Children in preschool and kindergarten learn basic measurement concepts such as bigger and smaller, longer and shorter, and full or empty. Children in these grades learn to use a calendar, and learn to tell time to the hour. Shape and color identification are taught. Money concepts are introduced, and the child learns the names and worth of coins. By the end of kindergarten a child will learn to count out loud from one to 20, and should be able to count 20 of something by touching each object and counting. Ordinal numbers are discussed, and the concepts of addition and subtraction are introduced.
First and second graders continue studying measurement by using both the English and metric systems to measure length, weight, time, volume and shapes. Skip counting by two, three, four, five, and 10 is taught along with multiplication and division concepts. Children will learn to read, write and count to 1,000, and will begin to learn the Roman numeral system. Fractions and decimals are introduced, and children will be able to write fractions of shaded parts of a whole picture. Addition and subtraction facts up to 20 are emphasized and drilled. Using money, calendars, and a clock are reviewed and expanded upon. Children will learn to count money in order to purchase an item, usually under $5. Calendars are used to find a specific day of the week, and time to within three minutes is taught. The child may learn to use basic charts and graphs to track information.
In third and fourth grades, students learn to read, and write numbers with five digits. They also learn the place value associated with each digit. Addition and subtraction facts up to 25 are mastered at this level, along with multiplication and division up to 144. Addition and subtraction out to seven digits is learned. Time is revisited, and students learn to tell time to the minute. Geometric shapes are covered, along with finding perimeter, area and volume. The ability to measure in the English and metric systems is refined. Multiplication to three or four digits is taught, as well as beginning division with one digit divisors. Charts and graphs are reviewed and expanded upon for organizing and understanding of data.
By the end of fifth and sixth grades, it is expected that a child add, subtract, multiply and divide any whole number out to six or seven places. Reading, writing, and understanding numbers up to 10 digits is taught. Factoring, exponents and integers are introduced. Children in fifth and sixth grades are taught to find equivalent fractions, work with mixed numbers, perform basic operations with fractions and decimals, and convert from fraction to decimal and vice versa. Ratio and percents are introduced, and the use of graphs and charts are increased. Calculators may be introduced at this time.
To prepare for algebra in junior high or high school, the student concentrates on manipulating numbers, solving real word problems, and word problems. Addition, subtraction, multiplication and division of integers, decimals, fractions and percents is reinforced, and square roots, prime numbers and absolute value are taught. At this level, the order of operations is taught and practiced as well. Basic math skills are practiced to ensure proficiency.