Math-In-CTE Lesson Plan Template s4

Change Compression Ratios Lesson #10

Lesson Title: Manipulating the Variable to Change Compression Ratios Lesson #10 Author(s): Phone Number(s): E-mail Address(es): Jeff Linko, Automotive Tech, Lenape AVTS (724) 763-7116 [email protected] Joe Fullerton, Mathematics, Lenape AVTS (724) 763-7116 [email protected] Lesson Objective: Students will demonstrate a working knowledge of how to use direct and indirect variation and its application in automotive technology, while recognizing it in other contexts. Supplies Needed: HP Books Auto Math Handbook by John Lawlor Copyright 1972 ISBN 1-55788-020-4

Mathematics Dictionary and Handbook by Eugene Nichols and Sharon Schwartz Copyright 1999, ISBN 1-882269-07-1 TEACHER NOTES THE "7 ELEMENTS" (and answer key) 1. Introduce the CTE lesson. This lesson will follow the lesson dealing with the calculation of compression Two 5.0 L Mustangs are preparing to race. The ratios. driver of the black Mustang has increased the piston displacement while the driver of the white The problems that you are solving here would use the same procedure that you Mustang has increased the chamber volume. used in the previous lesson. Please see notes in that lesson for assistance. Assuming every other variable is the same, which Mustang would you expect to win the race?

2. Assess students’ math awareness as it relates Piston Displacement (PD)  Chamber Volume (CV) Compression Ratio (CR)  to the CTE lesson. Chamber Volume (CV) 1. What affects compression ratio?

Math-in-CTE: Automotive Technology 1 Change Compression Ratios Lesson #10

2. Why is compression ratio when you are rebuilding an engine? Direct Variation- when two variables in an expression increase or decrease 3. What happens to the compression ratio if together. the piston displacement is increased and the Indirect Variation- when an increase in one variable in an expression causes chamber volume stays the same? What is another variable in the equation change to decrease and vice versa. the term for this? 4. What happens to the compression ratio if the chamber volume is raised and the piston displacement stays the same? What is the name for this? 5. What is the difference between direct variation and indirect variation? 3. Work through the math example embedded in For these two problems, you will need to calculate the compression ratios, and the CTE lesson. then compare them to the original compression ratios. 1. The compression ratio of a 5.0 L Mustang with a 302 CID, a piston displacement of 1. 618.60 cc and a chamber volume of 75 cc is Piston Displacement (PD)  Chamber Volume (CV) 9.25 to 1. If the driver would change the Compression Ratio (CR)  piston displacement to 647.70, would the Chamber Volume (CV) compression ratio increase or decrease? 647.70 cc  75 cc Find the new compression ratio. CR  75 cc 722.7 cc The compression ratio will increase. CR  75 cc CR  9.6 to 1

2. The compression ratio of a 5.0 L Mustang 2. with a 302 CID, a piston displacement of Piston Displacement (PD)  Chamber Volume (CV) Compression Ratio (CR)  618.60 cc and a chamber volume of 68 cc is Chamber Volume (CV) 10 to 1. If the driver would change the chamber volume to 80 cc, would the 618.60 cc  80 cc CR  compression ratio increase or decrease? 80 cc 698.60 cc The compression ratio will decrease. CR  80 cc CR  8.7 to 1 4. Work through related, contextual math-in- CTE examples. d  w 1. Given the formula HP  , what 1. The horsepower will increase as the distance increases. This is a direct 33,000 variation. happens to HP (horse power) as the d (distance) increases? Is this direct or indirect variation? W 2. Given the formula E = , what happens to I 2. The volts will increase when the watts is increased. the volts (E) when the watts (W) is increased? 5. Work through traditional math examples. 1. Seeing that the R is in the denominator of the fraction, it varies indirectly with I. E 1. Given the equation I = , I varies (directly R or indirectly) with R? Circle one.

E 2. Seeing that the E is in the numerator of the fraction, it varies directly 2. Given the equation R = , R varies I with R. (directly, indirectly) with E? Circle one. 6. Students demonstrate their understanding. See supplemental worksheet with Lesson #9. Use the worksheet and answer key provided by North Montco Technical Career Center. 7. Formal assessment. E 1. The ohms will decrease because this is an indirect variation. 1. Using the Ohm’s Law formula R = , I what happens to the ohms (R) when the amps (I) are increased? Is this a direct or indirect variation?

P 2. Yes, P varies directly and it will increase. 2. Assume that  k , does P vary directly T with k? Will it increase of decrease?

3. 3. A 284 CID (cubic inch displacement) Piston Displacement (PD)  Chamber Volume (CV) Compression Ratio (CR)  engine has a cylinder volume (piston Chamber Volume (CV) displacement) of 610.0 cc and a combustion chamber volume of 35 cc. What is the 610.0 cc  35 cc CR  compression ratio? If we increased the 35 cc chamber volume, will the compression ratio 645 cc increase or decrease from the value just CR  35 cc calculated? Calculate the compression ratio with a chamber volume of 42 cc leaving CR  18.4 to 1 everything else the same. The compression ratio will decrease if the chamber volume is increased.

610.0 cc  42 cc CR  42 cc 645 cc CR  42 cc CR  15.4 to 1

PLEASE NOTE THAT THE WORKSHEET IN LESSON 9 CAN BE USED WITH THIS LESSON.

Math-in-CTE: Automotive Technology 5