Introduction
A very long time ago this man named Pythagoras discovered the theorem about triangles. When the triangle has a right triangle (90 degrees) and the sauqre of the hypotenuse (which is the longest side out of the three sides) is equal to the sum of the squares of the other two sides (the shorter two). There is a magical formula and it is called 'Pythagorean Theorem formula'
Emily and Caden are sibilings, like sibilings, they go to school together every day and also have different opinions. They have two routes to get to the school, first route is going 3 blocks south, then 4 blocks east. The second route is going diagonal across and get to the school. Emily says the first route is faster, but Mark is older and have learned some math and did some timing so he says the second route is faster. Help them find out who is right and why!
Task
Your task is to find out which route is faster by using Pythagorean Theorem!
1) Read a little history and find out what the pythagorean Theorem formulas is (The following website could help and give you more information)
2) Draw out a map
- Draw a compass(label north, east, south, west) and measure units (One block=one inch) on the bottom right of paper
- Mark Emily and Caden's house in the middle of the paper
- Draw a line 3 blocks (inches) south from their house, then draw another line 4 blocks (inches) east. Then place the school there. connect the house and the school (it should be a diagonal line).
- Write down the length of them and name the sides a,b, and c for the longest side.
3) Find out the length for side c by using Pythagorean Theorem formula, you should have side a and b.
4) After finding out what side c is, add up a and b because that's one route then compare which route is shorter.
5) Answer the questions, who is right? Emily or Caden? And why?
6) Now create your own word problem using the pythagorean theorem and solve it!
Process
Here are some things you need to do!
- Read some history and learn some facts about Pythagorean Theroem in the following link. Write down 3 things you have learned from this link.
- Find out what the Pythagorean Theorem formula is and how to solve all the sides of the right triangle!
- Draw out the houses and school and label each side a,b, and c being the longest side. (After connecting the lines, it should end up to look like a right triangle)
- Using the Pythagorean Theorem formula find out the length of side c (Hypotenuse, the longest side)
- Compare the two routes
- Which route is faster? Who is right? Emily or Caden?
- Make your own story and solve it!
- Need more practices? Click practices and it will give you a good amount of practices!
- That was easy? Here are some games for you! Click games and it will link you to a fun game!
Evaluation
This is how you will get your points!
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1 |
2 |
3 |
4 |
Scores |
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3 facts |
No facts presented |
1 fact presented |
2 facts presented |
3 facts presented |
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Pythagorean Theorem Formula |
No formula presented/ incorrect formula and no examples |
Partial formula presented correctly and no examples
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Correct formula but no examples presented |
Correct formula and example presented on how to solve using formula |
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Drawing and Labeling |
No drawing presented |
Triangle only, no houses, schools or any labeling. |
Triangle and labeling presented |
Compass, measure units, school, and house are drawn out, also all 3 sides are labeled correctly. |
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Determine distance from house to school |
No answer |
Show all work using the incorrect formula and get incorrect answer |
Show all work using the correct formula but did some calculations wrong. |
Show all the work and using the formula correctly to find the answer and have the correct units. |
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Final answer |
No answer |
One sentence unclear answer |
Two sentence answer with almost every detail |
A very detailed paragraph explanation |
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Create your own problem and solve it |
No problem presented |
Create a problem with not much details |
Create a detailed problem but did not solve it |
Create a detailed problem and solved it correctly |
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Total |
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Conclusion
Congratulations! You are finally able to use and get a better understanding of this new formula to find out the sides of a right triangle and to help people that are like Emily and Caden out! Now people can get to school or work faster with the way you showed them and proved them!
Did you succesfully find out the correct answer today using the new formula you just learned? Were you able to make your own problem and challenge someone else?
Tell your teachers:
What's one thing you like about this?
What's one thing you dislike about this?
What's one thing you would change?
Credits
Teacher Page
Teacher's Introduction:
This WebQuest is to provide the things students need in terms of learning and getting a better understanding of Pythagorean Theorem. After the students complete the tasks, they should get a better understanding on this material and are able to use it to solve real world problems. This lesson will allow students learn things by themselves and get an opportunity to see things a different way and also get them thinking more!
This WebQuest is for students who are in 7th-8th grade.
Standards:
Explain a proof of the Pythagorean Theorem and its converse.
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.