Grade 3
By Knomi Learning · Updated
The short answer
A 3rd grader learns 25 math topics, in 7 units: Multiplication; Numbers to 1,000; Division; Fractions; Patterns and Problem Solving; Shapes, Area and Perimeter; and Time, Measurement and Data. That is 63 smaller skills in all, taught in the order below, each building on earlier ones.
Hop through numbers by 2s, 5s, 10s, and 100s, and sort the evens from the odds. These counting rhythms are the secret on-ramp to multiplication.
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Meet the biggest new idea of the grade: multiplication as equal groups, seen through skip-counting, arrays, and turn-around facts. Everything downstream — facts, division, area — grows from the pictures built here.
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Conquer every one-digit multiplication fact — friendly families first, then strategies like distributive splits for the tough ones — until each product has a strategy behind it.
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Mixed practice until every product comes quickly from memory, then stories with equal groups and arrays hiding inside them. Fluency here is the entry ticket to division, area, and grade 4.
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Get to know numbers up to 1,000 from the inside: what each digit is worth and where every number lives on the number line. This is the home base the whole grade's arithmetic leans on.
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Grow from two-digit facts to confident three-digit adding and subtracting within 1,000 — with several good strategies to choose from, and the standard algorithm for when regrouping gets serious.
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Round to friendly landmarks on the number line, then use those landmarks to predict a sum or difference before computing it. This is where the kid starts checking their own answers like a mathematician instead of waiting to be told.
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Put adding and subtracting to work: turn a story into an equation, draw a bar model to see the parts and the whole, and handle dollars and cents like a shopkeeper. Money is three-digit arithmetic in a costume kids already love.
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Meet division as fair sharing and grouping, then discover its secret: every division question is a multiplication question in disguise.
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Fact families turn known multiplication facts into division fluency, missing-number puzzles, and word problems where the kid decides whether to multiply or divide. When a division fact stalls, the fix is almost always the matching multiplication fact.
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Stretch the facts into bigger numbers: regroup factors to make friendly products, then multiply by multiples of ten by thinking in tens. A first glimpse of how multiplication scales up, and it leans on place value as much as on the facts.
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Cut wholes into truly equal parts, meet the unit fraction 1/b as the atom of the fraction world, and build every fraction a/b out of those atoms. The make-or-break ideas under every fraction the kid will ever meet.
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The pivotal move of the grade: fractions stop being pictures of pie and become genuine numbers with places on the number line — including fractions past 1 and the fraction names of whole numbers.
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Which fraction is bigger — and when are two fractions secretly the same number? Models first, then pure reasoning about numerators and denominators, always recorded with >, =, or <.
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Go pattern-hunting in the addition and multiplication tables, then flip it around: use rules to generate numbers with function machines. Tables stop being things to memorize and become things to explore.
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The capstone of the grade's arithmetic: expressions that mix two operations, and two-step stories solved with a single equation and a letter for the unknown — with estimation on hand to sanity-check every answer.
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Stop just naming shapes and start describing what they actually have — sides, square corners, parallel sides — then use those attributes to sort the surprisingly big family of quadrilaterals.
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Cover shapes with unit squares and count — then discover that the rows of squares are an array, so length × width was hiding there all along. Missing sides turn area into a playground for fact-family thinking.
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Slice a rectangle into two smaller ones and see the distributive property as a picture, then break L-shapes and staircases into rectangles and add the pieces. Decomposing a hard shape into easy ones is a move that reaches far beyond area.
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Walk the distance around a shape: add up side lengths, hunt for missing sides using shape properties, and discover the surprising fact that perimeter and area can disagree — same fence, different yards.
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Fractions leave the worksheet: find a fraction of a group of objects, share a shape into parts with equal areas, and solve stories where fractions do real work. The fraction spine and the sharing spine meet here.
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Read clocks to the exact minute, then measure how much time passes — using number-line jumps so clock arithmetic never turns into digit-subtraction traps.
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Get a physical feel for centimeters and meters, grams and kilograms, milliliters and liters — is a cat 4 grams or 4 kilograms? — then put all four operations to work on measurement stories.
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Turn numbers into pictures and back: picture graphs where one symbol means five, and bar graphs with jumping scales. The scale turns graph-reading into multiplication practice with a purpose.
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Fractions leave the worksheet and show up on a ruler: measure to the nearest half or quarter inch, then plot the results on a line plot and read the stories in the clusters and gaps.
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On Knomi's map, 3rd grade math has 25 topics in 7 units, made of 63 smaller skills.
The earlier topics 3rd grade leans on most are Missing Numbers and the Equal Sign (Grade 1); Adding and Subtracting Within 100 (Grade 2); Skip-Counting to 1,000 (Grade 2); Measuring Length with a Ruler (Grade 2); and Addition and Subtraction Facts to 20 (Grade 2). 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 63 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 3rd 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 3 map