The new Common Core Standards being phased into schools by the majority of states adapts more developmentally appropriate mathematical standards for fifth-grade students. Three major areas -- fractions, division and volume -- are where the emphasis will be placed when new tests are given. Deep mastery is expected and proficient problem-solving methods are hallmarks of the standards. How students are expected to adeptly manage these concepts is specified in one important word: proficiency.
Math and Common Core
The Common Core Standards, currently adopted by 45 states, can be accessed easily by teachers and parents at the Common Core website. These are teaching and learning guidelines determined to create mathematically proficient students who can understand the meaning of a problem and know methods to find its solution. Writers of the new standards indicate clearly that as students continue in school, they will be expected to deepen their understanding of numbers with increasing maturity and progress. Awareness of the math skills particular to each grade, and the resulting mastery of them, is the best way for parents to ensure that their child is ready to move on in complexity with number sense. Problem-solving strategies should be part of every grade's curriculum, and different ways to approach problems should be taught such as looking for patterns, making systematic lists and working backward.
Fifth-grade students are expected to add and subtract fractions with unlike denominators -- including mixed numbers -- by replacing given fractions with equivalent fractions. Multiplication and division operations with fractions are expected to be "understood" by applying previous understandings of these concepts to fractions. Because fractions are introduced in earlier grades, fifth-graders should be ready to rename amounts to manipulate and change numbers to be calculated more easily -- such 1/2 as 2/4 and 4/8 as equal amounts. A strong sense of how to work with mixed numbers made up of whole and fractional parts is also critical to success in fifth-grade math. Practice manipulating fractional portions, such as cutting into a pan of brownies or dividing a pizza, in cooking is one way to give a child a more visual assistance in this important skill set.
Fifth-graders will be expected to master and extend division to two-digit divisors -- 245 divided by 25, for instance -- and develop mathematical ease with whole numbers and decimals. A solid understanding of place value in the decimal places of tenths, hundredths, thousandths and so on factors strongly in the fifth-grade Common Core standards. Work with money automatically makes sense to children and provides the first experiences with manipulating numbers with decimal points. Eventually 10- and 11-year-olds become aware -- if they haven't already -- of the relationship between decimals and fractions, which leads the way into working smoothly with amounts less than a whole unit.
The Common Core Standards specify working knowledge of volume at the fifth-grade level as "Recognizing volume as an attribute of solid figures and understanding concepts of volume measurement." Counting cubes and calculating volume of a figure with the formulas, volume = length × width × height for cubes and volume = base × height for rectangular prisms, will be skills children master. A solid understanding, therefore, of the terms volume, length, width and height will be critical for success and can sometimes puzzle a child without tangible experience in handling prisms and talking about shapes. Work with blocks and guidance in building are ways in which children can increase their expertise with the language of geometry in preparation for mastering this skill. Because the Common Core Standards rely on student-driven problem solving, the fifth-grade child should excel when given ample time and opportunities to use multiple methods of mathematical reasoning.
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