By the end of second grade, students should be able to recognize a large array of numbers and understand simple relationships between them. Second graders can recognize whole numbers from zero to 1,000, in written and oral form. Counting forwards and backwards by tens and hundreds up to 1,000 also comes easily to second graders. They have the ability to compare numerical amounts using terms like "less than," "greater than" and "equal to" and their corresponding symbols. Basic addition and subtraction comes more easily to second graders, including working with two-digit numbers.
Children in the second grade can recognize all coin varieties and understand their dollar and cent notation. They ought to be able to make change for one dollar without problems. They should be able to understand measuring basics at this grade level. This includes being able to calculate area and perimeter of regular 2D shapes. Children in second grade math also have the ability to choose appropriate measurement tools for various measurements. They can measure length, width, height, capacity and weight. Second graders should understand time and temperature.
Geometric shapes come into play in second grade math, and students should be able to explore both 2D and 3D shapes. Their skill level allows them to understand the shapes that can result from combining other shapes or breaking down shapes into smaller shapes. Second graders are able to recognize certain geometric shapes in their environment and not just on paper. With algebra, second graders begin to understand numerical patterns. They can formulate simple algebraic expressions and fill in any blanks within simple number sentences. Multiplication and division may begin to appear within a second-grade math curriculum.
Second grade math students need to have skills in problem solving, reasoning, statistics and data analysis. They should be able to work out simple word problems. This curriculum introduces Venn diagrams, and second graders need to be able to read, understand and fill in statistical information in the diagram. Second graders should be able to make predictions about math and make connections between math problems. Problem-solving and justification of their reasoning should occur at this point. In addition, children in second grade need to be able to record numerical data in a systematic sense, as well as be able to translate that data into a bar graph or pie chart.