Algebra 1 is the first course in the American high school sequence and the one with the most riding on it: in New York and Texas its end-of-course exam is a graduation requirement, the SAT's largest section is built from it, and every course after it, Geometry, Algebra 2, Pre-Calculus and Calculus, assumes all of it. Parents search for the Algebra 1 syllabus for two reasons: a 9th grader (or an accelerated 8th grader) is about to start it and the family wants to know what is coming, or a student is in it and losing ground and the family wants to know where. This guide is the Algebra 1 curriculum unit by unit as US schools teach it, what each unit assumes, the exams, the five places marks are lost, a fifteen-question check for the summer before, and the mapping to CBSE for families from India.
The eleven units, in order
Textbooks differ in how they group things (Big Ideas, enVision, Illustrative Mathematics, Eureka and the open Khan Academy course all order the material slightly differently), but the content is the same because the state standards are the same. The order below is the commonest.
| Unit | What it covers | What it assumes | Weeks |
|---|---|---|---|
| 1. Expressions and the real numbers | Order of operations; variables and expressions; properties of real numbers (commutative, distributive); rational and irrational numbers; evaluating and simplifying expressions, combining like terms | Grade 8 number system, integer arithmetic | 2 to 3 |
| 2. Solving linear equations | One-step to multi-step equations; variables on both sides; equations with no solution or infinitely many; literal equations (solving for a chosen variable); ratio and proportion; percent problems as equations | Two-step equations from Grade 7 and 8 | 3 |
| 3. Linear inequalities | Solving and graphing one-variable inequalities; reversing the sign when multiplying by a negative; compound inequalities (and, or); absolute value equations and inequalities | Unit 2 | 2 |
| 4. Linear functions and graphs | Functions, domain and range, function notation f(x); slope as rate of change; slope-intercept, point-slope and standard forms; graphing lines; parallel and perpendicular lines; arithmetic sequences as linear functions; direct variation | Grade 8 slope and y = mx + b | 4 to 5 |
| 5. Systems of equations and inequalities | Systems by graphing, substitution and elimination; systems with no solution or infinitely many; word problems leading to systems; graphing linear inequalities and systems of inequalities | Units 2 to 4 | 3 |
| 6. Exponents and exponential functions | Laws of exponents including rational exponents; exponential growth and decay functions; comparing linear and exponential models; geometric sequences | Grade 8 integer exponents | 3 |
| 7. Polynomials | Adding, subtracting and multiplying polynomials; the distributive property at length; special products (squares of binomials, difference of squares) | Unit 1 | 2 |
| 8. Factoring | Greatest common factor; factoring trinomials with leading coefficient 1, then other leading coefficients; difference of squares; perfect-square trinomials; factoring by grouping; solving equations by factoring and the zero-product property | Unit 7 | 3 |
| 9. Quadratic functions and equations | Graphing parabolas from standard, vertex and factored form; the vertex, axis of symmetry and intercepts; transformations of y = x²; solving by factoring, square roots, completing the square and the quadratic formula; the discriminant; linear versus quadratic versus exponential models | Units 7 and 8 | 4 to 5 |
| 10. Radicals and sequences | Simplifying square roots; operations with radicals; sometimes rational functions and inverse variation; arithmetic and geometric sequences revisited with explicit and recursive rules | Unit 6 | 2 |
| 11. Statistics | Dot plots, histograms and box plots; measures of centre and spread, including standard deviation in some states; two-way frequency tables; scatter plots, correlation and the line of best fit, with residuals in some states | Grade 8 statistics | 2 to 3 |
Some states and textbooks add a short unit on piecewise and step functions, and the Regents course includes a little more on function transformations. None of that changes the shape of the year.
How the year is paced
A typical August-to-May year gives the first semester to units 1 to 5, the linear half of the course, and the second semester to units 6 to 11, the non-linear half. The midpoint matters: a student who ends the first semester able to graph a line from any form, solve a system and turn a word problem into an equation is in a good position, and a student who cannot is about to meet exponents, factoring and quadratics on a weak base. Most of the students who come to us "failing Algebra 1" come in February, and the problem is nearly always in the first semester.
The end-of-course exams
| State | Exam | What to know |
|---|---|---|
| New York | Regents Examination in Algebra I | Three hours; multiple choice plus constructed-response questions marked with partial credit; a pass (65) is required for graduation; the score goes on the transcript. The constructed-response questions reward written working and explanation. |
| Texas | STAAR Algebra I end-of-course | Required for graduation; online; multi-select and gridded-response items; a graphing calculator is provided on screen. |
| Florida | Algebra 1 EOC (B.E.S.T. standards) | Required for a standard diploma, or a comparable SAT or ACT score; 30 percent of the course grade by law. |
| Georgia | Georgia Milestones Algebra: Concepts and Connections | 20 percent of the course grade. |
| Most other states | No separate Algebra 1 exam | The content appears in the state's high school test or in the SAT or ACT, which about half the states give in school in 11th grade. |
For the exam states, one timed sitting of a released paper in April does more than another week of content. The constructed-response questions on the Regents in particular are lost by students who know the answer and write nothing down.
The five places students lose marks
- Fractions and negative numbers inside the algebra. Not an Algebra 1 topic, and the cause of most Algebra 1 failures. A student who cannot add 2/3 and −3/4 cannot solve an equation containing them, and the course is full of them. This is checked in the first class, and fixed in ten minutes a week while the course continues.
- Slope as a number rather than a rate. Students learn rise over run and lose the question that asks what the slope means: "the plan costs 15 dollars more for every month". Every linear word problem turns on it.
- Word problems into equations. The language is the barrier, especially for students whose home language is not English: "three less than twice a number" is 2x − 3, not 3 − 2x. We teach a four-line method (name the unknown, write the relationship in words, translate, check) and use it on every problem until it is automatic.
- Factoring. The unit where Algebra 1 is lost for most of the students who lose it. Trinomials with a leading coefficient other than 1, and knowing which factoring pattern applies, need more practice than any school gives: twenty minutes a day for three weeks, with the patterns on one page.
- The quadratic formula with sign errors. −b when b is negative, the square root of the discriminant, dividing the whole numerator by 2a. Students who write every step lose nothing; students who skip steps lose a question a page.
A fifteen-question readiness check
For the summer before Algebra 1. No calculator. Answers follow.
- Compute −7 + 12 − (−4).
- Compute 2/3 − 3/4.
- Compute (−3)² and −3².
- Simplify 5x + 3 − 2x + 8.
- Solve 3x − 7 = 11.
- Solve 2(x + 4) = x − 1.
- What is 15 percent of 80?
- Write 2⁵ × 2³ as a single power.
- Write 0.0034 in scientific notation.
- Find the slope of the line through (1, 3) and (4, 12).
- Write the equation of the line with slope 3 and y-intercept −2.
- Solve the system y = x + 2 and y = 3x − 4.
- Write "five more than three times a number n" as an expression.
- A right triangle has legs 6 and 8. Find the hypotenuse.
- Is y = x² a linear function? How do you know?
Answers: 1. 9. 2. −1/12. 3. 9 and −9. 4. 3x + 11. 5. x = 6. 6. x = −9. 7. 12. 8. 2⁸. 9. 3.4 × 10⁻³. 10. 3. 11. y = 3x − 2. 12. x = 3, y = 5. 13. 3n + 5. 14. 10. 15. No; the rate of change is not constant (or: its graph is not a line).
Thirteen or more right: ready. Ten to twelve: ready, with the missed questions as the first month's warm-ups. Fewer than ten: four weeks on Grade 8 before the course starts is worth more than anything done during it, and our four-week fix for students who are bad at algebra is the plan for that.
Algebra 1 against CBSE, for families from India
| Algebra 1 unit | Where CBSE covers it | The student from India is… |
|---|---|---|
| Expressions, real numbers | Class 8 (rational numbers), Class 9 (number systems, irrationals) | Ahead |
| Linear equations | Class 8 (one variable), Class 9 and 10 (two variables) | Ahead on solving; new to literal equations and the American word-problem vocabulary |
| Inequalities, absolute value | Class 11 (linear inequalities) | Behind by two years; the topic is new |
| Linear functions, slope, function notation | Class 9 (coordinate geometry), Class 11 (functions) | Behind on the function vocabulary and on slope as a rate |
| Systems | Class 10 (pair of linear equations in two variables) | Ahead on method, behind on graphing and on word problems |
| Exponents and exponential functions | Class 8 (exponents); exponential functions are not in CBSE school maths | Ahead on laws; the growth and decay functions are new |
| Polynomials, factoring | Class 8 (factorisation, identities), Class 9 (polynomials) | Ahead by a year |
| Quadratics | Class 10 (quadratic equations) | Ahead on solving; behind on graphing parabolas, vertex form and transformations |
| Radicals, sequences | Class 9 (surds), Class 10 (arithmetic progressions) | Ahead on surds; geometric sequences are new (Class 11) |
| Statistics | Class 9 and 10 (mean, median, mode, grouped data) | Behind on scatter plots, two-way tables, standard deviation |
The pattern is the usual one: ahead on manipulation, behind on functions, graphs, statistics and language. A student from India in Algebra 1 should not revise factoring; the first month should go to function notation, slope as a rate, exponential models and the word-problem method, which are the things the Regents and the SAT test and CBSE never taught.
Where to get help
Our Algebra 1 classes teach the eleven units in this order, one tutor with one child on a shared whiteboard, the student writing for most of the hour and every line read, the end-of-course exam practised from released papers in the spring, 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 runs the readiness check. The Algebra 1 page says what the class works on each term; our math tutors from India to USA page says how the arrangement works for US families. The Algebra 2 syllabus is the next guide.
Questions parents ask
1What is in the Algebra 1 syllabus?
2What grade is Algebra 1?
3Is there an exam at the end of Algebra 1?
4What is the hardest part of Algebra 1?
5Which CBSE class covers Algebra 1?
See how we teach this, 1-on-1 online →
Shobha
Founder and lead tutor, Science with Shobha
Teaching maths, science and English to children online since 2018. 500+ students, 20+ tutors, families in nine countries.