Mathematics (Unsolved Problems) By Miss Mwanda

Introduction

WELCOME FUTURE MATHEMATICIANS !!!!

1,032 Mathematician Illustrations & Clip Art

 

Grade: 11

In this WebQuest you will do a research and analyze information related to complex mathematical problems. Create and explain an equation that relates to the complex mathematic problem being analyzed.  

Keywords: Mathematics, unsolved problems, complex problems, discovery.

 

Mathematics is often taught as a history lesson. Because most learners think that Greeks or some ancient civilization discovered everything there is about Mathematics and today we just relearn what they figured out thousand of years ago. This couldn't be further from the truth. Mathematics is constantly growing and still has many.

 

For example; You already know the Pythagorean Theorem or A^2+B^2= C^2, but did you know that no solution exist for A^3+B^3= C^3? Its true, there are no positive integers that can substitute for A,B and C that will make that statement true (actually it is also true for any exponent higher than 2). This idea (conjecture) called Fermat's Last Theorem was proposed in 1637, but it took mathematics 385 years to evolve enough to be able to prove this idea, in 1994. 

It is also important to note that in mathematics "solving a problem" does not necessarily mean you end up with a specific answer. As in the example above, proving that no solution can possibly exist to a problem, is a way of "solving" a mathematical problem.  

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Task

 

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In a group of 5 learners, you will explore some links and dive deeper to find an unsolved math problem to share with the class. Remember! the report must be entirely in your own words, be original in both your assessment of the problem and your choice of the problem. Try to describe the problem as accurately as you can, the problems you will read about are very unique: The aim of this project is for  you to get exposure to exotic mathematics concepts and explore the edges of our current mathematical understanding.

ATTENSION: Bonus points will be given to learners who choose mathematical problems that no one else chose in the class!

I want you to consider your relationship to the problem's solution. Numerous learners tend to believe that they could never be successful in mathematics because they wrestle to understand math, however, this is probably because you see the questions and solutions with a different perspective than the mathematicians that wrote your book or developed the techniques you are learning about. Having your unique perspective and life experience could be exactly what is needed to solve a major unsolved problem.

Remember to be creative and do not be afraid to take risks in your descriptions, your grade will be determined by the effort you put into the project and not your ability to understand exotic mathematics. So have fun! 

 

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Process

LET THE JOURNEY BEGIN!

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TASK 1

1. Form a group of 5.

2. From the sources below choose an unsolved problem that interest you.

3. Go to these sources : http://mathworld.wolfram.com/UnsolvedProblems.html.

 

                                       

 

 

 

 

 

 

 

TASK 2

 

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Use MS Word for the task; you can use your books to make a draft of your report.

1. Compose a report about your unsolved problem:

  • Identify the problem with any common names you could find.

2. Write a short report (300-500 words) that provides the following:

 

 

TASK 3

1. Create your own equation to describe the problem.

You can look for ideas here: https://brilliant.org/wiki/setting-up-equations/#basic-steps-to-setting-up-equations

2. Define the term of the equation in your own words.

 

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TASK 4

1. Describe what steps you would take to solve this problem from where you are now.

Example: I would take a calculus course to study mathematics in college/university, and seek a graduate degree in ____ (a specific of mathematics), then begin tackling the problem. (not more than100 words).

 

 

TASK 5

1. Finally, you and your partners will create a presentation of your report using PowerPoint slides. It should be as follows:

  • 1st slide: Subject, Grade, Name and surname of group members.
  • 2nd slide: task 2 
  • 3rd slide: task 3
  • 4th slide: Task 4

2. You will do oral present of your project in class during your maths period. Your overall mark will be given after you complete the oral presentation.

NB choose 1 group member to do the whole presentation.

 

Task 6

DO NOT FORGET TO CITE YOUR SOURCE!

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Evaluation

THIS IS HOW YOUR WORK WILL BE EVALUATED. 

There are 2 rubrics to evaluate your project:

1st : to evaluate your written report.

2nd: to evaluate your oral presentation.

RUBRIC FOR REPORT

Aspect

 Excellent  5 Good 3 Weak 1

Total Score

 

 

Description of the problem 

(10)

The description of the problem is clear and provides sufficient evidence of learners' attempt to understand and convey the problem in the learners' own words

 

 The problem description is clear or provides sufficient evidence of students' attempt to understand and convey the problem in the leaners' own words. The problem description is either provides clear nor provides sufficient evidence of students' attempt to understand and convey the problem in the learners' own words.  

The equation of the problem.

(15)

The equation adequately describes the problem as explained by the student and the terms used in the equation are clearly defined and logically utilized 

 

 The equation adequately describes the problem as explained by the learner or the terms used in the equation are clearly defined and logically utilized. The equation either adequately describes the problem as explained by the learner nor are the terms used in the equation clearly defined and logically utilized  

Learners' path to solve the problem in the future.

(10) 

The learner outlines a future plan to solve the problem in adequate details and the plan is clear and actionable.

 

 The learner outlines a future plan to solve the problem in adequate details or the plan is clear and actionable 

The learner outlines a future plan to solve the problem neither in adequate detail nor is the plan clear and actionable.

 

  
Total score 35        

 

RUBRIC FOR ORAL PRESENTATION

Categories  Unsatisfactory Basic Excellent  Total score 

Mathematical Concepts

(5)

 Displays errors in knowledge of mathematical concepts. Explains mathematical concepts without difficulty, but expresses ideas in rudimentary form. Fully and eloquently articulates mathematical concepts. Develops connections among mathematical concepts.  

Mathematical Procedures

(5)

 Has difficulty explaining mathematical procedures. Explains mathematical procedures without difficulty Explains mathematical procedures without difficulty and provides full explanations for why mathematical procedures are valid or appropriate  

Mathematical Representations (equations, diagrams, graphs, tables, etc.)

(5)

 Representations are inappropriate or unclear. Representations clear and appropriate, but no connections are made between representations. Representations are clear and appropriate, with explanations of significant elements. Clearly explains connections among mathematical representations.  

Presentation Structure

(5)

 The presentation has no clearly defined structure, or the structure is chaotic. The presentation has a recognizable structure with an introduction and conclusion. The presentation has a clearly defined structure with elegant transitions and an effective introduction and conclusion  

Oral Communication

(5)

 Does not speak clearly or demonstrates consistent grammatical errors. Speaks clearly with no grammatical errors. Speaks clearly and effectively in a sophisticated manner.  

Total score 25

        

 

Overall mark for the project is 35+25= 60 marks

 

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Conclusion

Congratulations you have reached your destination!

 

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Now you have a richer understanding of mathematics that includes greater knowledge of questions that mathematicians are still working on. You also have a plan on how you could begin to solve this particular problem. Remember that your unique perspective, idea, and intuition might just be what is required to solve this problem. YOU CAN CHANGE THE WORLD!

 

Credits

https://www.quora.com/What-are-the-top-10-topics-for-a-mathematics-project-with-a-model-for-class-11-and-class-12

https://www.youtube.com/watch?v=OYAflCOm-W8&t=3s 

https://www.youtube.com/watch?v=6O90SWlfKe8&t=33s

https://youtu.be/8COArd_EREw

https://en.wikipedia.org/wiki/Mathematics#:~:text=Beginning%20in%20the%206th%20century,axiom%2C%20theorem%2C%20and%20proof.

Teacher Page

In this WebQuest learners will complete a research and analyze information related to complex mathematical problems. Create and explain an equation that relates to the complex mathematic problem being analyzed. 

Leaners will be in groups of 5 to complete the task. They will first  explore some links with information and videos to watch, to find unsolved mathematics problems. They will therefore choose an unsolved problem that interests them, write a report in their own words based on the unsolved problem, they are not required to come up with a solution of a problem.  They will complete 6 tasks.

 

The aim of this project is for the learners to get exposure to exotic mathematics concepts and explore the edges of our current mathematical understanding.