Prime Code Challenge: Math Encryption Project
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we, as mathematicians and code designers, use the properties of prime numbers, geometric patterns, and probability to develop a secure and innovative coding system that protects sensitive information in real-world scenarios?Essential Questions
Supporting questions that break down major concepts.- How can prime factorization be used to create a secret code?
- How do prime and composite numbers differ, and why is this important for code security?
- How can patterns in number sequences help us generate more complex codes?
- In what real-world scenarios is secure coding essential?
- How can we use mathematical operations and properties to encode and decode messages?
- How do geometric principles, like tessellations and angles, inspire creative coding techniques?
- How can probability help us assess the strength and reliability of our codes?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Understand and apply the properties of prime, composite, square, and triangular numbers.
- Use prime factorization to design and implement a secure coding system.
- Apply number patterns and sequences to generate complex codes.
- Utilize mathematical operations, including brackets and arithmetic combinations, to encode and decode messages.
- Incorporate geometric principles, such as tessellations and angle relationships, to enhance coding techniques.
- Assess code reliability using probability.
- Solve practical problems related to area and spatial reasoning to optimize code design.
- Communicate mathematical reasoning and problem-solving strategies effectively.
- Design algorithms that use rules to generate sets of numbers and identify emerging patterns.
Victorian Curriculum
Entry Events
Events that will be used to introduce the project to studentsPrime Rewards Program
A local business owner needs help creating a customer loyalty program based on prime numbers. Students explore prime factorization to develop unique customer codes and rewards, connecting math to real-world business strategies.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Prime Number Pioneers
Students will begin by exploring the definitions and properties of prime and composite numbers. They will identify prime numbers within a given range and differentiate them from composite numbers.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA chart or table that lists prime numbers up to 100 and explains the difference between prime and composite numbers with examples.Alignment
How this activity aligns with the learning objectives & standardsAddresses VC2M6N02 by focusing on understanding and identifying prime numbers, which is fundamental for the entire project. It also introduces composite numbers and their relationship to prime numbers.Factorization Masters
Students will learn how to break down composite numbers into their prime factors using factor trees and division methods. They will practice prime factorization with various numbers to understand its uniqueness.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA collection of factor trees or division ladders showing the prime factorization of various composite numbers.Alignment
How this activity aligns with the learning objectives & standardsFocuses on VC2M6A02 by requiring students to use mathematical operations to find factors, and VC2M6N02 by applying prime factorization to solve problems related to code creation.Code Creation Algorithm
Students will develop an algorithm to generate a unique code for each customer based on prime factorization. They will assign each letter of the alphabet a number and then use prime factorization of that number to create a unique code.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA written algorithm that explains how to generate a unique code for a customer, along with sample codes for different names.Alignment
How this activity aligns with the learning objectives & standardsDirectly aligns with VC2M6A03, as students design an algorithm to generate a unique code based on prime factors. Also supports VC2M6N02 by using prime number properties.Pattern-Based Code Expansion
Students will explore how number patterns and sequences, such as Fibonacci, can be used to generate more complex codes. They will create codes using these sequences and mathematical operations, including brackets and arithmetic combinations, to encode messages.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA detailed explanation of how number patterns and arithmetic operations can be used to generate complex codes, along with sample encoded and decoded messages.Alignment
How this activity aligns with the learning objectives & standardsThis activity supports VC2M6A01 by having students recognize and use number patterns, and VC2M6A02 by incorporating brackets and combinations of arithmetic operations to encode and decode messages.Code Refinement and Reliability Assessment
Students will refine their coding system based on feedback and testing. They will also assess the reliability of their codes using probability, determining the likelihood of code duplication or being cracked.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA refined coding system with an assessment of its reliability, including a discussion of potential weaknesses and suggestions for improvement.Alignment
How this activity aligns with the learning objectives & standardsThis activity builds upon the previous activities and reinforces VC2M6N02, VC2M6A01, VC2M6A02, and VC2M6A03 by applying all the learned concepts to refine and test the code system. It also introduces VC2M6P01 by assessing code reliability using probability.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioPrime Code Challenge Rubric
Prime Number Fundamentals
This category assesses the student\'s ability to accurately identify and explain prime and composite numbers, which is foundational for the coding project.Prime Number Identification and Explanation
Accuracy in identifying and listing prime numbers up to 100. Clear differentiation between prime and composite numbers with relevant examples.
Exemplary
4 PointsAccurately lists and identifies all prime numbers up to 100 with clear, comprehensive explanations and examples of both prime and composite numbers.
Proficient
3 PointsAccurately lists and identifies most prime numbers up to 100 with good explanations and examples of prime and composite numbers.
Developing
2 PointsIdentifies some prime numbers correctly but includes errors or omissions. Explanations of prime and composite numbers are basic and may lack clarity.
Beginning
1 PointsStruggles to identify prime numbers correctly and provides unclear or incorrect explanations of prime and composite numbers.
Prime Factorization Techniques
This category evaluates the student\'s ability to perform prime factorization using factor trees and division methods.Prime Factorization Proficiency
Skill in creating factor trees or using division ladders to perform prime factorization. Accuracy and completeness in breaking down composite numbers.
Exemplary
4 PointsDemonstrates mastery in creating factor trees and using division ladders for prime factorization. Accurately and completely breaks down a wide variety of composite numbers with detailed steps.
Proficient
3 PointsProficiently creates factor trees and uses division ladders for prime factorization. Accurately breaks down most composite numbers with clear steps.
Developing
2 PointsCreates factor trees and uses division ladders with some errors or omissions. Struggles to accurately break down composite numbers consistently.
Beginning
1 PointsStruggles to create factor trees or use division ladders effectively. Shows limited understanding of prime factorization.
Code Creation Algorithm Design
This category focuses on the student\'s ability to design an algorithm for generating unique customer codes using prime factorization.Algorithm Design and Code Generation
Clarity and completeness of the algorithm for generating unique customer codes based on prime factorization. Effectiveness in producing distinct codes for different inputs.
Exemplary
4 PointsThe algorithm is exceptionally clear, comprehensive, and effectively generates unique customer codes with detailed explanations and justifications for each step.
Proficient
3 PointsThe algorithm is clear, complete, and effectively generates unique customer codes with good explanations for each step.
Developing
2 PointsThe algorithm is somewhat unclear or incomplete, resulting in inconsistent code generation. Explanations may be vague or missing.
Beginning
1 PointsThe algorithm is unclear, incomplete, and ineffective in generating unique codes. Lacks explanations and demonstrates a limited understanding of algorithm design.
Complex Code Generation
This category assesses the student\'s ability to use number patterns and arithmetic operations to generate complex codes, including the clarity and accuracy of encoding and decoding instructions.Pattern-Based Code Complexity
Application of number patterns and arithmetic operations to generate complex codes. Clarity and accuracy of encoding and decoding instructions. Complexity and security of the generated code.
Exemplary
4 PointsDemonstrates innovative use of number patterns and arithmetic operations to generate exceptionally complex and secure codes with crystal-clear encoding and decoding instructions.
Proficient
3 PointsEffectively uses number patterns and arithmetic operations to generate complex codes with clear and accurate encoding and decoding instructions.
Developing
2 PointsShows basic understanding of number patterns and arithmetic operations but struggles to generate truly complex codes. Encoding and decoding instructions may be unclear or contain errors.
Beginning
1 PointsDemonstrates limited understanding of number patterns and arithmetic operations. Unable to generate complex codes or provide clear encoding and decoding instructions.
Code Reliability and Improvement
This category evaluates the student\'s ability to refine their coding system based on feedback and testing, and to assess its reliability using probability.Code Refinement and Reliability
Thoroughness in testing the coding system, incorporating feedback, and refining the algorithm. Accurate assessment of code reliability using probability, and insightful discussion of potential improvements.
Exemplary
4 PointsConducts extremely thorough testing, incorporates feedback effectively, and significantly refines the algorithm. Provides a highly accurate assessment of code reliability using probability and offers insightful, actionable suggestions for improvement.
Proficient
3 PointsConducts thorough testing, incorporates feedback, and refines the algorithm. Provides an accurate assessment of code reliability using probability and offers practical suggestions for improvement.
Developing
2 PointsConducts limited testing, partially incorporates feedback, and makes some refinements to the algorithm. Assessment of code reliability is basic and suggestions for improvement are limited.
Beginning
1 PointsConducts minimal testing, struggles to incorporate feedback, and makes few or no refinements to the algorithm. Unable to assess code reliability effectively or suggest meaningful improvements.