Mathematical Secrets: Exploring Cryptography
Created byRachel Hansen
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Mathematical Secrets: Exploring Cryptography

Grade 7Math3 days
★★★★★
4.0 (1 rating)
In this project, seventh-grade students explore the intriguing world of cryptography, utilizing mathematical principles to decode and create ciphers. Through an engaging inquiry framework, including activities such as an Escape Room Challenge and a Cipher Creator's Workshop, students apply mathematical concepts like substitution ciphers and numeric shifts. The project enhances critical thinking and problem-solving skills and reveals the historical impact of cryptography, guiding students to understand its significance in past and present contexts. Aligning with Common Core Standards, this comprehensive learning experience equips students with a strong foundation in mathematical applications within cryptography.
CryptographyMathematicsCiphersProblem-SolvingPatternsHistorical Significance
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we use math to unlock the secrets of cryptography in daily life and history?

Essential Questions

Supporting questions that break down major concepts.
  • What is cryptography and how is it used in everyday life?
  • How do mathematical concepts apply to creating and decoding ciphers?
  • Why is understanding equations important in the study of cryptography?
  • How can patterns and structures in math help us to understand and develop coding methods?
  • In what ways has cryptography shaped historical events and modern society?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Students will understand the basic principles of cryptography and its historical significance.
  • Students will be able to apply mathematical equations and concepts to solve cryptographic problems.
  • Students will learn how to use patterns and structures in math to create and decode simple ciphers.
  • Students will develop critical thinking and problem-solving skills through practical cryptography applications.
  • Students will explore the impact of cryptography on society and historical events.

Common Core Standards

7.EE.B.3
Primary
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically and applying properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.Reason: This standard relates to cryptography as it involves solving multi-step problems using mathematical operations, similar to decoding ciphers which may require conversion between different forms of numbers.
7.EE.B.4a
Primary
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.Reason: Developing ciphers and decoding require understanding and creating equations and inequalities, aligning well with constructing and solving mathematical problems.
8.F.A.1
Supporting
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.Reason: Understanding functions helps in recognizing patterns, which is key in decoding and creating cryptographic algorithms.

Entry Events

Events that will be used to introduce the project to students

Escape Room Challenge

Transform the classroom into an escape room where students must decrypt mathematical puzzles to "escape" within a time limit. This immersive environment promotes engagement and challenges them to apply their mathematical knowledge creatively to solve complex problems under pressure.
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Portfolio Activities

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.
Activity 1

Cipher Creator's Workshop

Students begin by crafting simple substitution ciphers using alphabetic shifts. This workshop introduces cryptography by allowing students to create their own secret messages. They'll use basic mathematical translations to assist in the encoding and decoding process, laying a foundational understanding of substitution methods.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Introduce students to the concept of substitution ciphers and the alphabetic shift technique (e.g., Caesar cipher).
2. Provide a step-by-step guide on how to create a substitution cipher using numeric shifts based on the alphabet.
3. Ask students to write a sentence and encode it using their cipher system.
4. Exchange ciphers with a partner to decode each other's messages.

Final Product

What students will submit as the final product of the activityA personalized substitution cipher and an encoded message.

Alignment

How this activity aligns with the learning objectives & standardsAligns with standard 7.EE.B.3 by engaging students in the conversion between numbers and letters and applying operations to create solutions.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Cryptography Portfolio Assessment Rubric

Category 1

Understanding of Cryptography

Measures students' grasp of cryptographic concepts and historical significance.
Criterion 1

Conceptual Understanding

Evaluates the student's comprehension of cryptography principles and their historical context.

Exemplary
4 Points

Demonstrates a sophisticated understanding of cryptographic principles and articulately explains their historical significance with detailed examples.

Proficient
3 Points

Shows a thorough understanding of cryptographic principles and provides a clear explanation of their historical context using relevant examples.

Developing
2 Points

Displays emerging understanding of cryptographic principles with a basic explanation of their historical context.

Beginning
1 Points

Shows initial understanding of cryptographic principles and struggles to explain their historical context.

Criterion 2

Application of Mathematical Concepts

Assesses the student's ability to apply mathematical concepts to solve cryptographic problems.

Exemplary
4 Points

Applies mathematical concepts innovatively to solve cryptographic problems, demonstrating exceptional integration of skills.

Proficient
3 Points

Effectively applies mathematical concepts to solve cryptographic problems, showing successful skill integration.

Developing
2 Points

Applies mathematical concepts inconsistently, showing partial skill integration in solving cryptographic problems.

Beginning
1 Points

Struggles to apply mathematical concepts, demonstrating limited skill integration in solving cryptographic problems.

Category 2

Cipher Creation and Decoding Skills

Evaluates students' ability to create and decode ciphers using mathematical operations.
Criterion 1

Cipher Creation

Measures the student's ability to create a substitution cipher using numerical shifts.

Exemplary
4 Points

Creates a highly effective substitution cipher using complex numerical shifts, demonstrating exceptional creativity and understanding.

Proficient
3 Points

Successfully creates a substitution cipher using numerical shifts, demonstrating solid understanding.

Developing
2 Points

Creates a basic substitution cipher with some errors in numerical shifts, showing emerging understanding.

Beginning
1 Points

Struggles to create a functional substitution cipher, demonstrating limited understanding of numerical shifts.

Criterion 2

Cipher Decoding

Assesses the student's ability to decode ciphers accurately and efficiently.

Exemplary
4 Points

Decodes ciphers with high accuracy and efficiency, demonstrating exceptional problem-solving skills.

Proficient
3 Points

Accurately decodes ciphers with few errors, demonstrating solid problem-solving skills.

Developing
2 Points

Decodes ciphers with some accuracy, but with several errors, showing basic problem-solving skills.

Beginning
1 Points

Struggles to decode ciphers accurately, demonstrating minimal problem-solving skills.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning
Question 1

What did you find most challenging about applying mathematical concepts to cryptography during this project, and how did you overcome it?

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Required
Question 2

On a scale from 1 to 5, how well do you understand the use of equations in creating and decoding ciphers after this project?

Scale
Required
Question 3

Which essential question from the unit do you feel you have the best understanding of, and why?

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Question 4

How do you think the skills and concepts you've learned in this project can be applied to real-world situations or future learning experiences?

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Required
Question 5

Which entry event (e.g., Escape Room Challenge) was most impactful to your learning and why?

Multiple choice
Required
Options
Escape Room Challenge
Cipher Creator's Workshop