### Mathematics Courses

**Objective:** The OFALycée program brings greater complementarity to pupils by merging the French program with the American program to provide a comprehensive education with emphasis on reasoning, critical thinking, geometry and programming. This complete math education is a true asset for pupils in high school, higher education and professional life.

**Duration:**

**4th to 8th Grade:** 1 hour (2×30 minutes) of synchronous lessons per week.

**9th to 11th Grade:** 1 hour (2×30 minutes) of “office hours” meetings per week in groups of max. 6 pupils with the teacher. Video clips available.

**12th Grade:** Specialty education: 1.5 hours (2×45 minutes) of “office hours” meetings per week in groups of max. 6 pupils with the teacher. Video clips available.

**Calendar:** September to June

**Our Approach:** At OFALycee, we believe that we can offer one of the most comprehensive math programs in the world, combining two experiences, with different approaches, taught in two different languages.

The mathematics courses offered at OFALycée capitalize on the American experience of our pupils and the program covered in “Middle School” and “High School” in order to prepare them for the specific skills of the French system.

The American system is particularly effective in preparing pupils for mastery of algebra by offering a large number of practice exercises. This approach insists above all on technique, and thus abandons reasoning. At OFALycée, we want to improve this approach by emphasizing the meaning, on the basis of each method, convinced that if a pupil understands the why of a technique, he can better memorize and retain it.

As an organization preparing our pupils for the French baccalaureate, we strongly support the French mathematics program. The French approach develops reasoning skills in pupils by emphasizing an analytical approach. The properties of the course are demonstrated and a rigorous and detailed writing of the solutions is expected. However, by emphasizing reasoning, less time is spent on developing algebraic mastery in the pupil. We believe that these skills are essential for the learning and progression of our pupils towards mastering complex concepts.

At OFALycée, we have developed a program combining the best that both programs have to offer. Each approach builds complementary skills that will serve the success of our pupils.

**Workload: Middle School**

The course content covered during the sessions is available on the platform and should be reviewed before each session.

From one session to the next, exercises are given. These exercises require between 10 minutes and 30 minutes of personal work. Several types of exercises are possible:

**On paper:**Geometric constructions, justifications, algebraic calculations, problem solving.**On software:**constructions of dynamic figures on Geogebra, programming on Scratch.

The workload corresponds to approximately 1 hour of personal work per week.

**Workload: High School**

In high school, a large part of the content is given in the form of video clips and documents available on the platform. The meetings allow you to review the content of these videos in order to answer any questions, correct the exercises and focus on specific methods.

From one session to the next, the pupil may be asked:

- To watch the video clips associated with the session.
- To complete the given exercises. These exercises can require between 30 minutes and 1 hour of personal work.

These exercises are usually to be delivered through the platform. They may require the use of a graphing calculator, dynamic software such as Geogebra or programming in Python (repl.it)

The workload corresponds to approximately 2 hours of personal work per week.

**Geometry:**

- Geometry elements: Points, lines, segments. Alignment and set membership.
- Distance and circle.
- Angles and measurements.
- Perpendicular and parallel.
- Axial symmetry. Mediator of a segment.
- Triangles and quadrilaterals. Perimeters and areas.
- Solids and Volumes.
- Landmarks.
- Numeration.
- Numerical calculations: Operations on whole numbers, fractions, decimals.

**Programming:**

- Instructions suites.
- Loops.
- Programs applied to calculation and displacement algorithms.

**Software used, sites:**

- Geogebra: Dynamic geometry software, 3D, spreadsheet.
- Scratch, blockly: Graphical programming language.

**Geometry:**

- Central symmetry
- Angles and parallelism.
- Properties on triangles. Remarkable lines of a triangle.
- Parallelograms.
- Areas.
- Geometry in space. Volumes
- Landmarks.

**Algebra:**

- Numerical calculations.
- Equations and problem solving.
- Statistics, probabilities.

**Programming:**

- Instructions suites.
- Loops.
- Conditions.
- Programs applied to calculation and displacement algorithms.

**Software used, sites:**

- Geogebra: Dynamic geometry software, 3D, spreadsheet.
- Scratch, blockly: Graphical programming language.

**Geometry:**

- Introduction to the proof: Deductive reasoning, property, reciprocal property.
- Pythagorean theorem and reciprocal.
- Plane transformations: Translations and rotations
- Geometry in space: Pyramids and cones. Volumes.
- Landmarks.

**Programming:**

- Parallel programs.
- Conditions.
- Loops.
- Concept of computer variable.
- Programs applied to calculation and displacement algorithms.

**From geometry to algebra:**

- Proportionality in triangles. Enlargement and reduction
- Trigonometry.
- Resolution of geometric situations.

**Equations and problem solving.**

**Statistics and probabilities.**

**Geometry:**

- Introduction to logic: Properties and reciprocals.
- Pythagorean theorem and reciprocal.
- Thales’s theorem and converse.
- Transformations of the plane: Homothety, similar triangles.
- Trigonometry.
- Geometry in space.

**Programming:**

- Parallel programs.
- Conditions.
- Loops.
- Concept of computer variable.
- Create blocks.
- Programs applied to calculation and displacement algorithms. Fractals and game creation.

**Functions and algebra:**

- Resolution of geometric situations by functions.
- Notion of functions and associated vocabulary.
- Affine functions.

**Probability and statistics.**

**Software used, sites:**

- Geogebra: Dynamic geometry software, 3D, spreadsheet.
- Scratch, blockly: Graphical programming language.

*TI 84 + graphing calculator recommended.*

**Analysis:**

- Functions: Definition set, image and background, graphic representation.
- Usual functions.
- Variations and extremum.

**Algebra:**

- Sets of numbers, arithmetic. Intervals and absolute value.
- Development, factorization, remarkable identities.
- Sign study, inequalities.
- Cartesian equation of a line, system resolution.

**Vector geometry:**

- Identification in the plan.
- Vectors and translations.
- Vectors and coordinates.

**Statistics and probabilities:**

- Figures: Absolute and relative growth rate, associated coefficient. Successive developments. Reciprocal rate.
- Descriptive statistics.
- Probability and sampling.

**Programming:**

- Introduction to the Python language.
- Types of Variables: Integer, float string.
- Tests
- Loops.
- Programs applied to content: Finding a solution or a maximum by scanning, calculating the length of a curve, probabilistic simulations.

**Software, sites:**

- Geogebra.
- Repl.it: Collaborative coding platform.

*TI 84 + graphing calculator recommended.*

**Analysis:**

- Polynomial functions, quadratic polynomials.
- General information on functions.
- Derivative at a point, derivative functions and variation studies.
- Exponential function.
- Numerical sequences.
- Trigonometric functions.

**Algebra:**

- Quadratic polynomials
- Numerical sequences.

**Vector geometry:**

- Scalar product.
- Applications of the dot product.

**Statistics and probabilities:**

- Inferential statistics.
- Conditional probabilities. Sampling.

**Programming:**

- Introduction to the Python language.
- Types of Variables: Integer, float string.
- Lists
- Tests
- Loops.
- Programs applied to content: Search for a solution by Newton’s method, calculation of terms and sums of sequences. Probabilistic simulations.

**Software, sites:**

- Geogebra.
- Repl.it: Collaborative coding platform.