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# Matrix Transformations

Lesson 10 of 12

## Objective: SWBAT apply matrix operations to perform transformations in the coordinate plane.

## Big Idea: Students employ the transformation matrices they discovered yesterday to manipulate figures in the plane.

*54 minutes*

#### Discovery & Application

*35 min*

Although I will lead today’s activities, I like to have my students seated in teams so that they can discuss the problems and help each other through any difficulties they face. I plan to use mixed ability groups today. I feel that it would be okay to have a student take the lead, if necessary, without inhibiting other students from learning from our work today.

After the Warm Up is complete, I will start off with Page 4 of the Matrix Transformations Flipchart. I plan to give students about 5 minutes to explore linear shifts of a geometric figure. Students will be working on a large grid. The point of this activity is to refresh students' memory of how changes in the x-coordinate cause a horizontal translation, while vertical translation results from change in the y-coordinate. It is also important for students to see the diagonal slide that results from a two-dimensional shift.

After this review, the goal of the lesson gives students time to practice using matrices to perform transformations in the coordinate plane (**HSN-VM.C.12**). On pages 5-6, I will help students to accurately model a geometric figure in the coordinate plane. Then, I will relate this to our work yesterday with the discovery of transformation matrices. There are questions to check for understanding of this concept on pages 7-8.

The remaining pages are designed for independent practice (**MP1, MP2**). The tasks are fun for students, so direct instruction is not really required. Students know, but come to better understand, that scalar multiplication of a matrix dilates the figure. I find it helps for them to persevere and infer that multiplying by a 2x2 matrix results in rotations and/or reflections of a figure (

**MP1, MP7**). Students should be encouraged to understand how these 2x2 matrices are derived and NOT memorize them (see lesson on determining the matrix for transformations).

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#### Wrap Up

*5 min*

Today is the last day of new learning for students in this unit. In light of this fact, I plan to have students reflect on their learning by completing a **Think-Pair-Share**. I will ask students to identify 3 things they have learned during this unit, then pair up and share what they learned with their tablemates. My goal for this wrap-up is for students to reflect on what have done, and to motivate them to begin to think synthetically about what they understand well and what they will want to focus on learning with more depth before the Unit Test.

#### Resources

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#### Homework

*4 min*

Before ending class, I will remind students that they should be completing the Matrices Test Review for homework as preparation for tomorrow's class. Students will be expected to have their packet done. I will give them a clicker Homework Quiz at the start of class to hold them accountable.

#### Resources

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Environment: Suburban

- 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