Math-in-CTE Lesson Plan Template
Lesson Title: Human Body Levers / Lesson # 23Author(s): / Phone Number(s): / E-mail Address(es):
Helene Crist / (732)473-3100 ext. 3174 /
Eileen Verde / (732)473-3100 ext. 3152 /
Occupational Area: Health and Fitness Technology
CTE Concept(s): Safe Lifting & Carrying Techniques to protect against injury. Human Body Levers.
Math Concepts: Ratio & Proportion
Lesson Objective: / Students will identify how different levers are classified, explore the advantages & disadvantages of different classes of levers, model different joints in the human body by the different classes of levers and to interpret observational data & draw conclusions based upon those observations.
Supplies Needed: / Calculator, Effort/Resistance Proportion Mechanical Advantage Equation, Worksheets
The "7 Elements" / Teacher Notes
(and answer key)
1. Introduce the CTE lesson.
Improper lifting technique can lead to back, leg & arm pain. Poor technique can cause both acute injury, & serious chronic effects on the body. Learning the proper technique to lift will help avoid future musculoskeletal injuries. These techniques can be used in the fitness setting as well as any other workplace & home to prevent injury.
These safe lifting precautions & tips can be applied to the general workplace, picking up equipment or dumbbells off the floor during exercise workouts and for use in the home/yard.
Since the human body is made up mostly third-class levers, its movements are adapted more to speed than to strength. (short force arm/long weight arm) Most of the bones of the limbs (arms & legs) act as levers. These levers are powered by muscles. There are 3 classes of levers: 1st, 2nd & 3rd class levers. / Safe Lifting:
1.Plan ahead before lifting. (ask: do I really need to lift this?)
2. Lift close to you body.
3. Feet shoulder width apart.
4. Bend your knees and keep your back/spine nice & straight.
5.Tighten the muscles of your “core” (abdominals & connecting musculature)
6. Lift with your legs, not using your back.
7. If your feel you are straining, stop & get help.
Tips:
a. Never bend your back to pick something up.
b. Hold the object close to your body.
c. Don’t twist or bend.
d. Keep your eyes up.
2. Assess students’ math awareness as it relates to the CTE lesson.
A. What is a lever & what are it’s parts?
B. What is a 1st class lever & identify a human body example?
C. What is a 2nd class lever & identify a human body example?
D. What is a 3rd class lever & identify a human body example? / Answers:
A. *A lever is a rigid rod able to rotate about a fixed point known as a fulcrum, formed by the joint.
*Any force applied to the lever is called the effort.
*A force that resists the motion of the lever, such as the downward force exerted by a weight on the bar, is called the load or the resistance.
*The contraction of the muscles is the effort & the body part of the body concerned is known as the resistance or load. *Bones of the body act as levers (a mechanical device) which create a mechanical advantage of strength or speed.
B. In a first class lever, the weight & force are on opposite sides of the fulcrum. An example is the joint between the skill & the atlas vertebrae of the spine; the spine is the fulcrum across which muscles lift the head.
C. In the second class lever, the load is between the fulcrum & the force. A smaller effort can be used to advantage over a larger weight. An example of this lever is the wheelbarrow. A human body example if the Achilles tendon, pushing or pulling across the heel of the foot.
D, In the third class lever, the force is between the fulcrum and the load. In this case, there is no force advantage-force is NOT increased. A larger force is actually needed to move a smaller weight, so there is a force disadvantage. The use of this lever is in the gain in speed of movement of the weight. An example of a third-class lever in the human body is the elbow joint; when lifting a book, the elbow joint is the fulcrum, across which the biceps muscle performs the work.
3. Work through the math example embedded in the CTE examples.
A. Determine the amount of effort required to lift a 5 pound weight with your hand if the bicep in your arm is anchored one inch below your elbow (fulcrum) and 18 inches is the distance from your hand to the elbow. What is the Mechanical Advantage to a 3rd Class Lever? / A. Answer: 1/18 = 5/x x = 90 lbs
B. Mechanical Advantage formula is:
Resistance Force: Effort Force
5 pounds:90 pounds
Mechanical Advantage = 0.056. As this number is less than 1 there is no Mechanical Advantage.
4. Work through related, contextual math-in-CTE examples.
A .Determine the amount of effort required to lift a 10 pound weight with your hand if the bicep in your arm is anchored one inch below your elbow (fulcrum) and 16 inches is the distance from your hand to the elbow. What is the Mechanical Advantage to a 3rd Class Lever?
B. Determine the amount of effort required to lift a 15 pound weight with your hand if the bicep in your arm is anchored 1 inch below your elbow (fulcrum) and 17 inches is the distance from your hand to the elbow. What is the Mechanical Advantage to a 3rd Class Lever? / A. Answer: 1/16 = 10/x x = 160 lbs
Mechanical Advantage = 10:160 = 0.063
B. Answer: 1./17 = 15/x x = 255 lbs
Mechanical Advantage = 15:255 = 0.059
5. Work through traditional math examples.
A. Find the ratio of 15 to 20 in decimal form.
B. Find the ratio of 2 to 20 in decimal form.
C. Find the missing value in the proportion 1/7 = 11/x.
D. Find the missing value in the proportion 1/9 = 25/x. / A. 15:20 = 0.75
B. 2:20 = 0.10
C. X = 77
D. X = 225
6. Students demonstrate their understanding.
For each of the three classes of levers, students will explain the advantage gained by using that type of lever.
Students will list which type of lever we find most often in the human body.
Students will explain how a muscle exerts force.
Students will explain how to calculate effort force required lifting an object using the examples listed above.
7. Formal assessment.
1. Determine the amount of effort required to lift a 15 pound weight with your hand if the bicep in your arm is anchored 1 inch below your elbow (fulcrum) and 17.5 inches is the distance from your hand to the elbow. Then find the Mechanical Advantage value.
2. Determine the amount of effort required to lift a 15 pound weight with your hand if the bicep in your arm is anchored 1 inch below your elbow (fulcrum) and 15.5 inches is the distance from your hand to the elbow. Then find the Mechanical Advantage value.
3.Determine the amount of effort required to lift a 15 pound weight with your hand if the bicep in your arm is anchored 1 inch below your elbow (fulcrum) and 20 inches is the distance from your hand to the elbow. Then find the Mechanical Advantage value.
4. Is there a Mechanical Advantage to lifting with your arms? Explain.
5. Simplify the ratio 8:20 into decimal form.
6. Find the value of x in the proportion 1/13 = 16/x / Answers
1. 1/15 = 17.5/x x = 262.5 pounds
MA = 15:262.5 = 0.57
2. 1/15 = 15.5/x x = 232.5 pounds
MA = 15:232.5 = 0.65
3. 1/15 = 20/x x = 300 pounds
MA = 15:300 = 0.05
4. There is no mechanical advantage to lifting with our arms. The only advantage is speed, so the tendency to lift incorrectly is great which can lead to injury
5. 0.04
6. X = 208.
NOTES: www.brianmac.co.uk/levers.htm
“Bones as Levers” by M. Poarch – 2002 http://science-class.net
www.mayoclinic.com for a slide show of proper lifting techniques