The Common Core Standards, currently being implemented in 45 states, establish the critical math concepts that should be learned at each grade level. According to the standards, objectives for fifth grade fall into four broad areas: operations and algebraic thinking, number and operations, measurement and data, and geometry. Students also work on making reasonable estimates and understanding answers in a real-life context. In the classroom, students focus on three main topics: multi-digit operations, fractions, including decimals, and volume.

## Fractions

Fifth-grade students begin to add and subtract fractions with different denominators by converting to fractions with the same denominator and applying previously learned ideas. They also begin to multiply and divide fractions by whole numbers and whole numbers by fractions. Putting problems in a real-life context helps students see whether or not their answers make sense. For example, in the problem 4 divided by 1/2, the answer is "8." Students often give the incorrect answer as "2," but four pies divided into halves gives you eight pieces.

## Multi-Digit Operations

Fifth-grade students work to become very comfortable with addition, subtraction and multiplication of multi-digit numbers. Division by two-digit numbers is introduced and related to their understanding of the base-10 number system and properties of operations. Estimating an answer prior to solving the problem can help students see potential mistakes. A simple example problem might be: if 580 tickets are divided between 95 students, estimate how many tickets each student will have. Approximately 600 tickets and 100 students means that 580 divided by 95 should yield an answer of about 6.

## Decimals

Once students are comfortable with the four operations with multi-digit numbers, these ideas are extended to decimals. It is critical that students understand the relationship between finite decimals, fractions and whole numbers. For example, 0.25 is equivalent to 25/100 and multiplying by 100 in either case equals 25. The goal is to be able to add, subtract, multiply and divide numbers to the hundredths place. The standards emphasize becoming comfortable with these operations as well as accuracy.

## Volume

Critical math concepts in fifth grade include graphing points on the coordinate plane, classifying two-dimensional objects and understanding volume. To understand volume, students are introduced to the idea of a cube with three dimensions as a unit of measure. Specifically, they find the volume of right rectangular prisms by seeing them as layers of cubes and answering questions, such as how many cubes are in one layer and how many layers are required to fill up the prism. The volume of real-life objects is found by multiplying three dimensions: length, height and depth.

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