STHI / F / 01
Middle school math
Pre-algebra and geometry.
Open the syllabusUnited States · Grades 7 to 12 · Stanford Online High School
Stanford Online High School is unusual in two ways that matter for math. It places students in a math course by what they know, not by their grade, and its math program puts written proof at the center. So the honest preparation is not a trick for an entrance test; it is solid algebra and geometry, and the habit of explaining why an answer is true. This guide sets out the OHS math sequence from its own 2026-27 catalog, the 2027-28 admission timeline and testing rules, and original practice in the style of thinking OHS asks for.
Teaching math and coding live since 2020 · 10,000+ students · ages 6 to 67
In short
Stanford Online High School is a selective online school for academically advanced students in grades 7 to 12. It places students in math by demonstrated content knowledge, runs a sequence from Prealgebra to university-level courses with a strong focus on proof, and takes 2027-28 applications until January 7, 2027. Modern Age Coders is not connected with Stanford. We teach the algebra, geometry and proof-writing that sequence builds on, live online in our high school mathematics course, as a group of 15 to 20 or one to one.
Math that is ready for OHS
Each one aims at understanding and clear written reasoning, the two things a proof-focused program expects.

STHI / 01
The full sequence, taught with reasons, for grades 9 to 12.
Open the syllabus →
STHI / 02
Pre-algebra and geometry for grade 6 to 8 applicants.
Open the syllabus →
STHI / 03
Problem solving and proof beyond the school syllabus.
Open the syllabus →Stanford OHS
Stanford Online High School is an online middle and high school run by Stanford University. Its admissions FAQ says it serves academically advanced students in grades 7 to 12, and its criteria page says plainly that admission is competitive.
The Acceptance Criteria page says "Admission to Stanford OHS is competitive" and that, to keep classes small, "we are unable to accept all qualified applicants". The committee reviews each application holistically, and "no one item is the deciding component".
For younger students, the school says it typically encourages students "to apply for grade 7 when they are in grade 6 or ages 11 to 12".
Stanford OHS offers three enrollment levels. Full-time students take 4 to 5 yearlong courses; part-time students take 2 to 3; a single-course student takes "1 yearlong course or 2 semester-long courses".
The school estimates "8-10 hours per week, per course" for a high school course. Many families start with a single math course while staying at their current school; one of the admission decision types is even "Admission Restricted to Mathematics/Science or Humanities".
Sources: Stanford OHS Acceptance Criteria and Enrollment Options, read 31 October 2026. Stanford and Stanford Online High School are names of Stanford University. Modern Age Coders is an independent online school with no connection to Stanford University or Stanford OHS, and we make no admission promise of any kind.
Math sequence
The 2026-27 OHS catalog lists a math ladder from Prealgebra to university-level analysis, each course with a stated prerequisite. The school says it places students "by age, grade level, and demonstrated content knowledge", so a strong grade 8 student may start well up the ladder.
| Course (code) | Level | Prerequisite as published |
|---|---|---|
| Prealgebra (JM007) | Middle school | None listed |
| Beginning Algebra (OM011) | High school | Prealgebra (JM007) |
| Intermediate Algebra (OM012) | High school | Beginning Algebra (OM011) |
| Geometry and Foundations of Proof (OM015) | High school | Beginning Algebra (OM011) |
| Precalculus with Trigonometry (OM013) | High school | Intermediate Algebra (OM012) and Geometry and Foundations of Proof (OM015) |
| Single-Variable Calculus (OM045) | High school | Precalculus with Trigonometry (OM013) |
| Advanced Problem Solving and Proof Techniques (OM050) | High school | Precalculus with Trigonometry (OM013) |
| Statistics and Data Analysis (OM061) | High school | Precalculus and Trigonometry (OM013) |
The catalog continues into university-level courses: Multivariable Calculus (UM150), Linear Algebra (UM51A), Number Theory (UM152), Discrete Mathematics (UM160), Real Analysis (UM115), Complex Analysis (UM106) and research seminars.
For Multivariable Calculus the stated route in is Single-Variable Calculus or Calculus C "with a grade of A- or better, or an AP Calculus BC Exam score of 4 or 5, or consent of instructor".
First, geometry here is "Geometry and Foundations of Proof", and it sits before Precalculus. Proof is not an extra at OHS; it is on the main road.
Second, the catalog says the school has "replaced all of our Advanced Placement (AP) courses with custom courses" and that students can still sit AP Exams locally. Preparation should aim at understanding, not at one exam's format.
Source: Stanford OHS Course Catalog 2026-27, Mathematics filter, and the OHS Mathematics page, read 31 October 2026. Course titles and codes are the school's; check the live catalog before planning.
Dates and testing
For entry in the 2027-28 school year, the application deadline is January 7, 2027, at 11:59 pm Pacific Time. A standardized test score is required only for some applicants, mainly those who were homeschooled recently.
| Step | Date as published |
|---|---|
| Deadline to apply if you want the optional online interview | November 11, 2026, 11:59 pm Pacific Time |
| Application deadline (standard timeline) | January 7, 2027, at 11:59 pm Pacific Time |
| Decision notification | March 2027 |
| Enrollment contract due | 10 days after decisions are released |
The Acceptance Criteria page requires a score from an approved test for applicants who were homeschooled, or attended a school taught in a language other than English, between September 2024 and December 2026. The test must be taken between September 2025 and December 2026.
For everyone else a score is optional, and the school says that if sent "there will be no advantage in the evaluation process".
OHS suggests the Middle SSAT or ISEE, PSAT 8/9 or PreACT 8/9 for grade 7 to 8 applicants; the Upper SSAT or ISEE, PSAT 8/9, PreACT 8/9 or PSAT 10 for grades 9 to 10; and the PSAT, PreACT, SAT, ACT or PSAT 10 for grades 11 to 12.
Applications also need "at least two recommendation forms (one Humanities/Social Science teacher and one Mathematics/Science teacher)". A homeschooled applicant can ask any adult who has taught them math.
Sources: Stanford OHS How to Apply and Acceptance Criteria, read 31 October 2026. The school also says "All responses, essays, and work submitted in the application must be the student's own." We never write or edit any part of an application.
Proof
By practising short, complete arguments early. The OHS Mathematics page names a "Focus on Proofs" and says "Proof-writing enables students to present clear and logical mathematical arguments." Here is a first proof, worked in full. It is ours.
Add the odd numbers in order: 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 = 16. Every total is a perfect square. A student who stops here has a guess, not a proof.
The claim to prove: the sum of the first n odd numbers is n squared. For n = 10, that predicts 1 + 3 + ... + 19 = 100, and adding them confirms it.
The k-th odd number is 2k - 1. Pair the first and last terms: 1 + (2n - 1) = 2n. The second and second-to-last also make 2n, and so on. There are n terms, so n / 2 pairs, each worth 2n, giving (n / 2) x 2n = n squared.
If n is odd the middle term has no partner, but the same total comes out by writing the sum forwards and backwards: twice the sum is n terms of 2n, so the sum is n squared. Either way the claim holds for every n.
| Part | What to write | Example: odd x odd is odd |
|---|---|---|
| Claim | State exactly what is true | The product of two odd numbers is odd |
| Set-up | Name things with letters | Let the numbers be 2a + 1 and 2b + 1 for whole numbers a and b |
| Reasons | Each line follows from the last | (2a + 1)(2b + 1) = 4ab + 2a + 2b + 1 = 2(2ab + a + b) + 1 |
| Conclusion | Say why the claim follows | It is 2 times a whole number, plus 1, so it is odd |
Notice what a proof is not: checking 3 x 5 = 15 and 7 x 9 = 63 shows examples, but only the letters cover every case. That shift, from examples to every case, is the habit to build before a course like Geometry and Foundations of Proof.
Practice
Whatever course a student hopes to enter, the course before it should feel secure. This self-check and practice set are ours, written at the Beginning Algebra to Precalculus level, with answers checked in Python.
| If your child can confidently... | They are probably ready to work on... |
|---|---|
| Work with fractions, ratios and negative numbers | Beginning algebra |
| Solve linear equations and graph lines | Intermediate algebra and geometry with proof |
| Factor quadratics and write short proofs | Precalculus with trigonometry |
| Use functions, logs and trigonometry fluently | Single-variable calculus and proof techniques |
| Problem | A good way in | Answer |
|---|---|---|
| Solve 3(x - 4) = 2x + 5 | Expand, then collect x on one side | x = 17 |
| Factor x squared - 5x + 6 | Two numbers with product 6 and sum -5 | (x - 2)(x - 3) |
| Slope of the line through (1, 2) and (4, 11) | Rise over run: 9 / 3 | 3 |
| A right triangle has legs 5 and 12. Hypotenuse? | 25 + 144 = 169 | 13 |
| 1 + 3 + 5 + ... + 19 | Ten odd numbers, so 10 squared | 100 |
| sin 30 degrees | Half an equilateral triangle | 1/2 |
| Prove odd x odd is odd | Write odds as 2a + 1 and 2b + 1 | See the proof above |
Related help: algebra 2 tutoring, precalculus tutoring, calculus tutoring and, for younger applicants, accelerated math online.
Where your child is
Our own description of how students grow from answers to arguments.
| Stage | What it looks like |
|---|---|
| 1. Answer only | Writes the final number, often correctly |
| 2. Shows working | Lists steps, but not why each is allowed |
| 3. Gives reasons | Each step is justified by a rule or fact |
| 4. Proves in general | Uses letters to cover every case and says why the claim follows |
Many strong students sit at stage 2 because school never asked for more. Moving to stage 3 is the single most useful step before a proof-based course.
Ask your child to explain one solution aloud each week. If they can say it, they can learn to write it.
Write every proof for a reader who was not there. If a step needs you to explain it out loud, write that sentence down.
Examples suggest; letters prove. Try your idea with numbers first, then with a and b.
The catalogue
Live courses that follow the same order the OHS ladder does, from pre-algebra to university topics.
STHI / F / 01
Pre-algebra and geometry.
Open the syllabusSTHI / F / 02
Pre-algebra to Algebra 1.
Open the syllabusSTHI / F / 03
MATHCOUNTS and AMC 8.
Open the syllabusSTHI / H / 01
Algebra to calculus.
Open the syllabusSTHI / H / 02
Functions and trigonometry.
Open the syllabusSTHI / H / 03
AB and BC content.
Open the syllabusSTHI / U / 01
Linear algebra to analysis.
Open the syllabusSTHI / U / 02
Data to hypothesis tests.
Open the syllabusSTHI / U / 03
Proof and hard problems.
Open the syllabusHow lessons run
Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.
Weekdays
Evening lessons after the school day.
Weekends
Longer sessions for proofs and problem sets.
1-on-1
For a student working well above grade level.
Every method comes with its reason.
Short proofs most weeks.
Never copied from any school.
Teachers mark the reasoning.
We teach math; the school decides.
Fifteen to twenty, or one to one.
Student work
Math investigations and code from older students in our classes. Browse student labs for more.

AI and ML
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AI and ML
A chatbot that answers mathematics and programming questions, built and deployed by a student.

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Web app
A weather forecasting site with live conditions for any location.
Fees
High school math is billed month to month, so a family can strengthen one course across the application season without a long contract.
Free first class
USD 0
no card required
Group batch
USD 100
a month, billed in US dollars
One to one
USD 150
a month, billed in US dollars
What families say
Reviews from parents on Google, copied exactly.
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Questions from families
The 2026-27 catalog runs from Prealgebra through Beginning and Intermediate Algebra, Geometry and Foundations of Proof, Precalculus with Trigonometry and Single-Variable Calculus, then university-level courses such as Multivariable Calculus, Linear Algebra and Real Analysis.
The school says it places students in courses by age, grade level and demonstrated content knowledge. Each course in the catalog lists a prerequisite, so the course before the target should be secure.
The How to Apply page gives January 7, 2027, at 11:59 pm Pacific Time. Families who want the optional online interview must apply by November 11, 2026, and decisions are released in March 2027.
Only for some applicants: those homeschooled, or at a school taught in a language other than English, between September 2024 and December 2026. For others a score is optional and, the school says, gives no advantage.
The school says admission is competitive and that it cannot accept all qualified applicants. It reviews applications holistically, so no single grade or score decides.
Stanford OHS serves grades 7 to 12 and typically encourages students to apply for grade 7 while in grade 6 or aged 11 to 12.
Yes. Single-course enrollment means one yearlong course or two semester-long courses, and the school estimates 8 to 10 hours a week for a high school course.
The catalog says the school has replaced its AP courses with custom courses, such as Single-Variable Calculus, and that students can still register for AP Exams in their local area.
Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.
No. Modern Age Coders is an independent online school and is not affiliated with Stanford University or Stanford Online High School. We teach math and never promise admission.
Elsewhere on this site
More for advanced US math students.
Working ahead of grade level.
Functions and trigonometry.
Limits to integrals.
The bridge to precalculus.
Problem solving for younger applicants.
For homeschooled applicants.
Part of the guide: US gifted and selective school tests
More guides: US state math tests by state · US math placement and college readiness tests · Homeschool and school math curricula guide · US math and coding competitions guide
Start here
Tell us your child's grade, the last math course they finished and which OHS course they are aiming for. The teacher will check what is solid.
It may help to read how our teachers work or scan the full catalogue beforehand.
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