Grade 8 is the most important year in the American math syllabus and the one parents know least about. It is the year the arithmetic of Grades 1 to 7 turns into algebra: slope, linear equations, systems and the idea of a function all arrive here, and the Algebra 1 course a year later assumes every one of them. It is also the fork between the two tracks, because about a third of students take Algebra 1 in 8th grade instead and reach calculus by 12th. This guide is the 8th grade math curriculum in the USA domain by domain, with what each unit assumes from Grade 7, a month-by-month plan for the standard year, the state test, the accelerated option, a twelve-question check, and a comparison with CBSE Class 8 for families from India.
The five domains, in the order schools teach them
The Common Core organises Grade 8 into five domains. Most textbooks and districts teach them in roughly the order below, with the number system first because exponents and roots are needed everywhere after.
| Domain | What the student learns | What it assumes from Grade 7 | Where marks are lost |
|---|---|---|---|
| The number system | Rational and irrational numbers; that every number has a decimal expansion; estimating square roots of non-perfect squares; placing β2 or Ο on a number line | Fractions to decimals, the four operations with negatives | Calling 0.333β¦ irrational; estimating β50 as "about 25" |
| Expressions and equations, part 1 | Integer exponents and their laws, including negative and zero exponents; square and cube roots as the inverses of squaring and cubing; scientific notation and operations in it | The order of operations, powers of 10 | Negative exponents (2β»Β³ is 1/8, not β8); adding numbers in scientific notation with different exponents |
| Expressions and equations, part 2 | Proportional relationships as lines through the origin; slope as a rate; the equation y = mx + b; solving linear equations in one variable with the variable on both sides, including ones with no solution or infinitely many; systems of two linear equations by graphing, substitution and elimination | Proportional relationships and the constant of proportionality; two-step equations | Reading slope from two points in the wrong order; a system "solved" by finding only x |
| Functions | What a function is (one output for each input); comparing functions given as tables, graphs, equations and descriptions; linear versus non-linear; building a linear function from a situation and interpreting its rate and starting value; describing a graph qualitatively | Reading a graph, the coordinate plane | Treating every relation as a function; confusing the rate with the starting value in a word problem |
| Geometry | Translations, reflections, rotations and dilations; congruence and similarity defined through transformations; angle facts for parallel lines cut by a transversal and the angle sum of a triangle; the Pythagorean theorem, its converse, and its use for distance in the coordinate plane; volume of cylinders, cones and spheres | Area and circumference of circles, angle relationships, scale drawings | Which coordinate changes sign in a reflection; using the Pythagorean theorem when the given sides are not legs |
| Statistics and probability | Scatter plots and the pattern they show; a line of best fit drawn by eye and its equation read as a rate; two-way tables of categorical data and the relative frequencies in them | Mean, median, probability from Grade 7 | Describing a scatter plot as "positive" without saying what increases with what; reading row and column frequencies off the wrong total |
The three ideas that Algebra 1 will assume completely are slope, the equation of a line and the solution of a system. A student who leaves Grade 8 able to find slope from two points, write y = mx + b from a graph or a story, and solve a system by substitution is ready for Algebra 1 whatever else was shaky.
A month-by-month plan for the standard year
Schools vary, but a typical August-to-May year runs like this, and a family can use it to know what is coming.
| Month | Unit | What to check at home |
|---|---|---|
| August to September | Real numbers, exponents, roots, scientific notation | Can the student write 0.00045 in scientific notation and explain why 5β° is 1? |
| October | Solving linear equations, including the variable on both sides | Can the student solve 3(x β 2) = 2x + 7 and say what 2x + 3 = 2x + 5 means? |
| November | Proportional relationships, slope, y = mx + b | Given two points, can the student find the slope and the equation? |
| December | Functions | Can the student tell from a table whether a relationship is a function, and whether it is linear? |
| January | Systems of linear equations | Can the student solve a system by substitution and check the answer in both equations? |
| February | Transformations, congruence, similarity, angle facts | Can the student give the coordinates after a rotation of 90Β° about the origin? |
| March | The Pythagorean theorem and distance; volume | Can the student find the distance between (1, 2) and (4, 6)? |
| April | Scatter plots, lines of best fit, two-way tables | Can the student read a line of best fit as "about 3 more for every 1 more"? |
| May | Review and the state test | The released test from the state, timed, once |
The state test
Every state tests Grade 8 math in the spring: the Grade 8 STAAR in Texas, the Grade 8 MCAS in Massachusetts, the New York State Grade 8 test, SBAC in California, Washington and others, the Florida FAST, the PSSA in Pennsylvania. The format matters more than parents expect: multi-select questions where two answers are right, questions that ask for an explanation in a sentence, a calculator section and a no-calculator section, and in several states an online test with drag-and-drop and graphing tools. A child who knows the content and has never seen the format loses a grade band. One timed sitting of the state's released test, in April, is enough to fix that.
Students taking Algebra 1 in Grade 8 usually sit the Algebra 1 end-of-course exam instead (the Regents Algebra I in New York, the STAAR Algebra I EOC in Texas, the Algebra 1 EOC in Florida), and in those states that score follows them onto the high school transcript.
The accelerated option: Algebra 1 in 8th grade
About a third of American students take Algebra 1 in 8th grade. Their districts compress the Grade 8 content into Grade 7, or run a "Grade 7 accelerated" course, and the Grade 8 year is the full Algebra 1 syllabus: everything above plus quadratics, exponential functions, polynomials and factoring. The track reaches AP Calculus in 12th grade and is the usual route for students aiming at engineering or science.
Placement is decided in Grade 6 or 7 by a test, a teacher recommendation, or both, and the five skills that decide whether a child is ready are fractions, negative numbers, proportional reasoning, two-step equations and turning a sentence into an expression. A child from India who arrives in Grade 6 or 7 is often a strong candidate for the accelerated track, because the computation is there; the risk is the vocabulary of American word problems, which the placement test is full of. We have written about what grade you take Algebra 1 and how the placement works; the Algebra 1 syllabus is set out unit by unit in its own guide.
A twelve-question check for the end of Grade 8
A student who can do these twelve, without help and without a calculator except where noted, has the year. Answers follow.
- Write 3β»Β² as a fraction.
- Write 0.00072 in scientific notation.
- Between which two whole numbers does β40 lie?
- Solve 4(x + 3) = 2x β 6.
- What is the slope of the line through (2, 5) and (6, 13)?
- Write the equation of the line with slope β2 through (0, 7).
- Solve the system y = 2x + 1 and y = βx + 7.
- Is the relation {(1, 4), (2, 5), (1, 6)} a function? Why or why not?
- The point (3, β2) is reflected in the y-axis. Where does it land?
- A right triangle has legs 9 and 12. How long is the hypotenuse?
- What is the volume of a cylinder with radius 3 and height 10, in terms of Ο?
- A scatter plot of hours studied against test score rises to the right. In one sentence, what does that show?
Answers: 1. 1/9. 2. 7.2 Γ 10β»β΄. 3. 6 and 7. 4. x = β9. 5. 2. 6. y = β2x + 7. 7. x = 2, y = 5. 8. No; the input 1 has two outputs. 9. (β3, β2). 10. 15. 11. 90Ο. 12. Students who studied more hours tended to score higher.
Ten or more right: ready for Algebra 1. Seven to nine: ready, with the missed topics revisited in the first month. Fewer than seven: the summer is worth spending on Grade 8, because Algebra 1 assumes all of it.
US Grade 8 against CBSE Class 8
Families from India ask whether Grade 8 in the USA is easier than Class 8. It is different, and the table shows how.
| Topic | CBSE Class 8 | US Grade 8 | The child from India is⦠|
|---|---|---|---|
| Rational and irrational numbers | Rational numbers and their properties | Irrational numbers, roots, decimal expansions | Behind on irrationals (they are Class 9 in CBSE) |
| Exponents | Exponents and powers, including negative exponents | The same, plus scientific notation and operations in it | Level |
| Linear equations | Linear equations in one variable, including the variable on both sides | The same, plus two-variable equations, slope and graphs | Ahead on solving; behind on slope and graphing |
| Systems of equations | Not in Class 8 (Class 10) | Systems of two linear equations | Behind |
| Functions | Not in Class 8 | Functions, linear and non-linear | Behind; the word "function" is new |
| Factorisation and identities | Factorisation, algebraic identities, division of polynomials | Not in Grade 8 (Algebra 1) | Ahead by a year |
| Geometry | Quadrilaterals, practical geometry (constructions), mensuration | Transformations, similarity, angle facts, the Pythagorean theorem in the coordinate plane | Ahead on mensuration; behind on transformations and coordinate work |
| Data | Data handling: bar graphs, pie charts, probability | Scatter plots, lines of best fit, two-way tables | Behind |
| Squares, cubes, roots | Squares and square roots, cubes and cube roots | The same, used for the Pythagorean theorem and volume | Level |
The practical plan for a child arriving in Grade 8 from Class 8: do not revise the Class 8 algebra, which is secure; spend the first term on functions, slope, systems and scatter plots, which are new; and keep the factorisation sharp, because Algebra 1 will want it a year early. A child in this position is usually a good candidate for Algebra 1 in Grade 8 if the school allows a late placement.
Where to get help
Our Grade 8 math classes teach the American year in the order above, one tutor with one child on a shared whiteboard, with the state test format practised from the spring, at 7 am before school, after 4 pm and on weekend mornings US time, from US$10 to $13 an hour. For a child from India we run the twelve-question check in the free first class and start where the gap is. The Grade 8 math page, and our online math tutors from India to USA page, say how the class works and what it costs.
Questions parents ask
1What is in the 8th grade math curriculum in the USA?
2Is 8th grade math the same as Algebra 1?
3What math should an 8th grader know before the year starts?
4How is Grade 8 math in the USA different from CBSE Class 8?
5Is there a state test for 8th grade math?
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Teaching maths, science and English to children online since 2018. 500+ students, 20+ tutors, families in nine countries.