, you will collect data, and then determine how the stopping distance of a typical car is affected.


Procedure:

Assume you just received a text from your best friend while you are driving.

1. Determine a short 3-5 word response.

2. Text the response one handed (this is how you do it while driving). Record the time it takes to text the message. Be sure to time yourself on the first attempt at texting. Note: your speed in texting will increase and flaw your results.


3. Find 9 additional people to text the same response. Record their time to text.

_________, _________, _________, _________, _________,

_________, _________, _________, _________, _________,

4. Find all 3 averages of the time (mean, median, mode). Decide which average best represents your data.

Mean __________ Median __________ Mode __________

5. Using the internet, (record your source here:____________________________) find the stopping distance of a car traveling 35 mph and 70 mph on dry pavement with normal reaction times.

35 mph stopping distance__________
70 mph stopping distance__________

6. How many additional feet will a driver travel while sending the text. Use the mean, median, or mode from part 4 above to determine the travel distance.

7. How many football fields will the driver travel in the total stopping distance of the car?

8. Is Car and Driver correct?

Monday, October 17, 2011

Cross Gable Framing Angles




Many homes have small gables along the front of the home. The photo at right shows an example of the type of gable above the front door that we are constructing for this year's house. The width of the gable immediately above the front door is 10 feet.

The main roof has a 3/12 pitch. The small gable will have a 3/12 pitch. It may be helpful to build a model of this portion of the roof out of balsa wood.

1. Find the measure of the angle that needs to be cut on the end of the board found in oval #1.

2. Find the measure of the angle that needs to be cut on the end of the rafter found in oval #2.

3. In oval #3, there are 2 angles that must be cut on the end of the rafter. This is called a compound angle. What are the measures of each of the two angles?

Note: Students will need to know the pythagorean theorem, slope, and right triangle trig.

Saturday, September 10, 2011

The Law of Diminishing Marginal Returns

A Fun Look at Economics and the Parabola

Goal: Students will simulate a factory that has the ability to add workers but can not add capital resources. Students will create a product called Nutterflutters in the class. The production process of the product will be analyzed mathematically.

Background information for the teacher: All CTE areas include an element of business and how to be successful in the world of work. In business, seldom are all of your resources unlimited and usually small changes are put into place to increase production (profits). If the marginal benefits (profits) are greater than the marginal (additional) costs, then the change was successful. Some resources such as additional labor can be added (temporary or long term) easily (relatively inexpensive investment) while other resources take planning and substantial ongoing expense. For example, expensive modifications/additions to floor space in a factory or additional production machinery may be cost prohibitive or may require extensive long range planning. We will be looking at The Law of Diminishing Marginal Returns which predicts that labor productivity will eventually fall as you add additional (marginal) workers to the production process, while keeping other resources fixed.

Materials needed: 1 large jar of peanut butter, 1 large jar of marshmallow cream, 1 box of graham crackers, 2 plastic knives, paper plates, and a roll of paper towels.

Time to complete activity: 45 minutes

Process:
1. Let students know that you are going to examine the Law of Diminishing Marginal Returns from economics and how it affects business decisions. Model at a desk/table how to make the Nutterflutter snack (I have heard them called peanut smores, flutternutters, etc). Let them know they will be eating the products at the end of the activity.

2. How to make a snack: Spread out 2 – 4 paper towels on the table. The paper towels represent the work area (factory space) and the work can not be on the bare table (health codes). Break a large graham cracker into fourths (small rectangles). Spread peanut butter on a graham cracker using a knife (must use a knife). Spread marshmallow cream on the other graham cracker using the other knife (must use a knife for “health codes”). Stack the 2 rectangle graham crackers to make a sandwich and then place it on the paper plate (represents your warehouse).

3. Choose a student (or two) to be quality control inspectors. Discuss what is a “good” snack and what would be rejected. Choose another student to be the timekeeper.

4. Select a student to be the worker at the factory. He/she will be making the snacks. He/she is to make as many complete snacks as possible in 1 minute. When the time is up, the inspector(s) will inspect the products to decide if they pass quality control. Count the number of completed snacks that pass inspection and record in the production table. Unacceptable ones are not to be counted. Marginal output is the number of additional products produced because another worker has been added. See the table below for an example of how to calculate marginal output.



Production Table

# workers.....# snacks produced.........................Marginal Output

.......0............................0............................................... N/A
.......1..................3 as an example..............................3 as an example
.......2..................7 as an example............................. 4 as an example
.......3
.......5
.......8
......etc

Your second worker added 4 more Nutterflutters, called the marginal output.

5. Select an additional student to join the already employed student (there are now 2 people on the production line). Remove the previous snacks made and replace with an empty paper plate. Students can not expand the work area (can not add paper towels), or use additional knives….remember the resources are fixed…the only variable is the number of workers. They are to repeat step 4 above by adding another worker.

6. Continue adding workers, being sure not to increase work area (paper towels represent the floor of the factory) and do not increase the number of knives or supplies. Continue adding students until the marginal output begins to drop or perhaps even go negative.

7. Graph the number of workers and marginal output. This should approximate a parabola. If your data is poor, be ready to adjust as needed. Extensions include writing the equation of a parabola, predicting using your equation, and general terminology.

8. Questions: How did specialization/division of labor/assembly line affect the production? Were the additional workers lazy? In this example, when would the factory hire and when would they quit hiring?

This activity has been around for a long time….done differently with different products produced. So, if you have done something similar, I do not want you to think I am taking credit for the creation of this activity. It is a lot of fun, and gives a real life example of the use of quadratics.

Sunday, March 20, 2011

Fascia Board Angles


The fascia board is a vertical board along the edge of the roof. It is designed as a way of enclosing the end of the rafters of a home. The white board in the photo is a fascia board. Because it is used as a trim/decorative board, the cuts and joints must be precise. The angle (located in the red circle) can be a tough angle to calculate. Many carpenters do not calculate this angle, but instead have it memorized for different roof pitches or use a t-bevel. A t-bevel is a tool that copies angles.

Please calculate the cut angle of the fascia for a 4/12, 5/12, 6/12 pitch roof. What degree measure does the cross cut miter saw need to be set at for your calculated angle? What is the cut at the peak of the roof for the same fascia board? Please show all drawings and calculations.

Saturday, February 12, 2011

Is Your Can Efficient?


In recent years the size and shape of drink cans have been varied. The traditional looking pop can is no longer the only option in purchasing your 12 oz (355 ml) soda. Half size pops, Monster drinks, coffee drinks, etc have filled the grocery shelves.
Your task is to design a cylindrical can (355 ml) that minimizes can production costs. The production costs can be minimized by using the smallest amount of material possible. When cans are manufactured, any material that does not get used in the can will be shredded and recycled. What should the dimensions of the new can be? Hint: 1 mL = 1 cm3

This problem lends itself to using a spreadsheet and graph from the spreadsheet. Please show work/formulas used in the spreadsheet as well as a graph.

Sunday, January 9, 2011

High School Mini Zoo Design


The high school plans to allow the Biology class to build a mini-zoo for small animals such as mice, hamsters, snakes, tarantulas, guinea pigs, etc. Due to budget limitations, costs will be a big concern and design economies must be considered. The cages will be built using 4 ft by 8 ft plywood sheets and 4 ft by 8 ft Plexiglas sheets as the materials. Eight cages will be built. Each cage needs to have a minimum of 360 square inches of floor space. Each cage will be 15 inches tall and one face (side) will have a window for viewing. The window must be at least 10 inches wide.
Your job is to design the “best” mini-zoo. Your solution should include scale drawings of the cages and a written description of the advantages of your zoo design. A material list of will need to be included telling how many sheets of Plexiglas and how many sheets of plywood. Show a cut diagram for how you plan to cut each sheet so that you have all of the pieces needed to construct the zoo cages. Show all math sub-problems used to verify that your solution meets the requirements of the mini zoo.