After Quiz Activities
I will use this page to have students investigate future or past topics after quizzes. Use this time to explore for yourself, find cool and interesting tidbits and just become a curious learner.
After 1.1 - 1.3 Quiz
Desmos Investigation into Function Transformations (What's My Transformation?)
1) Go to student.desmos.com and type in the class code shown at the front of the room.
2) Enter your first and last name after clicking "Continue Without Signing In," unless you want to use a Google sign in.
3) Go through the activity. Be sure to answer questions by writing COMPLETE SENTENCES. Also, click SUBMIT TO CLASS before going to the next slide when typing in a response.
4) Get as far as you can in class (preferably to slide 12) as this topic will be a nice preview and help set the foundation for a future lesson. With a few minutes left in class, I will tell you to pause your progress and close your device. It will not be homework so long as the class was making genuine progress after the quiz. (Note: Slide 13 is a real challenge if you want to push yourself).
5) Have fun exploring and learning!
2) Enter your first and last name after clicking "Continue Without Signing In," unless you want to use a Google sign in.
3) Go through the activity. Be sure to answer questions by writing COMPLETE SENTENCES. Also, click SUBMIT TO CLASS before going to the next slide when typing in a response.
4) Get as far as you can in class (preferably to slide 12) as this topic will be a nice preview and help set the foundation for a future lesson. With a few minutes left in class, I will tell you to pause your progress and close your device. It will not be homework so long as the class was making genuine progress after the quiz. (Note: Slide 13 is a real challenge if you want to push yourself).
5) Have fun exploring and learning!
After 2.1 - 2.3 Quiz
Desmos Investigation into the Fundamental Theorem of Algebra (Polynomials and Roots)
1) Go to student.desmos.com and type in the class code shown at the front of the room.
2) Enter your first and last name after clicking "Continue Without Signing In," unless you want to use a Google sign in.
3) Go through the activity. Be sure to answer questions by writing COMPLETE SENTENCES. Also, click SUBMIT TO CLASS before going to the next slide when typing in a response.
4) Get as far as you can in class as this topic will be a nice preview and help set the foundation for a future lesson. With a few minutes left in class, I will tell you to pause your progress and close your device. It will not be homework so long as the class was making genuine progress after the quiz.
5) Have fun exploring and learning!
2) Enter your first and last name after clicking "Continue Without Signing In," unless you want to use a Google sign in.
3) Go through the activity. Be sure to answer questions by writing COMPLETE SENTENCES. Also, click SUBMIT TO CLASS before going to the next slide when typing in a response.
4) Get as far as you can in class as this topic will be a nice preview and help set the foundation for a future lesson. With a few minutes left in class, I will tell you to pause your progress and close your device. It will not be homework so long as the class was making genuine progress after the quiz.
5) Have fun exploring and learning!
After 3.1-3.3 Quiz
Practice ACT Questions
Approximately 50% of the class will take the ACT this spring and 40% will take it the following spring. The math covered on the ACT goes from Pre-Algebra through what we cover in this class by this upcoming spring. Because that is a large breadth of material, it is important you practice pieces in chunks well ahead of time. When you take the actual math portion of the ACT, you will have 60 minutes to answer 60 questions, so around 1 question per minute. We are going to practice some today.
Using the PDF below, set a timer for 15 minutes and attempt just questions 1-15. You can check your answers in the key I've supplied. If you don't understand an answer, feel free to message me for help.
Using the PDF below, set a timer for 15 minutes and attempt just questions 1-15. You can check your answers in the key I've supplied. If you don't understand an answer, feel free to message me for help.
act_math_practice_test_1.pdf | |
File Size: | 3563 kb |
File Type: |
act_math_practice_test_1_key.pdf | |
File Size: | 1466 kb |
File Type: |
After 4.1-4.3 Quiz
Practice ACT Questions
Approximately 50% of the class will take the ACT this spring and 40% will take it the following spring. The math covered on the ACT goes from Pre-Algebra through what we cover in this class by this upcoming spring. Because that is a large breadth of material, it is important you practice pieces in chunks well ahead of time. When you take the actual math portion of the ACT, you will have 60 minutes to answer 60 questions, so around 1 question per minute. We are going to practice some today.
Using the PDF below, set a timer for 15 minutes and attempt just questions 16-30. You can check your answers in the key I've supplied. If you don't understand an answer, feel free to message me for help.
Using the PDF below, set a timer for 15 minutes and attempt just questions 16-30. You can check your answers in the key I've supplied. If you don't understand an answer, feel free to message me for help.
act_math_practice_test_1.pdf | |
File Size: | 3563 kb |
File Type: |
act_math_practice_test_1_key.pdf | |
File Size: | 1466 kb |
File Type: |
After _______ Quiz
A Story from the History of Math
Path of Shortest Descent: The Brachistochrone
The story of the brachistochrone begins in 1696. The Swiss mathematician Johann Bernoulli (for those in Calculus, he is the mathematician who tutored l'Hopital and from whom l'Hopital stole the famous rule used to evaluate limits) challenged the world to solve a simply stated problem:
"find the path that allows a ball to move down a ramp in the shortest amount of time."
Most believe it to be a straight line, but you may be surprised by the solution.
"find the path that allows a ball to move down a ramp in the shortest amount of time."
Most believe it to be a straight line, but you may be surprised by the solution.
Johann pulbished his challenge in a journal that read:
"I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise."
Bernoulli allowed six months for the solutions, but none were received during this period. At the request of another mathematician, the time was publicly extended for a year and a half. On January 29, 1697 the challenge was received by Isaac Newton, who found it in his mail, in a letter directly from Johann Bernoulli, when he arrived home from the Royal Mint at 4 p.m. He stayed up all night to solve it and mailed the solution anonymously by the next post. Upon reading the solution, Bernoulli immediately recognized its author, exclaiming that he recognizes a "lion from his claw mark." This story gives some idea of Newton's power, since Johann Bernoulli himself took two weeks to solve it. Newton also wrote, "I do not love to be dunned [pestered] and teased by foreigners about mathematical things."
Now, watch the video below concerning the brachistochrone in real life and then answer the questions below the video. (I have about 4 or 5 headphones to borrow in class above the calculators, otherwise use your own or turn on subtitles by clicking on the CC button in the lower right portion of the video)
"I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise."
Bernoulli allowed six months for the solutions, but none were received during this period. At the request of another mathematician, the time was publicly extended for a year and a half. On January 29, 1697 the challenge was received by Isaac Newton, who found it in his mail, in a letter directly from Johann Bernoulli, when he arrived home from the Royal Mint at 4 p.m. He stayed up all night to solve it and mailed the solution anonymously by the next post. Upon reading the solution, Bernoulli immediately recognized its author, exclaiming that he recognizes a "lion from his claw mark." This story gives some idea of Newton's power, since Johann Bernoulli himself took two weeks to solve it. Newton also wrote, "I do not love to be dunned [pestered] and teased by foreigners about mathematical things."
Now, watch the video below concerning the brachistochrone in real life and then answer the questions below the video. (I have about 4 or 5 headphones to borrow in class above the calculators, otherwise use your own or turn on subtitles by clicking on the CC button in the lower right portion of the video)
Questions for Brachistochrone Video (watch from 16:43 to 24:15):
1) The shortest distance (a straight line) produces the fastest or slowest path?
2) Qualitatively, the brachistrochrone is the fastest because it balances which two aspects of the movement?
3) What does tautochrone mean?
4) A brachistochrone is also a tautochrone, which means what in terms of where you drop the ball on the ramp and the time it takes to get to the bottom?
1) The shortest distance (a straight line) produces the fastest or slowest path?
2) Qualitatively, the brachistrochrone is the fastest because it balances which two aspects of the movement?
3) What does tautochrone mean?
4) A brachistochrone is also a tautochrone, which means what in terms of where you drop the ball on the ramp and the time it takes to get to the bottom?