I decided not to give direct instruction. Instead, I found this perfect handout on ILoveMath.org outlining in minute detail how to do exactly what I wanted students to do ... enter the coefficient matrix, enter the constant matrix, and then set up the product of the inverse of the coefficient matrix and the constant matrix.
I put students in groups of 3 or 4 and gave them all the handout. Included were 6 systems, 4 of which were 3 x 3; and then also a set of five word problems.
Before they began working, I asked teams to brainstorm elements of teamwork in math. Every team offered an element. We put them on the board and we agreed that we would work with those elements in mind. Most classes offered elements like these ... in the pic.Students read the detailed instructions, and worked through the plain problems. They checked their work with my key. Then they worked together to solve the word problems. If the whole team got stuck, they could ask questions, and I offered to counter their questions with questions. In a few instances I had to offer more assistance than questions.
Students worked for about an hour in their teams. They all learned to use their calculator to solve matrix equations and worked 11 problems. I was freed to help those that needed me most. A great day for sure!
Thanks for sharing, sounds fun. I am interested in knowing the differences between our (UK) curriculum and yours. At what age do you teach matrices, and is it taught to all pupils?
ReplyDeleteAdvanced students may be introduced to matrices in the middle school (grades 6 - 8) as enrichment. It is not a part of the curriculum until Algebra 2 (after algebra 1, and geometry). So typically students will not see matrices until grades 9-11. Matrices are taught to all students at that time. BUT we teach a limited number of skills. So students learned how to add/subtract and multiply by hand. We taught how to find the determinant and the inverse by hand - but only with 2x2 matrices. All the rest of the skills were practiced using a TI 83/84 calculator. We did not teach cramer's rule, or augmented matrices or gaussian this year.
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