Grade 3

Students develop fluency with addition and subtraction facts within 20 and use place-value reasoning to add and subtract one-, two-, and three-digit whole numbers within 1,000, with and without regrouping, including partial sums, partial differences, and mental work with multiples of 10 and 100. They estimate sums and differences by rounding to the nearest ten or hundred, find missing numbers and addends using inverse relationships, and represent computation with equations, models, number lines, expanded form, and standard algorithms. They apply these skills to one- and two-step addition and subtraction problems involving totals, differences, comparisons, remaining amounts, and unknown parts, while checking that solutions are reasonable.

Students collect categorical and numerical data using clear categories, tally marks, frequency tables, whole-number counts, and simple measurements with consistent units, including measurements in whole units, halves, or fourths. They create and interpret pictographs, bar graphs, line plots, and simple line graphs using titles, labels, keys, and appropriate scales, compare quantities, solve one- and two-step questions, and find the mode and range. Students identify possible outcomes, describe likelihood as impossible, unlikely, equally likely, likely, or certain, conduct simple chance experiments, and recognize fair and unfair games through informal comparisons of equally likely outcomes.

Students recognize, model, read, write, and compare decimals to tenths, connecting them to fractions, number lines, and place value. They identify common U.S. coins and bills, count collections, represent equivalent amounts in cents and decimal dollars to the hundredths, and compare, add, and subtract money amounts to find totals and simple change. They solve one- and two-step money problems involving prices, payments, totals, and differences using equations, models, aligned place values, and reasonable checks.

Interpret division as equal sharing and equal grouping using arrays, equal-group diagrams, number lines, repeated subtraction, and multiplication inverse relationships, distinguishing the dividend, divisor, quotient, and group size. Recall exact division facts through $10 \times 10$, including divisors 2, 5, and 10, and divide two-digit numbers within 100 by one-digit divisors using place-value models, multiples of 10, and informal partial quotients without formal long division. Solve whole-number division problems and equations with missing dividends, divisors, or quotients, write and interpret remainders less than the divisor, and estimate quotients for one-digit divisors and dividends within 1,000 using compatible numbers.

Students identify equal parts, halves, thirds, fourths, and unit fractions with denominators 2, 3, 4, 6, and 8, interpreting the denominator as the number of equal parts and the numerator as the number selected, and composing or decomposing wholes into unit fractions. They represent fractions with area, set, and number-line models; locate fractions from 0 to 1; recognize equivalent fractions and fractions equal to or greater than one. They compare fractions with the same numerator or denominator and use benchmarks such as 0, 1/2, and 1, solving simple word problems involving fractional parts and addition or subtraction with like denominators.

Students identify points, line segments, lines, rays, polygons, triangles, quadrilaterals, and common two-dimensional shapes, and classify them by attributes such as side lengths, vertices, right angles, parallel or perpendicular sides, and overlapping categories. They recognize angles as turns, identify and compare right, acute, and obtuse angles, identify and complete lines of symmetry, recognize congruence and translations, rotations, and reflections, and partition shapes into equal-area parts. Students identify common three-dimensional objects and their faces, edges, and vertices, distinguish solids from their two-dimensional faces, and relate familiar cubes, rectangular prisms, and simple prisms to informal nets.

Students represent one- and two-step whole-number situations with labeled drawings, equations, and unknowns, identify relevant or missing information, choose addition, subtraction, multiplication, or division, and solve problems involving addition and subtraction through 1,000 and multiplication and division within 100. They use inverse relationships to check calculations, estimate to assess reasonableness, find and correct errors, and compare strategies by explaining the role of place value and operation properties. Students explain solutions in words, create coherent word problems for equations, apply logical elimination to arithmetic and simple data or shape problems, and interpret remainders and intermediate results.

Students measure, estimate, compare, add, and subtract lengths using rulers, number lines, and appropriate customary or metric units, including common halves and fourths, and find perimeters or missing side lengths in whole-number polygons. Students understand area as covering with square units, find it by counting arrays or multiplying the whole-number side lengths of rectangles, and measure, estimate, compare, and solve problems with mass in grams and kilograms and capacity in milliliters and liters, recognizing that 1 kilogram equals 1,000 grams and 1 liter equals 1,000 milliliters. Students read time to the nearest minute, use a.m. and p.m., determine elapsed time within and across hours, interpret calendars, and solve measurement problems involving addition, subtraction, multiplication, division, comparisons, and missing measures while preserving appropriate units.

Students interpret multiplication as equal groups, repeated addition, number-line jumps, arrays, and area, and use commutative, associative, and distributive properties to reason about whole-number products generally within 100. They fluently recall basic facts with factors through 10, including multiplication by 0, 1, 2–10 and the 6s through 12, multiply multiples of 10 from 10 to 90 by a one-digit number, and multiply a two-digit number by a one-digit number using models, place-value decomposition, and partial products. They solve equal-group, array, area, multiplicative-comparison, and missing-factor problems, and estimate two-digit-by-one-digit products using compatible multiples of ten to judge the reasonableness of exact results.

Students identify, describe, generate, and extend growing and repeating patterns using whole numbers, visual representations, sequences, tables, and simple addition, subtraction, or multiplication rules. They determine and apply one-step input-output rules, complete missing entries, and recognize relationships in addition and multiplication tables, including sums and products within 100 and exact whole-number division relationships. Students understand the equals sign as expressing equivalent quantities, use symbols for unknowns, balance and solve one-step addition, subtraction, multiplication, and division equations, and write equations for one- and two-step whole-number word problems, with addition and subtraction quantities within 1,000.

Students represent, read, write, compose, and decompose whole numbers through 100,000 using standard, expanded, and word forms, identify digit places and values through the hundred-thousands place, and model numbers through 1,000 with base-ten blocks. They count forward and backward by 1s, 10s, 100s, and 1,000s, skip-count by 2s, 3s, 4s, 5s, 6s, 8s, 9s, and 10s, locate missing numbers and whole numbers on number lines through 1,000, and compare or order numbers through 100,000. They round whole numbers to the nearest 10 and 100 and estimate quantities using benchmarks such as 10, 100, and 1,000.