Families who search for the US math syllabus usually want one of three things: a parent arriving from India who wants to know what Grade 6 will teach and whether the child is ahead or behind; a parent of a 9th grader who has just met the words Algebra 1 and Geometry for the first time; or a student checking what high school math in the USA actually requires. This article is the whole ladder in one place, kindergarten to 12th grade, with the state tests attached and a table matching each American grade to the CBSE class that covers the same work. It is written from teaching the American sequence 1-on-1 to US families since 2018, including a good number who moved from India in the middle of it.
How the American math syllabus is organised
There is no national board and no national exam. Each state writes or adopts its own standards, and about forty states use the Common Core State Standards for Mathematics or a close rewrite of them. Texas uses the TEKS, Virginia its Standards of Learning, Florida the B.E.S.T. standards, and the content by grade in all of them is nearly the same, because the mathematics is the same. What differs is the name of the test, the grade in which a district places Algebra 1, and how much a given school stretches its strongest students.
Kindergarten to Grade 8 is taught by grade: every child in Grade 5 does Grade 5 math. From Grade 9 the syllabus is taught by course: Algebra 1, Geometry, Algebra 2 and so on, and a student's grade and course are no longer the same thing, which is why an American parent says "my daughter is in 10th grade taking Algebra 2" and an Indian parent finds the sentence odd.
Kindergarten to Grade 5: the elementary syllabus
Common Core organises each elementary grade into domains, and the same domains run through the years with the content growing. The table gives what a child is expected to be able to do by the end of each grade.
| Grade | Age | What the year teaches | The one skill that decides the next year |
|---|---|---|---|
| Kindergarten | 5 to 6 | Counting to 100, comparing numbers, addition and subtraction within 10, shapes | Counting on from any number, not only from 1 |
| Grade 1 | 6 to 7 | Addition and subtraction within 20, place value to 120, measuring length, telling time to the half hour | Addition and subtraction facts within 10 from memory |
| Grade 2 | 7 to 8 | Addition and subtraction within 1,000, place value to 1,000, money, time to five minutes, bar graphs | Regrouping (carrying and borrowing) understood, not only done |
| Grade 3 | 8 to 9 | Multiplication and division within 100, fractions as numbers, area and perimeter, the first state test | The multiplication facts to 10 × 10, by heart, by the end of the year |
| Grade 4 | 9 to 10 | Multi-digit multiplication, long division with one-digit divisors, equivalent fractions, adding fractions with like denominators, angles | Fractions understood as numbers on a line, not only as pieces of pizza |
| Grade 5 | 10 to 11 | Adding and subtracting fractions with unlike denominators, multiplying and dividing fractions, decimals to thousandths, volume, the coordinate plane | Fraction arithmetic done with understanding; this is where middle school math is lost or won |
Two things surprise parents from India. The first is how slowly arithmetic goes: multiplication facts are a Grade 3 target in the USA and a Class 2 target in most Indian schools. The second is how early reasoning, data and explanation begin: a Grade 3 state test asks the child to explain why an answer is reasonable, in a sentence, and an Indian child who can do the sum faster than anyone in the room can still lose the mark.
Grades 6 to 8: the middle school syllabus, and the bridge to algebra
Middle school is where the American syllabus does its most important work, and where a family arriving from India most often misjudges the child's position. The content looks easy to a parent who learned algebra in Class 6, but ratios, proportional reasoning and the use of variables are built slowly and deliberately here, and a child who skips them is the 9th grader who cannot do Algebra 1 word problems.
| Grade | Domains in the Common Core | What is new | The test |
|---|---|---|---|
| Grade 6 | Ratios and proportional relationships; the number system; expressions and equations; geometry; statistics and probability | Ratios and unit rates, dividing fractions, negative numbers on the number line, the first one-step equations, area of polygons, mean, median and the shape of a data set | The state test for Grade 6 |
| Grade 7 | The same five domains | Proportional relationships and the constant of proportionality, all four operations with negative numbers, two-step equations and inequalities, percent problems (tax, discount, interest), scale drawings, circles, probability | The state test for Grade 7 |
| Grade 8 | The number system; expressions and equations; functions; geometry; statistics and probability | Irrational numbers and square roots, integer exponents and scientific notation, linear equations and slope, systems of two equations, functions as a concept, transformations and similarity, the Pythagorean theorem, volume of cylinders, cones and spheres, scatter plots | The state test for Grade 8, or the Algebra 1 end-of-course exam for accelerated students |
Grade 8 is the fork. On the standard track a student takes Grade 8 math; on the accelerated track the student takes Algebra 1 in Grade 8 and the Grade 8 content is compressed into Grade 7. Our separate guide to the Grade 8 math syllabus goes through that year domain by domain with a month-by-month plan.
Grades 9 to 12: the high school math syllabus in the USA
High school math in the USA is four courses, taken one a year, and the sequence is the same in most of the country.
| Year on the standard track | Course | What it covers | The test attached |
|---|---|---|---|
| 9th grade | Algebra 1 | Linear equations, inequalities and functions; systems; exponents and exponential functions; polynomials and factoring; quadratic functions and equations; one- and two-variable statistics | An end-of-course exam in many states: the New York Regents Algebra I, the Texas STAAR Algebra I EOC, the Florida Algebra 1 EOC |
| 10th grade | Geometry | Congruence and similarity through transformations, proof, triangles and their centres, right-triangle trigonometry, circles, coordinate geometry, area and volume, a little probability | A Geometry Regents in New York; the SAT's geometry questions |
| 11th grade | Algebra 2 | Functions and transformations, complex numbers, polynomial and rational functions, radicals and rational exponents, exponential and logarithmic functions, sequences and series, the unit circle and trigonometric functions, probability and the normal distribution | The Algebra II Regents in New York; the SAT, which most students sit in 11th grade |
| 12th grade | Pre-Calculus, AP Statistics, or a fourth-year course the state allows | Pre-Calculus: polynomial, rational, exponential, logarithmic and trigonometric functions, identities, polar coordinates, vectors, sequences, an introduction to limits | AP Precalculus or AP Statistics in May, if the AP version is taken |
On the accelerated track the whole sequence moves up one year: Algebra 1 in 8th grade, Geometry in 9th, Algebra 2 in 10th, Pre-Calculus in 11th, and AP Calculus AB or BC in 12th. A few schools offer a doubly accelerated route that reaches Calculus BC in 11th and a multivariable or linear algebra course in 12th. We have written separately about what grade you take Algebra 1 and what grade you take calculus, so the detail of the tracks is there.
Integrated Math. California and a few other states replace Algebra 1, Geometry and Algebra 2 with Integrated Math 1, 2 and 3, which teach the same content mixed across the three years: Math 1 has linear functions, systems, the start of geometry and statistics; Math 2 has quadratics, more geometry, proof and probability; Math 3 has polynomials, logarithms, trigonometry and the rest of Algebra 2. A student who moves between an integrated district and a traditional one lands with gaps on both sides, and the first month with a tutor is spent finding them.
Graduation. Most states require three or four math credits for a high school diploma, with Algebra 1 and Geometry nearly always among them. Calculus is never required for graduation; it is required, in practice, by selective engineering and science admissions.
The syllabus for each course, in detail
Each high school course has its own guide on this site, with the units in order, the state tests, and where students lose marks: the Algebra 1 syllabus, the Algebra 2 syllabus and the Pre-Calculus syllabus. The Grade 8 syllabus has one as well. This article is the map; those are the territory.
The state tests, grade by grade
| Grade | What is tested | Examples by state |
|---|---|---|
| 3 to 8 | The grade's math standards, every spring | STAAR (Texas), MCAS (Massachusetts), the NY State tests (New York), SBAC (California, Washington and others), FAST (Florida), the PSSA (Pennsylvania) |
| 8 or 9 | Algebra 1, as an end-of-course exam, where the state has one | Regents Algebra I (NY), STAAR Algebra I (TX), Algebra 1 EOC (FL), the Georgia Milestones |
| 10 | Geometry, in some states | Regents Geometry (NY); the Biology and Geometry EOCs in Florida |
| 11 | Algebra 2 in New York; the SAT or ACT, which about half the states give in school | Regents Algebra II (NY); the SAT as the state test in Connecticut, Michigan, Illinois and others |
| 11 or 12 | AP exams in May for AP courses | AP Precalculus, AP Calculus AB and BC, AP Statistics |
The grade 3 to 8 tests matter less than parents fear: they grade the school more than the child, and a poor score has no consequence for the child's record in most states. The end-of-course exams matter more, because in New York and Texas they are graduation requirements, and the Regents score goes on the transcript colleges see.
US grades matched to CBSE classes
This is the table families moving from India ask for. It matches by content, not by age, because the two systems order the content differently: CBSE front-loads arithmetic and algebra, the Common Core front-loads data, reasoning and the explanation of method.
| US grade | Age | CBSE class with the same age | Where the US content sits in CBSE | What the child from India is usually ahead in | What the child is usually behind in |
|---|---|---|---|---|---|
| K to 2 | 5 to 8 | Classes 1 and 2 | Class 1 and 2 | Mental arithmetic, number facts | Explaining a method in words, measurement in inches and feet |
| 3 to 5 | 8 to 11 | Classes 3 to 5 | Class 3 to 5, with fractions a year earlier in CBSE | Multiplication tables, long multiplication and division | Fractions as numbers, data and graphs, multi-step word problems |
| 6 | 11 to 12 | Class 6 | Class 6 and 7 (ratio, integers), Class 8 (some data) | Integers, basic algebra | Statistics, unit rates, explaining reasoning |
| 7 | 12 to 13 | Class 7 | Class 7 and 8 (proportion, percent, simple equations) | Equations, percent arithmetic | Probability, scale drawings, two-step inequalities |
| 8 | 13 to 14 | Class 8 | Class 8 (exponents, linear equations) and Class 9 (irrational numbers, Pythagoras is Class 7 in CBSE) | Algebraic manipulation, exponents | Functions, scatter plots and lines of best fit, transformations |
| 9 (Algebra 1) | 14 to 15 | Class 9 | Class 8 to 10 (linear equations, polynomials, factorisation, quadratics are Class 10) | Factorising, solving equations | Exponential functions, two-variable statistics, word problems in American vocabulary |
| 10 (Geometry) | 15 to 16 | Class 10 | Class 9 and 10 geometry, plus proof written out at length, which CBSE does less of | Theorems, trigonometric ratios | Formal two-column proof, transformations, coordinate proof |
| 11 (Algebra 2) | 16 to 17 | Class 11 | Class 11 (complex numbers, sequences, trigonometric functions, logarithms are Class 11) | Trigonometric identities, sequences | Logarithm applications, the normal distribution, modelling questions |
| 12 (Pre-Calculus or Calculus) | 17 to 18 | Class 12 | Class 12 (calculus) is close to AP Calculus AB; Pre-Calculus is mostly Class 11 | Differentiation and integration techniques | Applied and modelling questions, the AP free-response style |
The practical reading of the table: a child arriving from CBSE is usually a course ahead in computation and a course behind in American vocabulary, data and reasoning, and both are true at once. The second one costs marks on every state test and on the SAT; the first one is wasted if the child is not stretched. We check both in the first class and start where the gap is.
What a parent can do with this
- Find the grade and the course. For Grades K to 8, the grade. For 9 to 12, the course, by name, from the school's course catalog or the counsellor, and which track the child is on.
- Check the one skill that decides the next year, from the tables above. In elementary school it is almost always fractions by Grade 5; in middle school, proportional reasoning by Grade 7; in high school, factoring and slope by the end of Algebra 1.
- Know the test attached to the year, and from Grade 3 practise its format once a term, not only its content: the explanation questions, the multi-select items, the calculator sections.
- If the child arrived from India, do not teach the CBSE syllabus alongside; teach the American course to a high standard, then stretch with harder problems on the same topics, Kangaroo and AMC 8, once the school work is secure.
Where to get help
Our math tutors from India to USA teach the American sequence in the American order: Common Core from Grade 1, the state test formats, then Algebra 1, Geometry, Algebra 2, Pre-Calculus and AP Calculus, one tutor with one child on a shared whiteboard, at 7 am before school, after 4 pm and on weekend mornings US time, from US$10 to $13 an hour. The first 30-minute class is free and finds the gap. The grade pages for Grade 1 to Grade 8 math and the course pages for Algebra 1, Geometry, Algebra 2 and Pre-Calculus say what each year's class works on.
Questions parents ask
1Is there one national math syllabus in the USA?
2What is the high school math syllabus in the USA?
3Which US grade matches CBSE Class 8?
4When do American students take algebra?
5Do US schools teach calculus?
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