Title – Active Learning using the Pythagorean Theorem

By – Dolores Bencivengo

Primary Subject – Math

Grade Level – 9

Standards Addressed:

3 Mathematics

Specific Objectives:

• Students will be able to evaluate length using the Pythagorean Theorem.
• Students learn to justify their answer through evaluating actual measurements.

Required Materials:

• pencils
• paper
• rulers
• optional markers

Step-By-Step Procedures:

• Define the Pythagorean theorem as a relation between the three sides of a right triangle.

  • Remind students:
    
    The hypotenuse is the longest side as well as the opposite side of the 90
    
    ^o
    
    angle.
    

  • The formula is:
    
    a2 + b2 = c2
    

    
    Where “a” and “b” must be labeled for the sides and “c” for the hypotenuse for the formula to be accurate!
    

• To solve the labeling issue, have students use the following formula:

  • The less error prone formula is:
    
    (side)
    
    ²
    
    + (side)
    
    ²
    
    = (hypotenuse)
    
    ²
    
    

• Model a right triangle and label the sides and hypotenuse.

• Model using the Pythagorean Theorem in two ways:
  1. Use the above-mentioned formula to find the length of the hypotenuse.
     
  2. Use the above-mentioned formula to find the length of a missing side.

  For example 1:

  1. Use a real world object large enough for the students to observe it being measured; chart paper works well.
     
  2. Measure two sides of the object.
     
  3. Use the Pythagorean Theorem to evaluate the length of the hypotenuse (
     
     separating the object into two right triangles
     
     )
     
  4. Evaluate the actual measurement (with ruler) to justify your answer.

  For example 2:

  1. Use a real world object large enough for the students to observe it being measured; chart paper works well.
     
  2. Measure only one side of the object and the hypotenuse.
     
  3. Use the Pythagorean Theorem to evaluate the length of the missing side.
     
  4. Evaluate the actual measurement (with ruler) to justify your answer.
     

Plan For Independent Practice:

• Students are given a ruler and asked to find objects within the classroom to measure. They must find four objects to measure following example 1 and four objects to measure following example 2.
  
• Students are to evaluate to find the missing lengths showing all work.
  
• Students are to draw their objects with all sides labeled and all work shown on unlined paper, coloring if preferred.

Closure:

• Have students restate in their own words how to evaluate the length of a side of a right triangle using the Pythagorean Theorem.

Assessment:

• On-going assessment as students are working, as well as on the completed project turned in.

Extensions (Gifted):

• Students could draw a scaled image
  
• Students could use the scale/scaled image to find ratio/proportion between drawn picture and actual image.

E-Mail

Dolores Bencivengo

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