Grades 7–8 · Ages 12–14

Young Fermats - Geometry and Trigonometry

Angles, triangles, Pythagorean, coordinate geometry, area & volume — a real intro to proof-style thinking.

Length120 minutes · once a week
Tuition$489 / month
Location226 W 79th St, UWS
FormatIn-person · max 6 students
Marcelo Ambrozio, lead math teacher at School of Math

Your teacher

Marcelo Ambrozio

Co-Founder & Lead Math Teacher

MBA · B.S. Applied Mathematics, Northwestern · 20 years coaching MIT, Harvard & Stanford candidates. Meet the team →

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Young Fermats - Geometry · Grades 7–8

$489 / month — tuition (recurring) · $99 one-time registration (placement test, written diagnostic, learning plan)
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About the course

What students learn

Young Fermats Geometry runs alongside Algebra Ignite for middle-school students who are ready for a full intro geometry term. We cover angle relationships, triangle congruence, Pythagorean reasoning, coordinate geometry, area and volume — and introduce the proof-style thinking that pays off in high-school honors geometry. Courses are rolling — a student can join at any meeting and continue into the next term without losing the thread.

A typical class

Sample class format · 120 minutes

Every Young Fermats - Geometry class follows the same structure so students walk in knowing what to expect and walk out with a corrected mini-quiz in hand.

0:00 – 0:30
30 min

Puzzles & Enigmas

Warm-up with logic puzzles, math riddles, and short brain-teaser problems. The point is to switch the brain on without yet introducing today’s topic — students arrive at different focus levels and this 30-minute block evens the room.

0:30 – 1:00
30 min

Subject — concept & guided practice

First half of today’s topic. One geometry topic per meeting — angle relationships, triangle congruence, Pythagorean, coordinate geometry, or area/volume. Concept-first: the instructor demonstrates one or two worked examples, then students try guided practice with the teacher walking the table.

1:00 – 1:05
5 min

Brain break

A short break — water, stretch, a quick chat. Five minutes is enough to reset focus without losing the rhythm of the class.

1:05 – 1:30
25 min

Subject — word problems & applications

Second half of the topic, focused on word problems, abstraction, and math applied to real situations — the place where rote knowledge turns into real understanding. Examples we use: Calculating the diagonal of a TV screen from its dimensions (Pythagorean theorem).; Figuring out the volume of paint needed for a real wall in your room.; Mapping the height of a Manhattan skyscraper using similar triangles and a shadow..

1:30 – 2:00
30 min

Mini-quiz — corrected in class

A short timed mini-quiz on today’s topic, then we correct it together — question by question, out loud, with the right strategy spelled out for each item. Parents get the corrected paper at the end of the session so they know exactly where their child stands.

Syllabus arc

48-class rolling syllabus

Courses are rolling — a student can join at any class and continue without losing the thread. Here’s the full topic arc:

  • Class1Points, lines, planes, and the basics of angles.
  • Class2Angle pairs — complementary, supplementary, vertical.
  • Class3Parallel lines cut by a transversal.
  • Class4Triangle angle sum and exterior angles.
  • Class5Triangle congruence — SSS, SAS, ASA, AAS.
  • Class6Triangle inequality and triangle classification.
  • Class7Pythagorean theorem and its converse.
  • Class8Pythagorean word problems — distance and diagonal.
  • Class9Similar triangles and proportional reasoning.
  • Class10Coordinate plane — distance and midpoint formulas.
  • Class11Slope and parallel/perpendicular lines on the plane.
  • Class12Area of triangles, quadrilaterals, and composite figures.
  • Class13Circles — circumference and area.
  • Class14Volume of prisms, cylinders, and cones.
  • Class15Surface area of common 3D shapes.
  • Class16Coordinate proof — proving triangles and quadrilaterals on the plane.
  • Class17Special right triangles — 30-60-90 and 45-45-90.
  • Class18Circles — arc length, sector area, and inscribed angles.
  • Class19Surface area of prisms, cylinders, cones, spheres.
  • Class20Volume of prisms, cylinders, cones, and spheres.
  • Class21Transformations — translations, reflections, rotations, dilations.
  • Class22Two-column proof — congruent triangles and parallel-line theorems.
  • Class23Locus and constructions — compass-and-straightedge and the equation of a circle.
  • Class24Cumulative geometry review — proofs, coordinate geometry, area, and volume.
  • Class25Right-triangle trigonometry — sine, cosine, tangent.
  • Class26Solving right triangles — missing sides and angles.
  • Class27Angle of elevation and depression — real-world applications.
  • Class28The reciprocal ratios — cosecant, secant, cotangent.
  • Class29Trigonometric ratios for special angles — 30°, 45°, 60°.
  • Class30Radian measure — converting between degrees and radians.
  • Class31Arc length and area of a sector in radians.
  • Class32The unit circle — coordinates of key angles.
  • Class33Sine and cosine as functions on the unit circle.
  • Class34Graphs of sine and cosine — amplitude and period.
  • Class35Graphs of tangent, cotangent, secant, cosecant.
  • Class36Phase shifts and vertical shifts of trigonometric functions.
  • Class37Solving trigonometric equations on a given interval.
  • Class38Fundamental trigonometric identities — Pythagorean, reciprocal, quotient.
  • Class39Sum and difference identities for sine, cosine, tangent.
  • Class40Double-angle and half-angle identities.
  • Class41Verifying trigonometric identities — proof-style practice.
  • Class42Law of sines — solving oblique triangles.
  • Class43Law of cosines — solving SAS and SSS triangles.
  • Class44Area of a triangle with trigonometry — SAS area formula.
  • Class45Vectors — components, magnitude, direction, and addition.
  • Class46Polar coordinates and converting between polar and rectangular.
  • Class47Cumulative trig review — identities, equations, and applications.
  • Class48Cumulative geometry + trig mock exam — full-length assessment.
  • Frequently asked

    Common questions from parents

    How large are SOMATH classes?

    Every SOMATH class is capped at 6 students. That is the number that lets one teacher see every student's work in real time, correct silent mistakes before they become habits, and pace to the room instead of the average. Larger groups defeat the whole point of small-group teaching, so we hold the cap firmly.

    Where do classes meet?

    In person at 226 W 79th Street, 1st Floor, New York, NY 10024 — one block from the 79th Street 1 train and a short walk from the B and C at 81st Street. We do not offer online classes; the small-group model relies on shared whiteboard work and in-room feedback.

    What is included in registration?

    $99 one-time registration covers a placement test, a written diagnostic, and a personalized learning plan delivered within 48 hours. Workbooks, problem sets, and printed practice tests are included at no extra charge. The $99 registration is separate from monthly tuition.

    Can we pause or cancel?

    Yes. Cancel anytime with 15 days written notice — no long-term contract. Up to 4 weeks of free pause per year to cover travel or family events, and one free make-up per month for a missed class (subject to available seats in another cohort).

    Do you offer a free trial or evaluation?

    Yes. Every new family starts with a free 60-minute evaluation in our classroom plus a written diagnostic delivered within 48 hours. There is no charge and no commitment — the diagnostic is yours to keep whether you enroll or not. Book at schoolofmath.us/evaluation or call (646) 668-6151.

    Does this course include Regents Geometry preparation?

    Yes. The syllabus covers everything on the New York State Geometry Regents (transformations, triangle congruence and similarity, right triangle trigonometry, circles, and coordinate geometry) with practice sets drawn from released Regents exams in the final classes. Students preparing for other geometry curricula are supported equally.