Cramers Rule - Solving Systems of Equations
Lesson 8 of 12
Objective: SWBAT efficiently solve systems of equations using determinants of matrices.
Once they settle into their seats, students should answer the Warm-Up Clicker Questions located on page 2 of the Flipchart - Cramer's Rule. The questions ask students to solve a system of equations problem using matrices. The context is calculating the cost of an individual item, given information about multiple item purchases. My goal for this activity is for students to quickly review solving systems by using inverse matrices. I will encourage my students to solve these using matrices, but I will not require it (MP4, MP7). I will observe that strategies students choose to use and ask them about their choices.
During this Warm-Up, I allow students to use calculators. It is beyond the scope of this class (time-wise and content-wise) for students to find the inverse of a 3x3 matrix a calculator (see HSA-REI.C.9). One issue that requires attention, then, is the interpretation of the outputs from the calculator. My students often get confused when they get to the stage of texting their answer to me. They are asked for the cost of the eraser, but the calculator will return three values, the costs of a pencil, a pen, and an eraser. For the benefit of students who were not picking up on the structure of the answer matrix I ask, "What were the three unknowns in the system of equations?" If this does not help them, I suggest a "longer path." I encourage students to try all the different amounts to see which satisfies one of the equations in the system. Although this is not very efficient, it tends to help students to construct a meaningful understanding of the structure of the answer matrix.
Closure + Homework
Today marks the end of a big concept, solving systems of equations using matrices, so this will be a good time to check in with my students. To close out today’s lesson, I have students complete a 3-2-1 Assessment. The scope of the questions includes our progress in this matrices unit thus far. The prompts are included on page 3 of the Flipchart-Cramer's Rule. I plan to address some of the questions during the beginning of class tomorrow and on the test review day.
As the students complete the 3-2-1 reflection, I assign the Homework: Matrices Test Review (Problems #1-17) for homework. Instead of practicing using a variety of homework assignments, student should be working to complete their test review. On the test review day students will be expected to have their packet done. In order to assess their progress with the homework, I will give them a clicker Homework Quiz at the start of class on the Review Day.