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# Here (side)2+ (side)2= (hypotenuse)2solves the Pythagorean theorem problem occurring when the hypotenuse is mislabeled “a” or “b” instead of “c”

Subject:

Math

Grade:

9

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!*

- Remind students:
- To solve the labeling issue, have students use the following formula:
- The less error prone formula is:
**(side)**^{ 2 }+ (side)^{ 2 }= (hypotenuse)^{ 2 }

- The less error prone formula is:
- Model a right triangle and label the sides and hypotenuse.
- Model using the Pythagorean Theorem in two ways:
- Use the above-mentioned formula to find the length of the hypotenuse.
- Use the above-mentioned formula to find the length of a missing side.

For example 1:

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

For example 2:

- Use a real world object large enough for the students to observe it being measured; chart paper works well.
- Measure only one side of the object and the hypotenuse.
- Use the Pythagorean Theorem to evaluate the length of the missing side.
- 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 !