In second grade, students should be reviewing content knowledge learned in kindergarten and first grade to strengthen their fundamental math skills. Kids in this age group are beginning to move from learning math skills to using math skills for more advanced learning. While standards for second-grade math vary from state to state, there are common principles that all grade two students need to know and understand.
Operations and Algebraic Thinking
Students in second grade should be able to represent and solve problems involving addition and subtraction of numbers 1 through 100. They should be able to skip count and work with groups of equal objects in preparation for learning multiplication and division. Sample math problems in this category should include finding the sum and differences of numbers, addition and subtraction fill-in-the-blank problems, completing skip counting and other number pattern sequences, and using plus and minus signs to make number sentences true. For example, presented with the problem 24 ? 13=37, children should know a plus sign replaces the question mark.
Number and Operations in Base Ten
Understanding and using place value to perform basic operations is another concept that second-grade students should have exposure to. For instance, shown a picture containing one hundreds block, three tens blocks and 5 single blocks, children should figure out the total number of blocks shown is 135. Students should also be able to give the value of a specific digit in a number as well as to identify digits in ones, tens, hundreds and thousands places. An example problem would be "Which numeral is in the tens place in 1,025?" Other base-ten operation problems include regrouping numbers and making conversions between place values.
Measurement and Data
Second graders need a firm understanding of measurement, including length, time and money. Math problems about measurement ask students to complete tasks like determining the length and height of objects, giving the time using analog and digital clocks, representing values of money using different combinations of coins and bills, and adding and subtracting money. Students in this age group are also working on representing and interpreting data. Math problems in this area involve using information to construct charts and graphs as well as answering questions on given data such as a project requiring kids to make a chart comparing the favorite candies of their peers.
Besides knowing names and characteristics of basic shapes, second-grade students should be able to reason with shapes and their attributes. Math problems on geometry should ask students to draw shapes and identify the number of sides, angles and vertices. In addition to these tasks, students should be able to discriminate and identify shapes within other objects. For example, shown a drawing of a triangle or rectangle divided into sections, students should identify the number of triangles inside the larger shape.
Students in second grade need to engage in abstract reasoning and be able to construct and deconstruct arguments. Knowing which mathematical operation or principle to use to determine a solution to a problem is an important skill for kids at this level. Word problems are a valuable tool in promoting the use of logic and reasoning. For example, second-grade students should be able to solve problems similar to the following one: "Three sisters, Mary, Molly and Jane wear different color skirts to school. Their skirt colors are red, blue and yellow. Mary's skirt is not red and not blue. Molly's skirt is not blue. What color skirt does each girl have on?"
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