Pythagorean Theorem Activity for Day 1

Grade Level Junior Subject: Pythagorean Theorem Prepared By: Amr Safwat & Duratio n:

Analyze Learners Overview & Purpose (STEMcinnati theme) Education Standards Addressed

What will learn and why it is useful. What state/county education standards that this lesson satisfies. Students will learn about the Pythagorean Theorem and about useful real life applications. They apply the theorem in a practice manner by constructing a ramp and using laser What state/county education standards that this lesson satisfies. beams. Physical Science: L.9D. 21. Demonstrate that motion is a ACS will be addressed later in the text measurable quantity that depends on the observer's frame of reference and describe the object's motion in terms of position, STEM will be addressed during the following four days as follows: velocity, acceleration and time.

Science: Travelling of laser rays, calculating speed and velocity Mathematics: 3a. Make, test and establish the validity of Technology: Reflection of light for light bulbs and methods to measure and calculated conjectures about geometric properties and relationships using different slopes counterexample, inductive and deductive reasoning, and paragraph Engineering: Building of bridges and ramps for various applications. Using lasers as or two-column proof, prove the Pythagorean Theorem; 4. security tools in banks and museums Calculate distances, areas, surface areas and volumes of Math: During the three days the students will have to measure different volumes, slopes composite three-dimensional objects to a specified number of distances. They also have to calculated slopes and develop linear equations. significant digits.

Note: The entire lesson is based on three days 45 minute period.

Teacher Guide Student Guide Select Goals and Objectives Goals and Catch (2 minutes): Have a Laser Distance Meter or The teacher will need a laser Materials Needed Objectives Ultrasonic distance ruler and measure the distance between distance meter or an ultra Paper (Specify skills/information that will the teacher and the opposite wall, then the teacher can sonic distance meter. (The Pencil be learned.) measure the distance to the upper corner of the wall. In the second one is not that Goal is to develop a sense the Calculators usage of Pythagorean theorem by next step he will draw the two measured lines on the board accurate like the first one, but Wooden frames using real life application during and ask the students how we can find the height between the still it is enough for the Mirrors that can be fixed to class period. two lines. purpose of this lesson.) the frame The teacher should at that point mention that in real life For details on the wooden Objectives are to 1) identify Laser beams lasers or other types of light waves are used to measure frame, mirrors and laser different applications where Sheets of paper with bull Pythagorean theorem can be distances between two points. In construction Laser Distance source please see eyes used. Meters are used to get the exact built distance or height of attachments at the end of this Measuring tools for distance 2) Demonstrate how Pythagorean two objects. A mobile GPS apparatus measures uses radio document. Theorem applications can be used Rulers outside the classroom. waves to compare the relative time of current location and 3) Experience Pythagorean the time off at least three satellites to calculate the exact Theorem by measuring different location on earth. objects using a variety of The teacher can draw a person standing on the earth and measuring tools. three satellites and three circles around the three satellites and show them where these circles intersect. The point of intersection is the point where the person is standing. By calculating the three distances the exact location of the person can be obtained. (Or show the student a glass with water and let a laser beam travel through the water.)

Ex. Catch and pre-assessment (7 minutes):

Option 1: The teacher needs to have enough laser distance meters. The students will build groups of 4 to 5 students and go outside and start measuring the heights of light poles.

Option 2: The teacher will bring 4 to 5 wooden frames where mirrors and, a laser source and a bull eye can be installed. The will have to calculate the travelled distance of the laser beam form point a to point b using n numbers of mirrors.

Pre-assessment questions 1. For a giving rectangle triangle with sides a=4m and b=3m, calculated c? 2. A laser beam is reflected ones see drawing, how far did the beam travel? 3. A concrete slide or ramp goes 3m high and it has the following dimension 2m wide, and 0.20 m thick. The slide stands on two columns which are 4 m apart from each other. Calculate the volume of the slide? 4. How can I get the length of b if a and c are given for a rectangle? Select Instructional Activity (20 minutes) Strategies – Option 1:  The teacher will ask the students to form Information groups of 4 or 5 people (Give and/or demonstrate necessary information) Option 2:  The teacher will ask the students to form groups of 4 or 5 people

Utilize Technology Each group has to submit all their Other Resources sketches and all calculations. (e.g. Web, books, etc.)

Require Learner Option 1: Laser Target Range Participation Common Misconceptions: Finder a. Students don't identify the variables as different  Each group will get a http://www.nextag.com/Sonin- legs on a right triangle Activity 10075-DT110BUNDLE- b. Students generalize that the Pythagorean laser distance meter (Describe the independent activity Includes-573954857/specs-html to reinforce this lesson) Theorem applies to all triangles and not only to and go outside to http://www.trimble.com/gps/how right triangles measure the heights of gps-triangulating.shtml a few objects http://gpsinformation.org/dale/th Essential question: Why do we need to learn about eory.htm Pythagorean Theorem?  They have to follow the teacher to make a sketch for measurement

Option 2:

 Each group will get a wooden frame and 3 or 4 mirrors and a laser source

 They have to follow the teacher’s instructions and use 2, 3, and 4 mirrors and calculate each time the laser’s traveled distance

 They have to make a sketch for each setting

Evaluate (Assessment) (2 minutes) At the end of DAY 1 the teacher should make Students should answer these Additional Notes sure that the students understood the objectives of this questions after 30 minutes of the (Steps to check for student day. These formative questions can be asked by the end class. understanding) of class.

1. Why do we need to learn about this theorem? Activity for Day 2- Pythagorean Theorem Grade Level Junior Subject: Pythagorean Theorem Prepared By: Amr Safwat & Duratio n:

Analyze Learners Overview & Purpose (STEMcinnati theme) Education Standards Addressed

What will be learned and why it is useful. What state/county education standards that this lesson Students will learn about the Pythagorean theorem and about useful real life satisfies. applications. They apply the theorem in a practice manner by constructing an ramp and using laser beams. Physical Science: L.9D. 21. Demonstrate that motion is a measurable quantity that depends on the observer's STEM will be addressed during the following four days as follows: frame of reference and describe the object's motion in terms of position, velocity, acceleration and time. Science: Travelling of laser rays, calculating speed and velocity Technology: Reflection of light for light bulbs and methods to measure and Mathematics: 3a. Make, test and establish the validity calculated different slopes of conjectures Engineering: Building of bridges and ramps for various applications. Using lasers as about geometric properties and relationships using security tools in banks and museums counterexample, inductive and deductive reasoning, Math: During the three days the students will have to measure different volumes, and paragraph or two-column proof, prove the slopes distances. They also have to calculated slopes and develop linear Pythagorean Theorem; 4. Calculate distances, areas, equations. surface areas and volumes of composite three- dimensional objects to a specified number of significant Note: The entire lesson is based on a 45 minute period. digits.

Teacher Guide Student Guide Select Goals and Objectives Goals and Catch (5 minutes): The teacher will The Students will have to build a ramp. Materials Needed Objectives show the students some maps online The maximum inclination for a slope in  Paper (Specify skills/information that will and show them how we can calculate Ohio is 8% (1:12).  Pencil be learned.) the distance from one place to the other The students will be given this number Goal is to develop a sense the  Scissors usage of Pythagorean theorem by using Pythagorean Theorem. and they will need to figure the length of  Cardboard using real life application during their ramp.  Rulers class period. 

Objectives are: 1) Describe what is that needed to be considered while constructing a concrete ramp to get from one level to higher level. 2) Determine how much concrete we will need to build this ramp.

Select Instructional Activity (35 minutes): The teacher will Strategies – explain to the students the dimension and limitations that they will need to Information consider while they are building their (Give and/or demonstrate necessary ramps. information)

Other Resources Utilize Technology (e.g. Web, books, etc.) Require Learner After the students have their design they Participation have to show it to the teacher before the actually can build it. After approval they Activity are allowed to build their ramps. (Describe the independent activity to reinforce this lesson) Students should sit with their group members and discuss how they want to build the ramp. They have to come up with some ideas and calculations and write them down. When the students are down with their ramps the teacher will come and verify and accept their ramp if they were built according to their designs.

Evaluate (Assessment) During this class the teacher should go The student are required not to exceed Additional Notes around and ask the students the the given maximum inclination of 8% (Steps to check for student following formative questions just to when they build their ramp. A maximum understanding) make sure that the students are on the distance to the or horizontal length of right track. part of the ramp should be given. The students will need to build to ramps 1. Do you think your design will hold and connect them to each other. Which all requirements? means that in order to get from one level to the next one the ramp will go with an inclination of 8% t 2. Are there any other ways or designs that are easier and use less material?

Height between floor level 1 and ceiling level 2 Height between level 1 & 2

Max length of ramp Activity for Day 3 – Group Discussion and designing class

Grade Level Junior Subject: Pythagorean Theorem Prepared By: Amr Safwat & Duratio n:

Analyze Learners Overview & Purpose (STEMcinnati theme) Education Standards Addressed

What will be learned and why it is useful. What state/county education standards that this lesson Students will learn more about the wastewater cycle and the different treatment ways. satisfies. They will focus on the biological treatment using microorganisms and they will also learn about all the input and output variables. What state/county education standards that this lesson satisfies. STEM will be addressed during the following four days as follows: Physical Science: L.9D. 21. Demonstrate that motion Science: The physical treatment methods within a wastewater treatment plant. is a measurable quantity that depends on the observer's Technology: The different treatment technologies specially the primary treatment frame of reference and describe the object's motion in methods are being introduced to the students. The students should terms of position, velocity, acceleration and time. also develop ways to make sure that the water has been cleaned. Engineering: Students will learn how different engineering professionals work Mathematics: 3a. Make, test and establish the validity together in a wastewater treatment plant and explore the how of conjectures about geometric properties and engineering applications are used in real life. relationships using counterexample, inductive and Math: During the three days the students will have to measure different volumes and deductive reasoning, and paragraph or two-column calculate used water and amounts of water after each physical treatment proof, prove the Pythagorean Theorem; 4. Calculate process. They also will learn to calculate different volumes. distances, areas, surface areas and volumes of composite three-dimensional objects to a specified Note: The entire lesson is based on a 45 minute period. number of significant digits.

Teacher Guide Student Guide Select Goals and Objectives Goals and Catch (5 to 10 minutes): Materials Needed Objectives The teacher should try to bring a Paper (Specify skills/information that will leveling instrument and show it to the Pencil be learned.) students and let them try it out. Goal is to develop a sense the Calculators usage of Pythagorean theorem by Gloves using real life application during Goggles class period.

Objectives are to 1) Explain how engineers make use of the Pythagorean Theorem on a daily base.

Select Instructional Activity (20 minutes): Students should The students will have to measure the Strategies – finish their ramps and calculate the time travelled and the distance the amount of concrete they would need to marble rolled down and they will need to Information order for that ramp. compute the velocity of the marble. (Give and/or demonstrate necessary Optional (The ramps can be used to information) calculate accelerations and velocities by Optional Problem to be solved. letting marbles roll down the ramp.) Buckling Sidewalk A concrete sidewalk between two buildings has been poured during 25°C. It consists of two slabs. Each slab is 3m long. The temperature is in the summer 48°C determine the y the buckled distance of the two slabs. dT= 23°C alpha= 12x10-6 dL= 12x10-6 x 3m x 23°C = 0.000828 Y=sqrt((3.000828²-3²))=0.0741m Presentation (5 minutes) Utilize Technology Definition of Pythagorean Theorem In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

ACS

Real World Applications: During this class the teacher will explain where the Pythagorean theorem is used in construction and architecture. Examples are the steel bridge over the Ohio river or the ramps used in parking garages.

Careers: At that point the teacher should also tell the students about the different engineering disciplines that use this theorem on a daily bases. Civil engineers have to use it all the time when the design construction pits, bridges, ramps and stair cases. Electrical engineers use it when they are designing different audio systems and light systems (GPS or Cell phone towers).

Societal Impact: Facts about Cincinnati, street lights and disabled friendly city structures like ramps on the sidewalks for disabled people. Require Learner Participation

Activity (Describe the independent activity to reinforce this lesson)

Evaluate (Assessment) (10 minutes) By the end of this class the Additional Notes Students will need to answer the (Steps to check for student assessment questions again. understanding) 1. For a giving rectangle triangle with sides a=4m and b=3m, calculated c? 2. A laser beam is reflected ones see drawing, how far did the beam travel? 3. A concrete slide or ramp goes 3m high and it has the following dimension 2m wide, and 0.20 m thick. The slide stands on two columns which are 4 m apart from each other. Calculate the volume of the slide? 4. How can I get the length of b if a and c are given for a rectangle?

Feedback This lesson went pretty well. The students had a lot of fun working with the lasers. The week when I taught my lesson was short schedule week, which meant that each period lasted only for 35 minutes instead of 45 minutes as originally planned. The students were not able to finish up their first assignment on the first day, so we had to give the students a few minutes during the next day to finish up their first assignment. The rest of the second day the student were introduced to the their second assignment, which was to go outside the classroom and measure the distance and height of different objects. The measuring rulers that we purchases were not laser measuring tools and were not very accurate. We had to change the originally planned scope for this activity. Originally, we wanted to ask the student to measure the height of a flag pole or the height of a door frame. The problem that we faced with the purchased ultrasonic measuring rulers (UR), that we couldn’t get accurate measurements when we tried to measure holding the under a certain angle in respect to the wall. The main issue with the UR is that it has to face the wall perpendicular in order to get accurate readings. The new assignment for the students was to go to the auditorium and measure the distance and height to ceiling on top of the stage. The students had in the next step to calculate the diagonal distance applying the Pythagorean Theorem. The students were also asked to find ways to measure to measure the width of the stage using indirect ways. Most of the students had a hard time to figure how to use measure the width and height of the stage. At the beginning of the last day I discussed with the students and showed them different real life application of the Pythagorean Theorem. In the next step the importance of using different ways to measure diverse object or distances by applying different ways. The students went back to the auditorium to measure the distances between the wall and the ceiling. By the end of this class most students understood how and why we can make use of Pythagorean Theorem in real life. Since we only had 35 minutes every day we couldn’t do the ramp exercise with the students. I think that this lesson can be taught in three days but the teacher should only let the students work on two exercises. If the teacher on or two more days that he/she can spend on this topic it is preferred to go through all the exercises. Attachments