# Math

Here at RCS, we strive to reach the highest standards in the Kindergarten through Gr. 12 math programming. RCS is using the JUMP MATH Program for grades K-4 with much success! This program allows for more practice and deep understanding of basic mathematical concepts in our primary grades. Teachers have been excited to see math skills and grade transition improve since this implementation. Grades 5-9 use the Math Makes Sense program which allows students to use a textbook style format to introduce multiple strategies for understanding important concepts.

The High School mathematics program at RCS consists of all three pathways in the Western and Northern Canadian Protocol for Math. These pathways include Workplace and Apprenticeship Math, Foundations of Math, and Pre-Calculus Math for grades 10, 11, and 12. Calculus 30 is offered as well as Advanced Placement Calculus and a locally developed Calculus 30L which focusses on advanced Integration techniques and other university calculus concepts.

We have implemented our own locally developed assessments for K-8 with the goal of multiple assessment views of student progress throughout the year. Students will receive testing on Number Sense outcomes all year long to inform instruction practices and to evaluate programming. Our students always score higher than average on Division, Provincial, National, and International assessments.

As our division is no longer sponsoring High School assessments, RCS will implement the National Cat IV Spring Math assessment for grade 9 and 12 in 2019. In 2018 our 15 yr old students took the internationally agreed two-hour PISA assessment. Students were assessed in science, mathematics, reading, collaborative problem solving and financial literacy. These, and other assessments, provide RCS staff and admin with objective benchmarks for instructional and programming improvement.

Our Team meets regularly to ensure the scope and sequence of math concepts implemented in each grade flow smoothly from year to year and make allowances for student capabilities through differentiated instruction, the use of Educational Assistants, and through purposeful Professional Development for our many Math specialist teachers.

### High School Mathematics – In Depth Look

*Math 9*

In Mathematics 9, students continue to develop an understanding and appreciation for the order and beauty of creation as revealed through shape, pattern and number relationships. In Math 9, students build a solid understanding of the basic concepts related to algebra, polynomials, and powers and roots. Trigonometry and geometry are also explored. Problem solving and applications are integrated in the units of study to help students see how their mathematical skills can be put to use outside of the classroom. A simple scientific calculator is an essential tool for the course.

*Foundations and Pre-Calculus 10*

The Foundations and Pre-Calculus Math 10 course is a pre-requisite course for both the Pre-Calculus 20/30 pathway and the Foundations of Math 20/30 pathway. Topics covered in FMP 10 include Measurement, Trigonometry, Polynomials & Factoring, Radicals & Exponents, Functions (with an emphasis on linear functions), and Systems of Equations. Students should successfully complete Math 9 before enrolling in FMP 10.

*Workplace and Apprenticeship Math 10*

Apprenticeship and Workplace Math 10 is a course that emphasizes the application of numerical and mathematical concepts. This course is intended to prepare students to either enter directly into the workplace after high school or to pursue a trade. After completing WP 10, students would need to complete WP 20 in order to meet the minimum graduation requirement for mathematics. It would not be possible to move to one of the other grade 11 math pathways without first completing FMP 10.

*Foundations of Math 20/30*

The Foundations of Math pathway is designed for students whose post-secondary plans include Arts, Humanities, Social Sciences, (non-math related programs such as science, engineering, medicine, etc). Emphasis will be placed on applications of mathematics, rather than on theoretical mathematics.

This pathway is the best choice for students who do not have a strong desire for math related careers but wish to keep doors open to as many post-secondary opportunities as possible. Because the topics are quite different from the Pre-Calculus pathway, students who really enjoy Math might opt to take courses in both pathways to equip themselves with a more well-rounded understanding of mathematical concepts.

*Foundations Math 20 topics include*: Mathematical reasoning, properties of angles and triangles, trigonometry, statistics, systems of linear inequalities, quadratic functions, and proportional reasoning.

*Foundations 30 topics include*: Set Theory and logic, combinatorics, probability, Polynomial, exponential, and logarithmic functions, Sinusoidal functions, and financial mathematics.

*Workplace and Apprenticeship Math 20/30*

The Apprenticeship and Workplace pathway has been designed to meet the needs of students who are planning to pursue Trades or another field of work or study that does not have an additional math requirement. This pathway emphasizes problem solving and application of mathematical concepts to real-world situations. It is the preferred pathway for most college Trades programs, but the other pathways are often listed as acceptable alternatives for the same programs.

*Topics in Apprenticeship and Workplace Math 20* include measurement calculations & unit conversions, scale diagrams & models, personal budgets and financial management, manipulation of formulas, slope, unit analysis & proportions and creation & interpretation of different types of graphs.

*Topics in Apprenticeship and Workplace Math 30* include logical reasoning, limitations of measuring instruments, sine law and cosine law, properties polygons, transformations , leasing vs purchasing, small business finances, linear relations, measures of central tendency, percentiles, and probability.

*Pre-Calculus 20*

The Pre-Calculus pathway is designed for students who anticipate pursuing post-secondary programs which will involve a lot of theoretical mathematics, such as Sciences, Engineering or Business. Emphasis will be placed on solving complex equations (including absolute value, radical, rational and quadratic equations), expanding trigonometric understanding to involve degrees and radians, factoring complex polynomials, analyzing quadratic, absolute value & reciprocal functions, solving systems that involve equations in two variables, and analyzing arithmetic and geometric number sequences.

This pathway is designed for students who have a good aptitude for Math and are interested in thinking about number concepts in abstract, theoretical ways. Students choosing this pathway should have strong scores in Math 10 units such as Factoring Polynomials, Roots & Powers and Functions. Students who really enjoy Math might opt to take BOTH Pre-Calculus and Foundations pathways (especially at the grade 12 level) in order to gain a good understanding of both theoretical and applied mathematics.

Pre-Calculus 20 is not a good choice for students who do not enjoy Math or who have struggled significantly in Math 10.

*Pre-Calculus 30*

Students who have successfully completed Pre-Calculus 20 can enroll in Pre-Calculus 30. This course is designed for students who anticipate pursuing post-secondary programs which will involve theoretical mathematics, such as Sciences, Engineering, Mathematics, or Business. Emphasis will be placed on solving complex equations (including polynomial, radical, trigonometric, exponential, logarithmic and rational), transformations of functions, analyzing square root, radical, polynomial, trigonometric, exponential, logarithmic and rational functions, composition of functions, permutations and combinations and the binomial theorem. There is a great deal of application in this course, and it is imperative that the student have a solid mathematical foundation.

*Calculus 30*

This course is designed for the student intending to take calculus at the post-secondary level. The student will become familiar with the strange new words and symbols used in this branch of Mathematics. Among the many topics to be covered are functions, limits, continuity, derivatives, relative maxima and minima, and integrals. A student taking this course must have completed Pre-Calculus 30.

**AP Calculus AB / Calculus 30 L**

*Calculus 30 runs first semester, September to January. Advanced Placement (AP) Calculus extends to mid-May culminating in the International AP Exam. The second semester class will be called Calculus 30L which includes all AP concepts (over and above regular Calculus 30 concepts) and advanced integral calculus concepts. A Calculus 30L syllabus will be given beginning of second semester to those students who chose to move onto the AP Exam. Calculus 30L runs January to June. *The material in AP Calculus AB and Calculus 30L cover most of the concepts in Calculus I and Calculus II in University level course offerings. Students completing Calculus 30, AP Calculus AB, and Calculus 30L usually do extremely well in their first two calculus courses in university.*

AP Calculus AB topics include: Derivatives of Trig functions and their inverses, Applications of trigonometric derivatives, Derivatives of Exponential and Log functions, Exponential Growth and Decay, Differential Equations, Slope Fields, Reimann Sums, Integration by parts, Integration using partial fractions, and Integration by trigonometric substitution.

**Calculus 30 L topics include: **

All AP Calculus AB topics, Rolle’s Theorem, Separable differential equations, slope fields, L’Hopital’s Rule, exponential growth and decay, logistic growth, volumes of solids of revolution, Euler’s method, approximation methods, applications of the definite integral (to discuss net change motion on a line, consumption over time, area, volume, length of a curve, and surface area of a solid of revolution).