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Pre-Algebra Unit 4: Pythagorean Theorem

last edited by 1 year, 2 months ago

Pre-Algebra Unit 4: Pythagorean Theorem

Unit Driving Question

How can the Pythagorean Theorem be used in real-world situations?

Essential Questions

1. What is the special relationship between the sides of a right triangle?

2. In what situations does the Pythagorean Theorem prove beneficial? Why?

Big Ideas

1. Pythagorean Theorem utilizes the special relationship between the three sides of a right triangle.
2. Pythagorean Theorem can be used to find the distance between two points on a coordinate plane.

Technology Resources

1 Lesson

• The Areas of Squares and Their Sides (OpenUp): This introductory lesson lays important groundwork as students estimate side lengths of squares with known areas using tools such as rulers and tracing paper. They also review key strategies for finding area that they encountered in earlier grades that they will use to understand and explain informal proofs of the Pythagorean Theorem.

Big Ideas for Development Lessons

Big Idea 1: Pythagorean Theorem utilizes the special relationship between the three sides of a right triangle.

OAS-M: PA.GM.1.1

Key Resources

1. Proving the Pythagorean Theorem Part 1 (OpenUp): In the warm-up of this lesson students use the Pythagorean Theorem to find the hypotenuse of a right triangle. In the first activity they prove the Pythagorean Theorem using, in part, a diagram they encountered in a previous lesson. They reason abstractly using equations and the geometry of the triangles and squares to find relationships between quantities.

2. Proving the Pythagorean Theorem Part 2 (OpenUp): In this third lesson on the Pythagorean Theorem students work with the theorem in more challenging ways. In the warm-up, students use the the Pythagorean Theorem to determine that a triangle is not a right triangle. They argue that sincea2+b2is not equal toc2for the given side lengths, the triangle cannot be a right triangle. In the first classroom activity, they work through a second proof of the Pythagorean Theorem using transformational geometry.

3. SpiderBox (Illustrative Mathematics): The purpose of this task is for students to work on their visualization skills and to apply the Pythagorean Theorem.  This task allows students to explore how concrete models can help them visualize three-dimensional objects that are drawn in a two dimensional representation.
4. Stations Activity-Properties of Right Triangles (Stations 1-3 only): Students will work in collaborative groups to complete station activities providing opportunities to develop concepts and skills related to applying properties of right triangles, specifically the Pythagorean theorem. Students may have an opportunity to complete station 4 in Geometry classes.

Big Idea Probe

Unit 5: Big Idea 1 Probe Janes TV (Mars): In this task, you will need to work out the actual dimensions of TV screens, which are sold according to their diagonal measurements.

Evidence of Understanding

Algebraically solve questions dealing with right triangles.

• Create the Pythagorean Theorem by using various visual representations.

• Find missing sides of right triangle using the Pythagorean Theorem.

• Understand the difference between the legs (a and b) and they hypotenuse (c)  and their placement on the triangle and within the equation.

• Understand that Side length might not end up as rational numbers.

• Irrational numbers might need to be used to represent side lengths.

• Classify triangles using the Pythagorean Theorem

• Determine if a triangle is a right triangle or does not have a right angle.

• Analyze real-world questions involving right triangles

• Use the Pythagorean Theorem to solving for missing real-world values.

• Use information to draw models to aid in solving real-world questions.

Big Idea 2:  Pythagorean Theorem can be used to find the distance between two points on a coordinate plane.

OAS-M: PA.GM.1.2

Key Resources

1. Finding Distances on a Coordinate Plane (OpenUp): In this lesson, students continue to apply the Pythagorean Theorem to solve problems. In all activities students compute distances between points in the coordinate plane in varying contexts. This is probably the most common application of the Pythagorean Theorem in mathematics and students will see it again and again in high school and college mathematics courses.

2. Finding the Distance Between Points (Illustrative Mathematics): The goal of this task is to establish the distance formula between two points in the plane and its relationship with the Pythagorean Theorem. Students should already be familiar with applying the Pythagorean in concrete situations.

3. Acting Out (Georgia Dept. of Ed.): In this task, students will apply the Pythagorean Theorem to real-world situations to find the distance between the houses of two students.

4. In this activity, students will apply Pythagorean Theorem to help Link defeat Ganon and save Zelda.

Evidence of Understanding

Find the distance between two points on a coordinate plane.

• Make the connection between graphs on a coordinate plane and points on a gridded map.

• Analyze distance in the coordinate plane and use distance to relate points and lines

• Calculate the distance between two points using the Pythagorean Theorem