Introduction
As secret agents infiltrating the hideout, you have discovered a major secret: THE SECRET ROOM IS IN THE ROOFTOP OF BLOCK THREE!
However, you are afraid that the enemy may intercept your message! What are you waiting for? Encrypt your message, ready to be sent to your boss! Don't wait before it's too late...
Task
In pairs, come up with a pair of encryption and decryption matrix as encryption and encryption keys for the message "THE SECRET ROOM IS IN THE ROOFTOP OF BLOCK THREE".
Task 1: Illustrate how your matrix (encryption key) is able to encrypt the message. Show the multiplication steps clearly.
Task 2: Derive a suitable matrix for decryption. Show your derivation steps clearly.
Task 3: Illustrate how the matrix (decryption key) works. Show the multiplication steps clearly.
Task 4: Individually, submit a 1-page reflection of about 300-350 words comprising:
- 3 concepts of matrices learnt during this webquest
- 2 aspects of teamwork learnt (i.e. strengths and weaknesses of partner)
- 1 question unresolved in this Webquest
Submit a print-out or a handwritten solution to all 4 tasks by the start of next lesson.
Process
Complete the following processes in this order:
2) Adding and Subtracting Matrices
3) Multiplying Matrices
b) Zero matrix
4) Inverse of an matrix (2 x 2)
a) Determinant
5) Encryption and decryption of a 2 x 2 matrix
Evaluation
| Criteria |
Exceeds Expectation 3 |
Achieving Expectation 2 |
Meeting Expectation 1 |
| Mathematical accuracy |
In the first 3 tasks, students demonstrate mathematical mastery and with minimum or negligible errors. Concepts of matrices are well-demonstrated through the encryption and decryption process. The matrix used for encryption and decryption are of order 3 x 3. |
In the first 3 tasks, students demonstrate strong mathematical mastery though sometimes errors made can be disastrous. However, these errors are few in number and not plenty. Concepts of matrices are understood and demonstrated through the encryption and decryption process. Knowledge of 2 x 2 is present though students find it challenging to process 3 x 3 matrices. Matrix used for encryption and decryption is of order 2 x 2. |
In first 3 tasks, students demonstrate numerous errors in mathematical mastery. Concepts of matrices poorly demonstrated through basic 2 x 2 matrices. Matrix used is identical to the examples used to demonstrate encyption...found in the Process page. |
| Reflection piece |
Able to point out both strengths and weaknesses of group mate. Identifies at least 3 concepts learnt related to matrices. At least 1 question posed. |
Only focuses on either a strength or a weakness of group mate. Identifies at least 2 concepts learnt related to matrices. At least 1 question posed. |
Does not answer to the question requirements. |
Conclusion
Matrices are very important and they can be used to solve real-world problems.
Click on the link here to see more of matrices in action!
