## Common Core Math 2 North Carolina Scope and Sequence

19 Nov

As Common Core Math becomes more widely used and debated, I continue to analyze the effectiveness of this new curriculum.  The traditional approach of teaching mathematics in high school was to teach Algebra 1, Geometry, Algebra 2, Pre-Calculus (or some type of equivalent such as a Functions and Modeling Class), and then Calculus / Discrete Math / Probability and Statistics.  You may wonder what the reason was for putting Geometry between Algebra 1 and Algebra 2.  My personal belief from experience is because students need to have a certain level of mathematical maturity to be able to handle topics in Algebra 2.  Geometry is usually an easier class so following the order Algebra 1, Geometry, Algebra 2 allows students to work in a progression from easier to harder and develop mathematical maturity along the way.  In fact, one school in our county tried switching to Algebra 1, Algebra 2, then Geometry for a year and found it didn’t work as well so they switched back.

With the new Common Core, states have the choice of implementing the standards with a traditional sequence such as Algebra 1, Geometry, Algebra 2 or doing an integrated approach which mixes topics into Integrated Math 1, 2, and 3.  North Carolina chose the integrated approach.  In Common Core 1 (Integrated Math 1), students learn a few units on Statistics and then focus mostly on Algebra 1 topics.  However, when they take Common Core 2, the students are taking a course that is almost all Algebra 2 concepts with even some concepts from Advanced Functions and Modeling (the course that would follow Algebra 2) added as well.  Very little Geometry is introduced in Common Core 2, it is almost exclusively a course on functions.

The first unit deals with transformational Geometry where students learn about reflections, rotations, and translations.  They also spend time just barely being introduced to the idea of congruent and similar triangles.  They do some review of distance formula, midpoint formula, midsegment of a triangle, and then the focus shifts to Algebra 2 topics.  The second unit deals with quadratic equations including converting to vertex form by completing the square, finding the x and y intercepts, and graphing.  There is a huge focus on translations of functions, starting with quadratics but moving into translations of every function type you can think of.  The third unit deals with radicals, rational exponents, solving exponential equations, solving equations with rational exponents and radicals.  Students solve equations by converting to the same base and using logs.  Students must understand, compute, and use inverse functions to solve equations and graph.  Students also do applications of exponential equations such as half-life and compound interest.  In the following unit, graphing becomes the focus again.  Students use translations and graph rational functions, greatest integer functions, absolute values, square root functions, cube root functions, cubic functions, log functions, and probably a few others I can’t think of.  They also solve rational equations and work with inverse variation.  The last unit deals with probability including permutations, combinations, independent and dependent events, and sample spaces.

You can see that these topics are rather advanced and that a student who is not a strong math student that tries to take this in their sophomore year (the year that most students who are not advanced would take it) are likely to struggle, especially given that North Carolina grades on a 7 point scale.  Whenever I talk to students that I tutor in this course, I constantly get reports that at least half, if not more, of their class is failing.  However, teachers will most likely give the student a D and move them along.