John has tutored algebra and SAT Prep and has a B.A. degree with a major in psychology and a minor in mathematics from Christopher Newport University.
After studying this lesson about Thales and Pythagoras, your students will be able to:
- Describe the early lives of Thales and Pythagoras
- Explain several of the contributions to geometry made by the two men
- Recount how these contributions are still used to this day
1 - 1.5 Hours
- Copy of the text lesson Thales & Pythagoras: Early Contributions to Geometry, along with the related lesson quiz
- Internet access
- Protractors (with a small center hole)
- Straw (not the bendy type)
- String (about one-foot in length)
- Tape (clear)
- Weight (small weight, a small metal nut will work)
- Print copies of isosceles right triangle found below in the activity instructions
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
- Let your students know they will be studying the two famous Greek mathematicians Thales and Pythagoras.
- Ask them if anyone is familiar with the two men, or has studied them previously.
- Read the short introduction to this lesson.
- Start the video Thales & Pythagoras: Early Contributions to Geometry and pause the video for the first time at 0:45.
- What does the field of geometry entail?
- Now, restart the video and pause this time at 2:14.
- What five contributions did Thales make to geometry?
- Next, restart the video again and pause this time at 3:32.
- What four contributions did Pythagoras make to geometry?
- Now, restart the video and pause for a final time at 4:02.
- Which of the contributions by the two men is used most today?
- Restart the video and watch the 'Lesson Summary' section on the two mathematicians.
- Have your students take the lesson quiz to demonstrate their newfound knowledge of the two men.
- Inform your students they will participate in an exciting hands-on activity that will combine some of the concepts taught by both Thales and Pythagoras.
- Tell them: We know that Thales was famously able to calculate the height of the Great Pyramid and that Pythagoras specialized in geometry. Today we are going to apply those concepts, and go outside and measure the height of a tall tree.
- Divide students into pairs and each pair will need to make a measuring device.
- First, thread about one inch of the string through the hole in the middle of the protractor's straight edge and fasten it with a piece of tape or simply tie it on.
- Next, attach your weight to the opposite end of the string and tape this or tie it on as well.
- Tell your class: Congratulations! You have just created your very own clinometer.
- Take the class outside.
- Students will continue working with their partner. Tell the pairs to:
- Pick out a tall tree, telephone pole, or building you wish to measure. You will need an ample clearing in which to walk away from the object.
- Locate the top of the tree by peering through the straw.
- Have your partner check to see the angle in which the string is falling across the protractor.
- Move backward or forward until the clinometer reads 45 degrees.
- Measure the distance on the ground from the tree to where you are standing.
- Have your partner measure the distance between the ground and your eyes.
- Add these two totals together and this also equals the distance to the top of the tree.
- Provide each pair with a copy of the following image of an isosceles right triangle.
- Ask students to review the image with their partner and develop an explanation for how and why this activity allowed us to find the height of the tree. Why was having the clinometer read 45 degrees important?
- Ask partners to record a written explanation that may be turned in later for grading purposes.
- Allow students to share their explanations with the class correcting any inaccuracies.
- Euclid was also from Greece, and by many experts is considered to be geometry's founder. Write a one-page paper detailing some of his major accomplishments.
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