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

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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.

Warm-Up

10 minutes

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.

Explanation and Practice

30 minutes

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.

 

 

Closure

10 minutes

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!