Reading Assessment Anchors Addressed:

R8.A.1.3.1

R8.A.2.1.2

R8.A.2.2

R8.A.2.3

Objectives:

The students will be able to use the Pythagorean Theorem to find the measure of a missing side of a right triangle in application problems.

The students will be able to convert customary measurements up to 2 units above or below the given unit.

The students will be able to convert time up to 2 units above or below the given unit.

The students will be able to use, describe, and/or develop procedures to determine measures of area.

The students will be able to identify, use, and/or describe properties of triangles and circles.

Instructional Strategies and Plan (include strategies used to help different types of learners, i.e. auditory, visual, etc):

Step1: Anticipatory Set

In groups of four, students will work on the following warm up problems (worksheet provided).

If a leg of a triangle is 3 ft long, and another leg is 4 ft long, what is the length of the hypotenuse?

Solve for “x” in the following right triangle.

Could these three measurements be the lengths of a right triangle’s sides?

(Show your work to prove your answers.)

a) 20 ft, 25 ft, 15 ft _________

b) 9 in, 40 in, 41 in _________

c) 18 cm, 15 cm, 8 cm _________

Each group will be responsible for explaining one of the previous problems on the board.

Step 2: Follow Up Practice Problems

In groups of four, students will work on the following word problems (worksheet provided).

Practice Problem 1

A hiker leaves camp and walks five miles due west, and then heads 12 miles due north. He calls the camp on his walkie talkie and tells them he is lost.

a. How far away from the camp is the hiker?

b. If the hiker walks at a rate of 2.5 miles per hour, how long, in hours and minutes, will it take him to get back to camp?

Practice Problem 2

A garden is in the shape of a right triangle. It has one side that is 21 ft long, and has a hypotenuse of 29 ft.

a. What is the length of the other side of the garden?

b. How many feet of fencing must be purchased to enclose the garden?

c. Assume the fencing must be purchased by the yard. If the fencing costs $11.95 per yard, how much money will you spend on fencing?

Each group will be responsible for explaining one of the previous problems on the board.

Step 3: Applying the Pythagorean Theorem

The students will go back to their seats and the PNC Park project is introduced. Each student will work on the project independently.

Materials/Resources: Packet includes diagram of ballfield, dimensions, and questions. Prior knowledge of Pythagorean Theorem is needed (see below).

Playing Ball at PNC Park

PNC Park is the fifth home of the Pittsburgh Pirates since their inception in 1887. The fledgling National League franchise first began play at Recreation Park, located at the corners of Grant and Pennsylvania Avenues along the Fort Wayne railroad tracks on the North Side. The club then moved to Exposition Park in 1891, which was situated along the Allegheny River between the new ballpark site and where Three Rivers Stadium formerly stood. After 18 years at Exposition, including hosting the first World Series in 1903, the Bucs moved to Forbes Field in Oakland on June 30, 1909. The club spent 61 seasons at Forbes, its longest tenure at any facility, before moving to Three Rivers Stadium on July 16, 1970.

Perhaps the strongest inspiration for PNC Park's design is the legacy of the Pirates themselves. Few cities can boast of a 115-year relationship with the same Major League ballclub.

PNC Park, which opened in spring 2001, is a classic-style ballpark, an intimate facility that embraces the progressiveness of Pittsburgh while saluting the spirit of early ballpark originals such as Forbes Field, Wrigley Field and Fenway Park.

The irregularly shaped, natural grass playing field measures 325 feet down the left foul line and 389 feet through the left field power alley. The park reaches its greatest distance of 410 feet at a nook located just left of center field.

The distance down the right field foul line is 320 feet, 375 feet down the power alley, and 399 feet to center field.

The outfield wall rises up to 21 feet behind right field (in honor of the Pirates legendary right fielder #21, Roberto Clemente) and drops down to just six feet in front of the left field bleachers.

From home plate to the Allegheny River is 443 feet, 4 inches.

** information courtesy of Major League Baseball

http://pittsburgh.pirates.mlb.com/NASApp/mlb/pit/ballpark/index.jsp

1. What is the total distance traveled around the bases by a player that hits a homerun?

2. What is the area of the infield (only inside the base paths)?

3. What is the distance from home plate to second base?

4. What is the length of a throw from third base to first base?

5. Home plate is 60 feet 6 inches from the pitcher’s mound. Is the pitcher’s mound centered? If not, is it closer to home or second base?

6. What is the length of a throw from the right field corner to third base?

7. What is the length of a throw from the left field corner to second base?

8. What is the area of the grass outfield?

Hints: average distance from home plate to back wall is 370 feet; see Infield Diagram for infield radius.

9. If one five-pound bag of grass seed covers an area of one hundred square yards, how many five-pound bags are needed to re-seed the outfield?

10. If a five-pound bag of grass seed costs $10.72, what is the total cost, including a 6% sales tax?

BONUS #1

Use the internet to find the dimensions of the three bases, home plate, and the pitcher’s mound to calculate the area of each and their combined area. All answers must be in square inches.

BONUS #2

Use the following conversion factor to solve the problem.

Pitched baseball = .025 mi/s

Home plate is 60 feet 6 inches from the pitcher’s mound. How many seconds would it take a ball to travel 60 feet 6 inches?

The students will be given two class periods to complete the project. The following day, the students will share their strategies and procedures used to solve the problems.

Interdisciplinary Connections:

· Reading – word problems

· Technology- overhead projector, calculator, Internet

· Other-History

Assessment Strategies:

· Formative Evaluation (checking student understanding during the lesson):

- informal observation

- opening activities (on the board)

- verbal feedback/checking for understanding

· Summative Evaluation (How will it be determined that the objectives were achieved?):

- answers to project

- 100% accuracy on numbers 1-5

- 75% accuracy on numbers 1-8

- 25% accuracy on numbers 1-10

Correctives/Remediation: Review Pythagorean Theorem and help students to pick out pertinent information concerning dimensions

Extensions/Enrichment: Field trip to PNC Park or go to the school baseball field and act out the questions

Special Accommodations (special needs students)

· Description of the Special Needs student selected:

Male student, disinterested in school, loves to draw

· Accommodations to use with this student:

- Preferential seating

- Immediate feedback

- Group work

- Periodic engagements with student (verbal and non-verbal cues)

- Challenge him to incorporate math in drawings

- Give reference page with an example of Pythagorean Theorem

Keyword: Pythagorean Theorem

Warm-Up Problems

4. If a leg of a triangle is 3 ft long, and another leg is 4 ft long, what is the length of the hypotenuse?

5. Solve for “x” in the following right triangle.

6. Could these three measurements be the lengths of a right triangle’s sides?

(Show your work to prove your answers.)

a) 20 ft, 25 ft, 15 ft _________

b) 9 in, 40 in, 41 in _________

c) 18 cm, 15 cm, 8 cm _________

Practice Problem 1

A hiker leaves camp and walks five miles due west, and then heads 12 miles due north. He calls the camp on his walkie talkie and tells them he is lost.

c. How far away from the camp is the hiker?

d. If the hiker walks at a rate of 2.5 miles per hour, how long, in hours and minutes, will it take him to get back to camp?

Practice Problem 2

A garden is in the shape of a right triangle. It has one side that is 21 ft long, and has a hypotenuse of 29 ft.

b. What is the length of the other side of the garden?

d. How many feet of fencing must be purchased to enclose the garden?

e. Assume the fencing must be purchased by the yard. If the fencing costs $11.95 per yard, how much money will you spend on fencing?

Playing Ball at PNC Park

** information courtesy of Major League Baseball

http://pittsburgh.pirates.mlb.com/NASApp/mlb/pit/ballpark/index.jsp

11. What is the total distance traveled around the bases by a player that hits a homerun?

12. What is the area of the infield (only inside the base paths)?

13. What is the distance from home plate to second base?

14. What is the length of a throw from third base to first base?

15. Home plate is 60 feet 6 inches from the pitcher’s mound. Is the pitcher’s mound centered? If not, is it closer to home or second base?

16. What is the length of a throw from the right field corner to third base?

17. What is the length of a throw from the left field corner to second base?

18. What is the area of the grass outfield?