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# Applications of Inverses - Decoding

Lesson 6 of 12

## Objective: SWBAT apply inverse matrices to solve a matrix equation.

*48 minutes*

#### Warmup

*5 min*

To begin today's class, I plan to give students a couple of minutes to discuss the codes on page 2 of the Flipchart. I introduce the task by challenging my students to determine what the coded phrases might represent.

As students complete their work decoding the 6 ciphers, I ask them to remain quiet and read the first two paragraphs of the Decode the Encode handout. Once all of the students complete their decoding, we will discuss the possible meanings of each string as a class.

After discussing the six codes, I will give students a minute or so more to read the first two paragraphs of Decode the Encode. When they finish reading, we will have a brief discussion of ways that codes are used to write things in other ways. I plan to ask students, “Do you know of any other ways besides codes and testing where we replace a message or information with other words, symbols, or numbers?” I expect students may come up with codes such as: zip codes, area codes, state abbreviations, etc.

**Teaching Note**: Prior to today’s lesson you will need to prepare the cards used in the Decode the Encode Activity in the application part of today’s lesson. I chose to copy these on card stock and just cut apart the five clues. If you want minimal prep work, you really could copy all the codes on one sheet just as it is. *You will also have to hide a small prize somewhere in the north-west corner of your classroom in a rectangular prism. *

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#### Closure + Homework

*3 min*

During the last three minutes of class, I will ask students to stop what they are working on so that we can summarize the Decode the Encode activity as a class. I will take questions from students and clarify any code they had difficulty decoding. I expect that this may be a bit hectic with some teams working to decode the codes and others already looking for the treasure. Even so, it is important to summarize each group's progress and address any difficulties that teams encountered.

At the end of class, I will ask my students to work on Matrices – Join the Madness for homework.

#### Resources

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Basic Matrix Operations
- LESSON 2: Matrices in the World Around Us
- LESSON 3: Determinants and Area of a Triangle (Day 1 of 2)
- LESSON 4: Determinants and Area of a Triangle (Day 2 of 2)
- LESSON 5: Inverses of Matrices
- LESSON 6: Applications of Inverses - Decoding
- LESSON 7: Solving Systems of Equations using Inverse Matrix Operations
- LESSON 8: Cramers Rule - Solving Systems of Equations
- LESSON 9: Determining the Matrix for Transformations
- LESSON 10: Matrix Transformations
- LESSON 11: Matrices Test Review
- LESSON 12: Matrices Exam