#### Kindergarten

Matches/sorts/names objects by size, color and shape; recites and recognizes numbers 1-20; one-to-one correspondence; counts/adds up to nine objects; knows addition/subtraction facts to six; evaluates objects by quantity, dimensions, size (e.g., more/less, longer/shorter, tall/tallest, bigger/same); writes numbers 1-10; understands concepts of addition and subtraction; knows symbols +, -, =; recognizes whole vs. half; understands ordinals (first, 5th); learns beginning concepts of weight, time (e.g., before/after; understands lunch is at 12:00; tells time to the hour), money (knows value of pennies, nickels, dimes), and temperature (hotter/colder); aware of locations (e.g., above/below, left/right, nearest/farthest); interprets simple maps, graphs and tallies.

#### First Grade

Counts/reads/writes/orders numbers to 99; begins learning addition and subtraction facts to 20; performs simple addition/subtraction problems (e.g., 23 + 11); understands multiplication as repeated addition; counts by 2s, 5s and 10s; identifies odd/even numbers; estimates answers; understands 1/2, 1/3, 1/4; gains elementary knowledge of calendar (e.g., counts how many days to birthday), time (tells time to half hour; understands schedules; reads digital clock), measurement (cup, pint, quart, liter, inch, cm, kg, Ib), and money (knows value of quarter; compares prices); solves simple number story problems; reads bar graphs and charts.

#### Second Grade

Identifies/writes numbers to 999; Adds/subtracts two and three digit numbers with and without regrouping (e.g., 223 + 88, 124 - 16); multiplies by 2,3,4, 5; counts by 3s, 100s; reads/writes Roman numerals to XII; counts money and makes change up to $10.00; recognizes days of the week, months, and seasons of the year on a calendar; tells time to five minutes on a clock with hands; learns basic measurements (inch, foot, pint, pound); recognizes equivalents (e.g., two quarters; one half; four quarts; one gallon); divides area into 2/3, 3/4, 10ths; graphs simple data

#### Third Grade

Understands place value to thousands; adds and subtracts four digit numbers (e.g., 1,017 - 978); learns multiplication facts to 9 x 9; solves simple multiplication and division problems (642 x or ÷ 2); relates division to repeated subtractions; counts by 4s, 1000s; learns harder Roman numerals; introduction to fractions (adds/estimates/orders simple fractions; understands mixed numbers; reads fractions of an inch) and geometry (identifies hexagon, pentagon); understands diameter, radius, volume, area; understands decimals; begins to learn about negative numbers, probability, percentage, ratio; solves harder number story problems

#### Fourth Grade

Adds columns of 3 or more numbers; multiplies three digit by two digit numbers (348 x 34); performs simple division (44/22); reduces fractions to lowest terms; adds/subtracts fractions with different denominators (3/4 + 2/3); adds/subtracts decimals; converts decimals to percents; counts/makes change for up to $20.00; estimates time; can measure time in hours, minutes, seconds; understands acute, obtuse, right angles; computes area of rectangles; identifies parallel, perpendicular, intersecting lines; calculates weight in tons, length in meters, volume in cubic centimeters

#### Fifth Grade

Multiplies three digit numbers (962 x 334); can work harder division problems (102 ÷ 32); adds, subtracts, multiplies mixed numbers; divides a whole number by a fraction; represents fractions as decimals, ratios, percents; adds, subtracts, multiplies, with decimals; understands use of equations, formulas, "working backward"; estimates products/quotients; begins to learn about exponents, greatest common factor, bases, prime factors, composite numbers, integers; understands percent, ratios; understands mean, median, mode; measures areal circumference of a circle, perimeter/areas of triangles and parallelograms, volume of cube; performs metric conversions; uses compass, protractor; reads scale drawings

#### Middle School

Masters order of operations in complex problems; multiplies/divides two fractions; adds, subtracts, multiplies divides decimals to the thousandth; understands real, rational, irrational numbers and different number bases; calculates square and cube roots; estimates percentages/proportions; calculates discount, sales tax, restaurant tip; understands markup, commission, simple interest, compound interest, percent increase/ decrease; understands angles (complementary, supplementary, adjacent, straight, congruent ... ); calculates volume of a cylinder; calculates arc/ circumference of circle; understands equilateral, isosceles, scalene, obtuse figures; organizes sets of data; graphs coordinates, transformations, reflections, rotations, equations with two variables; solves equations by substitution; begins to learn about conditional probability, permutations, factorial notation, relative frequency, normal curve, pythagorean theorem; deepens understanding of previously taught skills and concepts

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