Florida B.E.S.T. MA.912.NSO.4.2

MathGrades 9–12Represent and perform operations with matrices.

The Standard

Given a mathematical or real-world context, represent and solve a system of two- or three-variable linear equations using matrices.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students translate a two-variable or three-variable system into an augmented matrix. They apply row operations to solve for each variable, then interpret and check the result.
What Mastery Looks Like: Students organize equations into an augmented matrix with consistent variable columns. They use valid row operations, find the solution, and check it in the original equations.
Common Misconceptions: Students may place coefficients in the wrong columns or forget zero coefficients for missing variables. They may make sign errors during row operations or change only part of a row.
How to Assess It: Exit ticket: Use an augmented matrix to solve x + y + z = 6, x - y + z = 2, and 2x + y - z = 1. Show each row operation.

Lesson moves

Give pairs laminated equation cards and matrix tiles, then have them build an augmented matrix and row reduce it.
Ask students to explain why swapping two matrix rows does not change the solution set of the original system.
Run an error hunt where teams find and correct one faulty row operation in each worked matrix solution.
Model ticket sales with three ticket types, write equations from totals, and use a matrix to find how many were sold.

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