**Title:** Proofs into Practice: The Pythagorean Theorem in the Real World

**Description:**
The introduction of this lesson has students verifying the famous Pythagorean Theorem with a hands-on proof. Students will then apply the Theorem in one of two ways: by solving for the side lengths of a right triangle and by determining whether three side lengths could possibly form a right triangle. Finally, students will choose one of two real-life applicataions to explore, using the Pythagorean Theorem.
**Standard(s): **

[MA2015] GEO (9-12) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [G-SRT8]

**Subject:**Mathematics (8 - 12)

**Title:**Proofs into Practice: The Pythagorean Theorem in the Real World

**Description:**The introduction of this lesson has students verifying the famous Pythagorean Theorem with a hands-on proof. Students will then apply the Theorem in one of two ways: by solving for the side lengths of a right triangle and by determining whether three side lengths could possibly form a right triangle. Finally, students will choose one of two real-life applicataions to explore, using the Pythagorean Theorem.

**Title:** The Clock Tower-Enhancing mathematics in the career/technical classroom and providing relevance in the mathematics classroom.

**Description:**
This project resulted from the collaboration of a computer aided drafting teacher (pre-engineering), Chris Bond, and a math teacher, Lee Cable, (Hewitt-Trussville High School) to provide higher math expectations in CT and real life application in mathematics.
As a hands-on, technology based project this activity demonstrates use of the Pythagorean Theorem, Sine, Cosine and Tangent to find unknown heights of objects and can be adapted for use by the computer aided drafting or mathematics teacher. Clinometers are used as a surveying tool and AutoCAD is used as a drawing tool. Students use a clinometer and a ruler or a tape measure to find and then record the length and angle measurements of a right triangle to determine unknowns. This information is then used to find unknown lengths and angles and to then create a drawing in AutoCAD. Proportion and scale will be used to draw a scale drawing of the clock tower at the new Hewitt-Trussville High School. In the mathematics classroom, students will produce scale drawings using graph paper instead of AutoCAD. This lesson will need to be adapted for use by other schools by selecting a different building structure for measure.
**Standard(s): **

[MA2015] GEO (9-12) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [G-SRT8]

**Subject:**Architecture and Construction (9 - 12), or Mathematics (9 - 12)

**Title:**The Clock Tower-Enhancing mathematics in the career/technical classroom and providing relevance in the mathematics classroom.

**Description:**This project resulted from the collaboration of a computer aided drafting teacher (pre-engineering), Chris Bond, and a math teacher, Lee Cable, (Hewitt-Trussville High School) to provide higher math expectations in CT and real life application in mathematics. As a hands-on, technology based project this activity demonstrates use of the Pythagorean Theorem, Sine, Cosine and Tangent to find unknown heights of objects and can be adapted for use by the computer aided drafting or mathematics teacher. Clinometers are used as a surveying tool and AutoCAD is used as a drawing tool. Students use a clinometer and a ruler or a tape measure to find and then record the length and angle measurements of a right triangle to determine unknowns. This information is then used to find unknown lengths and angles and to then create a drawing in AutoCAD. Proportion and scale will be used to draw a scale drawing of the clock tower at the new Hewitt-Trussville High School. In the mathematics classroom, students will produce scale drawings using graph paper instead of AutoCAD. This lesson will need to be adapted for use by other schools by selecting a different building structure for measure.

**Title:** I Can Determine The Height Of A Rocket!

**Description:**
The lesson is intended to give students a fun real-world experience in applying their math skills. They will use trigonometric ratios to calculate heights of tall structures. They will also use the Internet to convert their calculations from standard to metric units and visa versa.
**Standard(s): **

[MA2015] GEO (9-12) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [G-MG1]

**Subject:**Mathematics (9 - 12), or Technology Education (9 - 12)

**Title:**I Can Determine The Height Of A Rocket!

**Description:**The lesson is intended to give students a fun real-world experience in applying their math skills. They will use trigonometric ratios to calculate heights of tall structures. They will also use the Internet to convert their calculations from standard to metric units and visa versa.

**Title:** How tall is the school's flagpole?

**Description:**
The purpose of this lesson is to help students apply math concepts concerning similar triangles and trigonometric functions to real life situations. The students learn how to take these concepts and use them to find measurements of objects that they are unable to measure in conventional ways.
**Standard(s): **

**Subject:**Mathematics (9 - 12)

**Title:**How tall is the school's flagpole?

**Description:**The purpose of this lesson is to help students apply math concepts concerning similar triangles and trigonometric functions to real life situations. The students learn how to take these concepts and use them to find measurements of objects that they are unable to measure in conventional ways.

**Title:** On Top of the World

**Description:**
If you were standing on the top of Mount Everest, how far would you be able to see to the horizon? In this lesson, students will consider two different strategies for finding an answer to this question. The first strategy is algebraic-students use data about the distance to the horizon from various heights to generate a rule. The second strategy is geometric-students use the radius of the Earth and right triangle relationships to construct a formula. Then, students compare the two different rules based on ease of use as well as accuracy.
**Standard(s): **

[MA2015] ALC (9-12) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)

**Subject:**Mathematics

**Title:**On Top of the World

**Description:**If you were standing on the top of Mount Everest, how far would you be able to see to the horizon? In this lesson, students will consider two different strategies for finding an answer to this question. The first strategy is algebraic-students use data about the distance to the horizon from various heights to generate a rule. The second strategy is geometric-students use the radius of the Earth and right triangle relationships to construct a formula. Then, students compare the two different rules based on ease of use as well as accuracy.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12