With addition and subtraction fact families under their belts, third-graders are required to take regrouping and carrying over to four-digit problems and to read and write whole numbers up to 1 million. They need to master all addition and subtraction facts through 10 + 10 and use basic facts to compute fact extensions, such as 80 + 70. They are also expected to be able to combine addition, subtraction, multiplication and division in problems that require more than one operation at a time.
Children in third grade need to be able to show the same numbers represented in different ways, as fractions, decimals and percents. They need to be able to understand place value. In this way, they begin to learn about numbers larger than 1,000, numbers that are less than one and numbers that are not whole. They learn to show fractions in diagram form so that they understand the meaning and use of the operation.
Number problems that make third-graders think about the answer are a large part of the curriculum: everything from rounding up and down to the nearest ten or hundred to estimating the capacity of a container. Measurement units involving money, time, area and volume, weight, length and perimeter in both U.S. and metric systems are represented using graphs and charts. Understanding measurement relationships are necessary skills for third-graders: how much time has elapsed, equivalent cents to dollars, inches to feet and yards, centimeters to meters and relating seconds to minutes, hours, days and weeks. Making reasonable estimates through models requiring the collection and representation of data make it possible for third-graders to understand probability and prediction.
Taking shapes to the next level with more complex plane shapes and solid geometric shapes are introduced in third grade. Intersecting lines, angles and movements start to be explored in reflection, rotation, translation and symmetry. Patterns children can see in the world around them are given an algebraic function on paper. Numbers are given symbols, and rules are used for functions to solve problems based on the arithmetic skills the children already have. Algebraic notation is written regularly -- for example, ">" meaning more than, "<" meaning less than and "=" meaning equal to. In this way, children are able to understand the order of operations, or recognize that numeric expressions can have different values, depending on the order in which operations are carried out. This is a necessary step for progressing to fourth-grade math and beyond.