Objective: 

Students will explore the relationship between functions and inverse functions by creating their own encryption and decryption algorithms, focusing on mathematical functions that can encode and decode messages.

Materials Needed: 

• Paper

• Pencils

• Function tables

• Graphing templates

• Cipher wheels (optional).

Steps:

• Introduction: 

  • Begin by introducing the concept of a function as a rule that assigns each input to one output, explaining that an inverse function “reverses” the process. 

  • Provide an example of an encryption function (e.g., adding 5 to each number in a sequence) and show how the inverse function (subtracting 5) decrypts the message.

• Group Activity: 

  • Students will work in pairs to create their own encryption function using addition, subtraction, multiplication, or division. 

  • Each pair will generate a table of inputs and outputs for their function and calculate the inverse to decrypt a message.

• Testing and Refining: 

  • Once their encryption and inverse functions are created, pairs will exchange encrypted messages and apply their inverse function to decode each other’s messages. 

  • Afterward, they refine their methods to ensure accuracy.

Equity and Access: 

Provide visual function charts or pre-drawn tables for students who need extra support, and ensure mixed-ability pairing to encourage peer learning.

Real-World Application: 

Discuss how encryption functions are used to secure digital data, connecting to modern cybersecurity practices that rely on functions and their inverses to protect sensitive information.

CS Practice(s): 

• Recognizing and Defining Computational Problems: Students analyze the mathematical relationship between functions and inverse functions, applying them to solve the problem of secure message transmission.

Standard(s):

• CA CCSS Mathematics 8.F.1

• CA CS 6-8.NI.6 

Objective: 

Students will use Scratch, App lab, or another coding platform to create encryption and decryption functions, applying basic mathematical operations such as addition or multiplication to secure and decode messages.

Materials Needed: 

• Computers or tablets

• Reference sheets with mathematical concepts

Steps:

• Introduction: 

  • Students learn the basic concept of encryption, where a message is transformed using a function, and decryption, where the inverse function is used to decode the message.

• Group Activity: 

  • In pairs, students will use a coding platform to create a simple encryption program. For example, they can write a function that adds 3 to each letter’s position in the alphabet to encode the message. 

  • They will also create a corresponding decryption function that subtracts 3 to return the message to its original form. For example, using Scratch’s “ask” and “answer” blocks, they will input and output encrypted messages.

• Testing and Refining: 

  • After completing their programs, students will exchange encrypted messages with another pair. 

  • They will use their decryption function to decode the message and debug their program if necessary. 

  • Students will discuss how their function’s complexity impacts the security of the encryption.

Equity and Access: 

Provide pre-made coding templates with example encryption blocks for students who need extra support. Pair students with varying coding experience to foster collaboration.

Real-World Application: 

Connect this lesson to real-world examples of simple encryption methods, like those used in basic website security or protecting personal information, and explain how encryption complexity is crucial in digital safety.

CS Practice(s): 

• Creating Computational Artifacts: Students code simple encryption and decryption programs, understanding how computational tools are used to secure and decode information.

Standard(s): 

• CA CCSS Mathematics 8.F.1

• CA CS 6-8.NI.6