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Project 16 : Pascal's Triangle

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Rakhee Mishra

                                                                             


Mathematics Project 16

 “Pascal’s Triangle: Patterns, Properties, and Possibilities”

📝 Task:

You are to research, explore, and creatively present the mathematical structure known as Pascal’s Triangle. The project should be compiled in a scrapbook, chart, booklet, or digital format.

🔍 Research Pointers (You are to find out and explain these in your own words):

Part A: Construction

1.     How is Pascal’s Triangle constructed?

2.     What are the rules for generating the next row?

Part B: Patterns and Properties

Explore and explain at least 5 of the following (more if you wish):

1.     Symmetry in Pascal’s Triangle.

2.     The sum of each row – what pattern do you see?

3.     Diagonals in Pascal’s Triangle and the number sequences they form (like triangular numbers, natural numbers).

6.     Fibonacci numbers hidden in the triangle.

7.     The powers of 11 in the early rows.

8.     The pattern of even and odd numbers (try coloring these).

9.     Any other interesting pattern or property you discover on your own.

Part C: Creative Presentation

Pick any one:

  • Create a colored chart or artwork based on patterns found in Pascal’s Triangle.
  • Write a short poem, paragraph, or comic that creatively tells the story of Pascal’s Triangle.
  • Make a model or 3D display.
  • Design a poster highlighting your favorite 3 patterns.

Part D: Reflection

Write a short reflection (100–150 words) on:

  • What you discovered about Pascal’s Triangle.
  • What surprised you the most.
  • How you felt doing this project.

✅ Final Submission Should Include:

  • Construction of the first 10 rows of Pascal’s Triangle.
  • Explanations of at least 5 properties or patterns.
  • Creative piece (artwork, model, poem, etc.).
  • Reflection paragraph.

📊 Marking Scheme (Total = 50 marks)

 

Component

Criteria

Marks

a

Pascal's Triangle Construction

Accuracy, neatness, visual clarity

10 marks

b

Exploration of 5+ Patterns

Understanding, clarity, correct examples

15 marks

c

Creative Element

Poster, model, poem, comic art, etc

10 marks

d

Reflection Paragraph

Thoughtfulness, personal insight

5 marks

e

Presentation & Organisation

Layout, headings, flow, visuals

5 marks

f

Extra effort

More than 5 patterns, uncommon property, exceptional creativity

5 marks

 

📌 Note to Students:

This is a research-based project. All explanations must be written in your own words. Use books, the internet, or videos to explore — but don’t copy-paste. Be original, be curious, and most importantly — enjoy the magic of patterns in mathematics!

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Location: Ajmer, Rajasthan, India

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