Grade 2

Students fluently recall addition and subtraction facts within 20, including zero, doubles, near-doubles, make-ten strategies, missing values, and adding or subtracting 10, 100, and multiples of 10 using place value through 1,000. They add and subtract two-digit numbers, including one-digit addends or subtrahends, with and without regrouping, add three two-digit numbers, and use partial sums and place-value representations for addition within 1,000. They solve joining, separating, comparison, part-part-whole, missing-addend, and two-step problems within 100, write related equations, and informally estimate sums and differences using friendly tens or hundreds through 1,000.

Students ask statistical questions, collect categorical and numerical whole-number data, use tally marks and simple frequency tables, and organize measurements to the nearest whole unit in line plots. They create and interpret pictographs with one-to-one or many-to-one keys of 1, 2, 5, or 10 and bar graphs with up to four categories and single-unit scales, comparing values, identifying greatest and least amounts, and answering one- and two-step addition or subtraction questions. Students identify possible outcomes, describe events as certain, impossible, likely, unlikely, or equally likely, conduct simple chance experiments, record repeated results, and compare observed frequencies without using formal probability calculations.

Students identify a whole and partition shapes, lengths, and collections into equal halves, thirds, and fourths, recognizing and naming one-half, one-third, and one-fourth. They represent these fractions with area, set, and number-line models, recognize the same fraction in different shapes, and understand that two halves, three thirds, or four fourths compose one whole. Students solve simple equal-sharing and missing-part problems and compare the unit fractions one-half, one-third, and one-fourth, understanding that more equal parts make smaller shares.

Students identify, describe, sort, and compare two-dimensional shapes by attributes such as straight or curved sides, open or closed boundaries, sides, vertices, right angles, and symmetry, recognizing circles, triangles, quadrilaterals, squares, rectangles, pentagons, and hexagons in varied orientations. Students identify and build familiar three-dimensional objects, including cubes, rectangular prisms, cones, cylinders, and spheres, by recognizing faces, edges, vertices, curved surfaces, and the two-dimensional shapes of their flat faces. Students compose and decompose two- and three-dimensional figures from smaller shapes and partition rectangles or circles into two, three, or four equal parts described as halves, thirds, or fourths.

Students identify relevant and missing information, choose addition or subtraction, represent situations with objects, drawings, number lines, models, tables, and equations, and solve whole-number problems within 1,000, including simple two-step problems within 100. They compare and explain strategies, organize work systematically, justify comparisons through 1,000 using place value, create stories for addition and subtraction equations within 100, and explain solutions in words for addition, subtraction, measurement, equal-group, and sharing situations. They check calculations using inverse operations and estimation, find and correct addition and subtraction errors involving regrouping, make reasonable conjectures from patterns and examples, and use logical elimination to identify possible solutions.

Measure, estimate, compare, add, and find differences between whole-number lengths using equal nonstandard units, centimetres, and metres, choosing appropriate units and explaining why consistent units are necessary. Compare and measure mass and capacity with nonstandard units, balances, grams or kilograms, and millilitres or litres, while informally comparing temperatures as hotter, cooler, or about the same. Read clocks to the hour, half hour, quarter hour, and five-minute intervals, distinguish a.m. and p.m., sequence events, find elapsed time in whole hours, read calendars, and solve simple measurement word problems involving consistent whole-number units.

Identify pennies, nickels, dimes, quarters, and one-dollar bills by value, and relate 100 cents to one dollar. Count, compose, compare, and represent amounts in different ways using coins, typically within one dollar, including choosing coins efficiently. Add and subtract whole-cent amounts, solve purchase and simple-change problems, and determine whether money is sufficient using common coins and bills.

Represent collections as equal groups and rectangular arrays, distinguishing the number of groups from the group size and connecting them to skip-counting, repeated addition, multiplication equations, and decomposed arrays, including groups of 2, 5, and 10 within 100. Form and partition exact equal groups or shares, solve for the total, group size, or number of groups using multiplication and division relationships, and recognize odd and even pairings. Solve equal-group and equal-sharing situations with objects, drawings, arrays, bar models, and equations, including missing-factor problems and grouping division within 100, without fractions, remainders, or formal division algorithms.

Identify, create, extend, and describe repeating and growing patterns using objects, shapes, numbers, tables, hundreds charts, and simple additive rules, including odd-even patterns and changes of 10 within familiar whole-number ranges through 1,000. Determine and apply consistent one-step input-output rules involving addition, subtraction, and familiar equal-group contexts, completing missing inputs or outputs without variables or complex formulas. Recognize equality and use symbols to solve, balance, and write addition and subtraction equations and story equations with whole numbers within 100, including unknowns in any position and reasoning with inverse operations.

Students mentally compose and decompose familiar two-dimensional shapes, complete simple spatial puzzles, and recognize matching shapes after turns, slides, or flips. They describe relative position, distinguish left and right from different orientations, follow and describe paths, and read simple maps using keys, directional language, and step-based distances. They identify front, top, and side views of simple three-dimensional objects and recognize quarter, half, and full turns and reflections.

Students read, write, name, compose, decompose, and represent whole numbers from 0 through 1,000 using hundreds, tens, and ones, including expanded form, word form, numerals, base-ten blocks, and the value of each digit. Students count forward and backward by ones, tens, and hundreds; skip-count by 2s, 5s, and 10s; locate missing and labeled numbers on number lines; compare and order numbers through 1,000 using place value and $<$, $>$, and $=$. Students identify even and odd numbers, estimate quantities through 1,000 using benchmarks, and round two-digit numbers informally to the nearest ten.