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# Determinants and Area of a Triangle (Day 1 of 2)

Lesson 3 of 12

## Objective: SWBAT calculate the determinant of 2x2 and 3x3 matrices.

## Big Idea: Students discover a method to calculate the determinant of a 2x2 matrix and practice using an inner-outer circles activity.

*50 minutes*

#### Warm-Up

*10 min*

To introduce this lesson, I will first use page 2 of today’s flipchart, Determinants and Area of a triangle (day 1 of 2), to introduce some facts about determinants and let students know that this is what we are studying today.

Then I would like to see if students can find the pattern to calculate the determinant of a 2x2 matrix without being told the how to find it. I will ask students to analyze the determinants of the problems in today’s Warm-up, determinants of 2x2 matrices in a **Think-Pair-Share**. This is also on page 3 of today’s flipchart to display to the class. I will give students about 2 minutes of independent think time to see if they can find the pattern on their own. Then I will ask students to team up for about 5 minutes to make sure they find a pattern that will solve for the determinant in each matrix given. That will leave a few minutes for teams to share what they discovered.

I am not sure if my students are going to be successful at finding the pattern. So if I find no teams have figured it out during the team time, I will present the hint on page 4 of today’s flipchart. My goal is for students to figure out the pattern themselves (or at least have a team mate describe the pattern in student friendly terms) to improve their retention and understanding of the formula used to calculate the determinate of a 2x2 square matrix.

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#### Explanation and Practice

*30 min*

Once students have shared their explanations as to how to calulate a determinant for a 2x2, I am going to formalize the process by presenting pages 2-4 of Determinants and Area of a triangle (day 1 of 2) to my class. This resource introduces the notation and methods for calculating the determinants of a 2x2 matrix. I emphasize to my students that the value of the determinant is a number, not a matrix. In order to demonstrate this I model the process using the examples on page 4.

Next, in order to give them some practice with calculating determinants I plan to have the class complete an Inner-Outter Circles activity** **with the Flash Cards.

After giving students time to work with the Flash Cards, I use the flipchart (pages 7-11) to introduce students to finding the determinant of a 3x3 matrix. I present two different methods to my students. I give my students the option to use whichever method they find more sensible. I will model the two methods using the problem on page 9. And then I will have students try their selected method on the problem located on page 11 of the flipchart.

**Teaching Note**:

- Since absolute value and a determinant use the same notation, it is not possible to use absolute value in this case.

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#### Closure

*10 min*

To close out today’s learning, present page 12 of the Determinants and Area of a triangle (day 1 of 2) flipchart. The closure task asks students to summarize their learning today by writing a **Postcard to Absent Student**. This is a challenging closer task. Students will have to be very precise in their explanations to be able to communicate this to an absent student!

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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