# Arithmetic

The branch of mathematics that includes numbering, counting, measuring, adding, subtracting, multiplying and dividing with real, nonnegative numbers. Simple arithmetic, or “numbers,” was taught in homes and schools in early America as a skill needed for farm management and the marketplace. The industrial revolution of the 19th century and the technological revolution of the 20th required children to learn complex arithmetic.

Formal arithmetic education usually begins in kindergarten and is completed by the end of fourth grade, and it is normally integrated with other subjects such as science, history and literature by teaching students to tell time, learn dates and solve story problems with numbers. Kindergartners usually learn to count from one to twenty, forwards and backwards and to pick up the count from any number. They also learn comparative concepts such as larger than, smaller than and to add and subtract numbers up to five. Most kindergartners also learn the use of balance scales, measuring instruments and pattern blocks, Cuisenaire rods (see CUISENAIRE NUMBER-IN-COLOR PLAN), plastic cubes, pumpkin seeds, acorns and other materials for weighing, counting, comparing, sorting and understanding that written and spoken numbers are conceptually the same as the equivalent number of objects.

First grade arithmetic progresses to include the following: counting forward and backward from 1 to 100; skip counting by twos, fives and tens; instant identification of numbers before and after any number from 1 to 100, the concept of place values; simple addition and subtraction of all single- and double-digit numbers; recognition of the inverse relationship between addition and subtraction; the use of the equality sign (=); the concept of fractions as parts of a whole; and the use of numbers in daily life to measure money, time, capacity, weight and temperature. First graders also extend their learning beyond arithmetic into other branches of mathematics by learning to recognize twodimensional geometric figures.

In second grade, students learn to master numeration to 1,000—adding and subtracting three single- and two-digit numbers and “rounding off” to the nearest ten or hundred. The standard curriculum also includes counting by odd and even numbers and to 1,000 by twos, threes, fives and tens. Measurement skills include mastery of money, time and the calendar.

Third graders progress to mastery of the multiplication tables through 12. They also learn to add and subtract four- and five-digit numbers, to multiply or divide two- and threedigit numbers by single-digit multiplicands and divisors and to recognize the inverse relationship between multiplication and division. Calculation skills also include mastery of fractions, decimals and the ability to convert from one to the other. Numeration skills extend into the tens and hundreds of thousands, millions and billions, and measurement skills advance to include length, area, volume, weight and time.

By the end of fourth grade, most schools expect students to have completed mastery of arithmetic, including addition, subtraction, multiplication and division of any combinations of two- and three-digit numbers. Students are also expected to have mastered place values, ratios, rounding and approximation of whole numbers, mixed numbers, decimals, fractions, the banking process, means, medians, modes and mental arithmetic. Story problems in the fourth grade prepare them for entering higher grades and the study of other branches of mathematics such as algebra, geometry and trigonometry.