# MS Course Guide All students engage in low stress, untimed adaptive assessment the first week of school to uncover what they know and what they are ready to learn. Students are placed into a math group based on their ability and learning profile, regardless of their age.

Pre-algebra I
This class covers topics typically found in 6th and 7th grade classes. This is a common place for many incoming middle school students to start, as well as some students coming out of the Acera elementary program.

Topics might include: operations with fractions and decimals; percent; factors and primes; probability; area and perimeter of triangles, angles relationships, volume and surface area; operations with negative numbers; order of operations; similarity; variables and patterns, graphs; descriptive stats: drawing graphs, understanding populations, central tendency and variability

Pre-Algebra II
This class covers topics typically found in 7th and 8th grade classes. It involves more exposure to pre-algebra topics, room to explore and develop mathematical intuition and logical reasoning, and exposure to some topics in Algebra I. Some entering students will start here, some Acera students will take this class after Pre-Algebra, and some Acera students will skip this class.

Topics might include: similarity; percent; probability; surface area and volume; ratio and proportion; variables, tables and graphs; exponents; linear and non-linear situations; solving one and two-step equations; evaluating expressions and recognizing equivalent expressions; transformations on the coordinate plane; bivariate data and sampling methods

Potential projects and activities: Art and Architecture; financial math; logic puzzles and number games, voting systems; figurate numbers

Intro to Algebra
This class covers material often found in 8th or 9th grade classes. The expectation is that all students will take this class at some point in their three years in middle school, unless they enter middle school past this level.

Topics include: Linear equations and functions: graphing, solving equations, modeling situations; systems of linear equations; linear inequalities; exponential expressions with integer and rational exponents; rational expressions; distributive law: factoring and multiplying polynomials; quadratic equations and quadratic modeling; radical expressions; line of best fit, correlation between variables

Applications and Statistics
This is an applied math class meant to reinforce algebra skills, emphasize connections between math and real world situations. It is appropriate for students who have completed Intro to Algebra, or similar background. It previews some topics in a typical Algebra II and Geometry class, but it is not a substitute for either. It also covers many topics not commonly found in middle or high school classes.

Topics might include: Recursively defined sequences; graphing lines and other functions; solving non-linear equations; modeling with exponential functions and introduction to logarithms; conditional probability; geometric constructions, tessellations and transformations; statistics: correlation, including linear and exponential regression, chi-square tests, and data collection methods; modeling physics problems with algebra; using similar triangles to measure objects; using parametric equations to create computer animations; voting systems and apportionment.  (Materials from Comap, For all Practical Purposes)

Discrete Math
This class is intended for students who have completed intro to algebra (or similar) and who have an interest in theoretical math and logic. It previews some topics in Algebra II, but is not a substitute for that course. (Would not be offered in the same year as Number Theory.)

Topics might include: Graph theory; Combinatorics and probability; Cellular Automata; Recursively defined sequences; Fractional linear transforms; Modular arithmetic and groups; Functions on finite sets (permutation groups); Finite projective geometry; Figurate numbers; infinite sets

Number Theory and Proofs
This class is intended for students who have completed intro to algebra (or similar) and who have an interest in theoretical math and logic. It previews some topics in Algebra II, but is not a substitute for that course. (Would not be offered in the same year as Discrete Math.)

Topics might include: Fibonacci numbers; Euclidean algorithm; Diophantine equations; prime factorizations; modular arithmetic and groups; continued fractions.

Geometry
This class is our version of a standard high school geometry class. It is intended for strong math students getting ready to test out of geometry in high school, and most students taking this class will be in 8th grade.

Topics include: Angles, congruent triangles, parallelograms and quadrilaterals; area and volume, circle properties, right triangle trigonometry, constructions, coordinate geometry, transformations; two-column and paragraph proofs; (Discovering Geometry textbook?)

Algebra II/Precalc/Linear Algebra
This is an advanced math class for highly capable math students. It covers many topics found in an honors-level Algebra II and Precalculus class in high school.

Topics might include: Matrices, matrix multiplication, determinants, transformations; Functions and transformations; exponential functions and growth, logarithmic functions;  Infinite series; Complex numbers and Euler’s formula; Gaussian integers; Conic sections; Metric spaces and absolute value inequalities;

Polynomials, remainder theorem and factor theorem.

Typical sequences

 6th grade 7th grade 8th grade 9th grade (after Acera) A. Pre-algebra I Pre-algebra II Intro to Algebra Geometry B. Pre-algebra I or II Intro to Algebra Applications and Statistics Geometry C. Pre-algebra I or II Intro to Algebra Discrete Math/Number Theory Honors Geometry D. Pre-algebra I or II Intro to Algebra Geometry Honors Algebra II E. Intro to Algebra Applications and Statistics Geometry Honors Algebra II F. Intro to Algebra Discrete Math/Number Theory Geometry Honors Algebra II G. Applications and Statistics Geometry Algebra II/Precalc Precalc/Calculus H. Number Theory Algebra II/Precalc Discrete Math Calculus I. Discrete Math Algebra II/Precalc Independent Study ???

Note: Not all classes will be offered each year. Class topics will vary based on teacher and student interest and pacing needs. Independent studies can be offered if/ when appropriate for students who have moved beyond this plan.