3.NOS.F: Develop understanding of fractions as numbers.

Develop understanding of fractions as numbers.

3.NOS.F.10Recognize and explain that a fraction represents a part of a whole. a. Partition shapes into parts with equal areas and express the area of each part using a unit fraction. b. Explain that a fraction 1/d represents one part of a whole that is divided into d equal parts, and that a fraction c/d represents c parts of size 1/d.3.NOS.F.11Explain a fraction of a set as the quantity formed by c items as part of the given set of d objects.3.NOS.F.12Represent a fraction as a number on the number line. a. Represent a fraction on a number line by defining the interval from 0 to 1 as the whole and partitioning it into d equal lengths. Recognize that each length measures and that the endpoints of the length starting at 0 represents the number on the number line. b. Represent a fraction on a number line by marking off c lengths of from 0. Recognize that the resulting interval has size and that the endpoint of the length locates the number on the number line.3.NOS.F.13Explain equivalence of fractions and compare fractions by reasoning about their size, recognizing that comparisons are valid only when the two fractions refer to the same whole. a. Represent two fractions as equivalent if they are the same size, or they represent the same point on the number line. b. Identify and generate equivalent fractions, (e.g., 1/2 = 2/4, 4/6 = 2/3.) and explain why the fractions are equivalent using concrete materials, drawings, number lines, or equations. c. Express whole numbers as fractions, and identify fractions that are equivalent to whole numbers, (e.g., express 3 in the form 3 = 3/1; recognize that 6 = 6/1; locate 4/4 and 1 at the same point on a number line). d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using concrete materials, drawings, number lines, and/or equations).

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