You may recall the scene from the movie, “The Matrix”, where Laurence Fishburne’s character (Morpheus) says, “The matrix is everywhere. It is all around us.” You might be asking yourself the following - what is a matrix and how does it relate to math?
Not too long ago, matrices (plural of matrix) were a regular part of a student’s high school mathematics instruction. Some students would have learned about matrices and their operations in Algebra II to be able to solve systems of linear equations using Cramer’s Rule, inverse matrices, and possibly Gaussian elimination with reduced row echelon form. Even some teachers in the past even included matrix operations in Geometry to find the final image coordinates of figures following individual or multiple geometric transformations. These approaches allowed students to eventually be able to solve more complex problems and explore mathematics in more detail. For example in AP Calculus BC, matrices can be an efficient tool when performing partial fraction decomposition to make a complex rational expression easier to integrate. Beyond calculus, there is a whole course colleges offer devoted to Linear Algebra that studies linear equations and functions as represented by matrices and vectors and their extensions to various realms within mathematics and beyond. For example, cryptography sometimes uses a process of substitution ciphers and invertible matrices to break or decode encrypted messages.
However due to the recent implementation of the Common Core State Standards, there was a restructuring of math content in Algebra I, Geometry, and Algebra II courses. As a result, systems of linear equations and inequalities mainly to Algebra I - a course that PARCC-assessed and an exam whose passing score first became a Maryland high school graduation requirement last year. Despite the Common Core State Standard HSA.REI.C.9 stating, “Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater),” the standard has a (+) sign in front of it - which means the standard is targeted for advanced courses. However, this means that matrices will likely be non-assessed on PARCC and therefore likely to not be taught to your child. While systems of equations and inequalities are likely to be revisited to some degree in Algebra II, most of the focus in that course is now being able to solve nonlinear systems graphically and algebraically; thus reducing the likelihood of your child receiving instruction regarding matrices.
Currently, there are only a handful of schools in our area (public and private) that are teaching matrices in any of their mathematics course offerings - and in most of those cases, only to a select group of students (namely, Algebra II Honors). This begs the question - what’s the big deal about matrices likely not being in your child’s high school mathematics curriculum?
Answer: Matrices are still assessed on the Math section of the ACT exam. On the official description of the math section on the ACT website, matrices are fair game to be assessed in the following contexts:
Students will understand and reason with numerical quantities in many forms, including integer and rational exponents, and vectors and matrices.
The student will find solutions to systems of equations, even when represented by simple matrices, and apply their knowledge to applications.
While matrices are not a significant point of emphasis within the Math section of the ACT exam, at least one question involving matrices have been tested on several of the recently released ACT exams and administrations. Why is this important? Why have I spent all this time reading about something that may be asked perhaps only once on the test, if at all?
Answer: Every point on the ACT matters. Getting a question wrong can be the difference of a whole point on the Math section scale score that is used to calculate your composite score that colleges likely look at as part of your application process. That point could be the difference for admission and/or thousands of dollars in scholarships and grants.
While this piece focuses on matrices, there are other items that the Math section of the ACT exam assesses that schools have eliminated or taught to only certain groups of students - such as application and use of the Law of Sines and Law of Cosines (some schools teach this in certain Geometry classes, but many others wait until Pre-Calculus, if at all), and Logic (a staple of Geometry curriculum in the past that I haven’t seen since the change in standards). The same arguments made for matrices could be made for these topics that could have a tangible impact on your ACT score.
With the upcoming ACT administration on March 20 offered to all Anne Arundel County Public Schools juniors (as well as future tests available to all public and private school students in April, June, and July), now is a great time to enroll your child at C2 Education to receive high-quality tutoring and instruction tailored to your child’s needs from Dr. Ron, Mr. Josh, and/or myself.
Students at C2 Education see on average a seven-point improvement on the Math section of the ACT exam and a six-point composite score increase. C2 Education tutoring services are not limited to the ACT exam, as students average 121 points higher on the Math sections of the SAT exam and a 122-point increase overall. Our tutors also work with students for curricular tutoring in Mathematics (elementary through calculus), English (elementary and secondary), Physics (regular through AP), and college prep.
Please give us a call (410-421-8080), an email (firstname.lastname@example.org), or check us out (601 Baltimore Annapolis Blvd., Suite 202, Severna Park, MD 21146) to schedule a time to begin your child’s journey to improved scores and grades with a free diagnostic assessment.
This blog post was written by our very own tutor (and math wiz) Jonathan Maggart.