Grade 7
By Knomi Learning · Updated
The short answer
A 7th grader learns 28 math topics, in 6 units: Proportional Relationships, Percents, Rational Numbers, Expressions and Equations, Geometry and Probability and Statistics. That is 91 smaller skills in all, taught in the order below, each building on earlier ones.
Your kid already finds unit rates like miles per hour with whole numbers. Now the amounts are fractions, such as half a mile in a quarter of an hour, and the same idea still works.
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Two quantities are proportional when one is always the same multiple of the other. Your kid learns to spot that in tables and stories, and to name the multiplier: the constant of proportionality.
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Every proportional relationship can be written as one short equation, y = kx. Your kid writes that equation from a table or a story and uses it to find any missing value.
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On a graph, a proportional relationship is a straight line through the origin. Your kid reads the unit rate off the graph and explains what each point means in the story.
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Maps, floor plans and models are scale drawings: the real thing shrunk or enlarged by one multiplier. Your kid uses proportional reasoning to move between the drawing and the real size.
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Your kid already finds a percent of a number. Now percents describe change, such as prices going up or crowds shrinking, and the key question is always 'percent of what?'
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Tax, tips, sales, commission and interest are percents your kid will meet for the rest of their life. Here they learn how each one works and how to chain them together.
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Your kid met negative numbers last year as places on the number line. Now they start doing arithmetic with them, beginning with what happens when positives and negatives are added.
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Subtracting a negative can feel upside down. Your kid learns why taking away a negative is the same as adding a positive, and how subtraction measures the distance between two numbers.
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The rules your kid learned for adding and subtracting integers carry straight over to negative fractions and decimals. This is where signs meet common denominators and lined-up decimal points.
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Why is a negative times a negative a positive? Your kid builds the sign rules from patterns and from the distributive property, so the rule is something they understand and not just remember.
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Division undoes multiplication, so the sign rules come along for free. Your kid divides with negatives and learns that a minus sign can sit in three places in a fraction and mean the same thing.
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Every fraction can be written as a decimal by dividing. Your kid finds that some decimals stop and others repeat forever, and that those are the only two things that can happen.
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This is where the whole number system comes together. Your kid multiplies and divides negative fractions and decimals, then uses all four operations in longer problems.
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Your kid simplified expressions like 2(3 + 8x) last year. Now the numbers can be negative or fractions, which is where most algebra slips happen and where careful habits start.
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Your kid moves from one-step equations to equations that take two moves to undo, like 3x + 5 = 20. They learn to solve them smoothly and to write them from word problems.
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A story with a rate and a starting amount, or equal groups with something added to each, turns into a two-step equation. Your kid learns to write the right equation, solve it, and answer the question that was asked.
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Some questions have a whole range of answers: 'at least', 'no more than'. Your kid solves inequalities much like equations, with one new twist: multiplying or dividing by a negative flips the sign.
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Your kid meets π, the number you get when you divide any circle's distance around by its distance across. From there come the two circle formulas and where they come from.
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When lines cross, the angles they make are tied together by a few simple rules. Your kid learns those rules and uses equations to find angles nobody measured.
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Give three measurements and ask for a triangle: sometimes there is exactly one, sometimes many, sometimes none at all. Your kid draws to find out, and learns the rules behind the surprises.
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Slice a block of cheese and look at the cut face: that flat shape is a cross section. Your kid learns to picture which shapes appear when a prism or pyramid is sliced in different directions.
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Your kid takes volume and surface area beyond boxes, to prisms with triangle or trapezoid ends and shapes built from several pieces, and solves the kind of problems a builder or packer would face.
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How likely is it? Your kid learns to put a number on chance, from 0 for impossible to 1 for certain, and to work that number out for coins, dice, spinners and bags of marbles.
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Flip a coin ten times and you probably won't get exactly five heads. Your kid learns how results from real trials relate to the probability on paper, and how to use each to predict the other.
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Two dice, a coin and a spinner, three coin flips in a row. Your kid learns to lay out every possible combination in a list, table or tree, and to find the chance of the ones they care about.
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You can't ask every kid in the country a question, but you can ask a well-chosen few. Your kid learns what makes a sample trustworthy and how far its results can be stretched.
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Are seventh graders really taller than sixth graders, or do the groups mostly overlap? Your kid compares two sets of data using both the typical value and the spread, and decides how convincing a difference is.
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On Knomi's map, 7th grade math has 28 topics in 6 units, made of 91 smaller skills.
The earlier topics 7th grade leans on most are Percents (Grade 6), One-Step Equations (Grade 6), Unit Rates (Grade 6), Area of Polygons (Grade 6) and Equivalent Ratios (Grade 6). A student who is quick and sure with those is ready. Each topic below lists exactly what it builds on.
Common Core is the spine. All 91 skills carry a Common Core reference, and the order follows the usual US course.
Every one of them has a full lesson on Knomi. The 7th grade map is open to anyone, with no account needed to look around.
Every topic above, with lines to what it needs first. Open it and look around, no account needed.
Open the Grade 7 map