Lesson 4: Applications of the Pythagorean Theorem & Real-Number Analysis
Duration of Days: 5
Lesson Objective
Students will master the application of the Pythagorean Theorem to solve for missing side lengths, verify right triangles using the converse, and solve multi-step real-world problems.
Students will also approximate square roots to determine distances on a coordinate plane and in scaled drawings.
How can we estimate the value of a non-perfect square root without a calculator?
How does the Pythagorean Theorem allow us to find the distance between points without a specific formula?
How do changes in scale affect the calculation of real-world distances?
Hypotenuse, Legs, Radical, Irrational Approximation, Converse of the Pythagorean Theorem, Perimeter, Area
8.NS.A.2: Use rational approximations of irrational numbers.
8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths.
8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points.
DOK Level 3 (Strategic Thinking). This lesson is a cumulative review.
Students often confuse the legs (a and b) with the hypotenuse (c).
Some may incorrectly assume the distance formula is a separate entity rather than an application of PT.
Students may also struggle with the order of operations when calculating.
Scaffolding: Provide a "Perfect Square Reference Sheet"
Challenge students with 3D applications (finding the diagonal of a rectangular prism)
Use graph paper for all distance problems
Exit Ticket
Performance Task