Students add and subtract whole numbers within 20 by modeling joining, separating, comparing, and finding missing parts, using counting on or back, making ten, doubles, near doubles, number bonds, and fact families. They interpret and write addition and subtraction equations, including the plus, minus, and equals signs, and solve one- and two-step word problems with unknowns in any position. They also add one-digit numbers to multiples of ten and add or subtract two-digit numbers without regrouping, using place-value reasoning within 100.
Ask simple questions about one attribute, sort objects into categories, collect categorical data, and record counts using tally marks or simple tables. Create and interpret one-to-one pictographs and simple bar graphs with small whole-number counts, identifying the most and least common categories and comparing two categories as more, fewer, the same, or how many more or fewer. List possible outcomes, conduct simple chance experiments, record results, and describe events as certain, possible, impossible, likely, or unlikely using informal language.
Students recognize, create, draw, and organize small equal groups, distinguishing the number of groups, the number in each group, and the total, including simple rows-and-columns arrays. They count equal groups by ones, twos, fives, and tens, with groups of five and ten typically supporting totals through 100, and represent groups through skip-counting, counting on, and informal repeated addition. They solve simple equal-group and equal-sharing situations, including sharing between two groups and identifying a possible leftover, without formal multiplication or division notation, algorithms, or generalized rules.
Recognize a whole and identify, name, and represent halves and fourths as equal parts of shapes, lengths, objects, or collections. Partition and share wholes into two or four equal parts, identify missing parts, and understand that two halves or four fourths compose one whole. Compare halves and fourths, recognizing that one half is larger than one fourth and that two fourths equal one half.
Identify, name, describe, and sort circles, triangles, squares, rectangles, hexagons, and other familiar two-dimensional shapes by their straight or curved sides, vertices, and defining attributes, regardless of size or orientation, and recognize open and closed figures and simple symmetry. Identify and compare cubes, rectangular prisms, cylinders, cones, and spheres by their flat or curved surfaces, faces, edges, and vertices, including how objects stack or roll. Compose and decompose two- and three-dimensional shapes, including partitioning rectangles into equal squares, recognizing that different arrangements can form the same whole.
Students interpret simple addition and subtraction situations within 20, identify relevant or missing information, choose an operation, create or interpret stories, and represent relationships with objects, drawings, equations, part-part-whole models, ten-frames, and number lines.
They compare numbers primarily within 100, justify comparisons, explain and organize solution strategies, check answers and correct addition or subtraction errors using objects, inverse relationships, representations, and reasonable-size estimates, including straightforward two-digit problems within 100 and number-line reasoning from 0 through 120.
They make and test simple conjectures, use logical elimination with small whole numbers and familiar shapes, and communicate known quantities, unknowns, relationships, and mathematical reasoning clearly in words and representations.
Students compare and order lengths, heights, capacities, and masses using direct comparison and equal-sized informal units, measure lengths by iterating units without gaps or overlaps, estimate lengths, and measure capacity with equal scoops while recognizing that appearance alone can mislead. Students describe temperatures with hot, warm, cool, and cold; identify morning, afternoon, evening, and night; sequence daily events, compare durations informally, read clocks to the hour and half hour, and use calendars to identify days and dates. Students solve simple measurement stories involving lengths and other measurable quantities by representing totals, differences, and missing parts with addition or subtraction within 20 using the same whole-number unit.
Students identify pennies, nickels, dimes, quarters, and a one-dollar bill and match each with its value: 1, 5, 10, 25, and 100 cents. They count and compose whole-cent amounts using equal groups and simple mixed collections, including pennies, nickels, dimes, and quarters, typically within 100 cents, while recognizing that different combinations can have the same value. They compare money amounts and choose coin combinations for small purchases by using counting, skip-counting, addition, and the symbols >, <, and =.
Students recognize equality as a relationship between two equal quantities and solve simple addition and subtraction equations with unknowns in any position using whole numbers and sums or differences within 20. They identify, create, compare, describe, and extend repeating and growing patterns with objects, shapes, colors, sounds, and small numbers, applying simple rules to predict missing or next elements and informally recognize odd-even alternation. They extend and identify number patterns by 1, 2, 5, and 10 within 0–100, use number charts and number lines to describe these relationships, and find or apply simple add-or-subtract input-output rules with familiar whole numbers.
Students describe and compare relative positions using above, below, left, right, beside, between, in front of, behind, inside, and outside, and follow one- and multi-step movement directions from a stated starting point.
They read simple picture maps, use keys and spatial language to identify locations, and describe or reverse short paths while recognizing quarter, half, and full turns.
Students complete simple shape puzzles and visualize familiar two-dimensional and common solid shapes as composed or decomposed parts, matching shapes after simple rotations or reflections without formal coordinates, measurements, or complex transformations.
Students count, recognize, write, and represent whole-number quantities from 0 through 100, including one-to-one counting of objects, zero, counting forward from any number through 120, and counting backward from 20 or 100 to 0. They compose, decompose, and identify two-digit numbers through 99 as tens and ones, understand that ten ones make one ten, and count by 2s, 5s, and 10s through 100. They compare and order quantities and numerals through 100, identify numbers before, after, and between within 0–120, locate missing and given numbers on number lines, recognize odd and even quantities through 20, and estimate collections of about 20 or fewer objects.