What Math Should a 6th, 7th, or 8th Grader Know?

My oldest came home from her first month of sixth grade asking me what a "unit rate" was, and I realized the math had quietly changed shape on me. It was not bigger numbers anymore. It was a different kind of thinking, full of ratios and negative signs and letters where the numbers used to be. I could still do the problems, but I could not have told you which ones were even supposed to show up in which grade.

So here is the map I built for myself. In short: sixth grade is the year of ratios, rates, and percents, seventh grade is proportional reasoning and negative numbers in full, and eighth grade is the on-ramp to algebra, with linear equations and functions. Almost all of it is aligned to the Common Core math standards that most U.S. states follow. Here is the grade-by-grade version.

What math should a 6th grader know?

Sixth grade is where ratios arrive and quietly take over. The headline idea is comparing quantities: a ratio, a unit rate, a percent. These are the same idea wearing three outfits, and they carry an enormous share of the math that follows.

• Understand ratio and unit-rate concepts, and use them to solve problems (including percents as a rate per 100).
• Divide a fraction by a fraction, and fluently divide multi-digit numbers and operate with multi-digit decimals.
• Extend the number line to negative numbers, and find absolute value and points in all four quadrants of the coordinate plane.
• Write and evaluate expressions with whole-number exponents and variables, and solve one-variable equations like x + 4 = 9.
• Find area of triangles and quadrilaterals, surface area from nets, and work with measures of center like mean and median.

If a child leaves sixth grade unsure whether a percent is a kind of ratio, or thinking of a variable as a mystery rather than a stand-in for a number, those are the gaps to close before seventh grade leans on them.

What math should a 7th grader know?

Seventh grade takes the ratio idea and makes it the main event. The word for the year is proportional, and negative numbers stop being a new visitor and become part of every operation.

• Recognize proportional relationships, find the constant of proportionality, and represent it as a table, graph, or equation.
• Add, subtract, multiply, and divide all rational numbers, including negatives, and understand why a negative times a negative is positive.
• Solve multistep percent problems: tax, tip, discount, markup, simple interest, and percent increase or decrease.
• Solve two-step equations and inequalities of the form px + q = r, and combine like terms in linear expressions.
• Work with scale drawings, angle relationships, circle area and circumference, and probability of simple and compound events.

This is the grade where earlier fraction gaps tend to surface. Proportional reasoning sits directly on top of fraction sense, so a child who never fully trusted that two-thirds is a single number often feels the floor go soft right here.

What math should an 8th grader know?

Eighth grade is the bridge year, the last stop before formal algebra. Much of it is algebra in everything but name: lines, slopes, functions, and solving for unknowns on both sides of an equals sign.

• Understand and graph linear equations, find slope, and solve equations with variables on both sides (including ones with no solution or infinitely many).
• Solve systems of two linear equations, by graphing and by algebra.
• Define and compare functions, and read rate of change from a table, graph, or equation.
• Use the Pythagorean theorem, and find the volume of cylinders, cones, and spheres.
• Work with integer exponents, square and cube roots, scientific notation, and the difference between rational and irrational numbers.

Some districts offer a full Algebra 1 course in eighth grade for students who are ready, but the standard eighth-grade track above is what algebra is built on. Either way, the through-line is clear: every year of middle school has been bending toward this.

Knowing the standard is not the same as mastering it

Here is the trap a list like this can set. It can leave you either reassured or alarmed, and both can be wrong. Standards describe what gets taught. They say nothing about what your specific child has actually learned. A kid can sit through every lesson on slope and still not believe, in their gut, that slope and unit rate are the same idea.

And keep the framing that makes any of this useful: a gap is not a verdict, it is a coordinate. If your seventh grader is strong on percents but wobbly on dividing negative numbers, that is not "bad at math." It is one nameable skill to go get. The point is to find what they have not learned yet, while there is still room to fix it before algebra.

How to check what actually stuck

The fastest way to turn this map into something you can act on is to measure against it. A short adaptive math assessment adjusts its difficulty to each answer, so in about eight minutes it finds the level your child can sustain and breaks the result down by topic, calibrated to NWEA MAP and iReady. Instead of "sixth-grade math," you get "solid on ratios, shaky on negative numbers," which is the only version that tells you what to do next.

If you want the elementary half of this map, the foundation everything above is built on, it is in what math should a 3rd to 5th grader know. And if you want the longer version of how the measurement works, it is all in how Test My Kid works. Find the one skill to work on this month, then go work on it. That beats guessing, which is exactly what I was doing in the cereal aisle that first week of sixth grade.