endpoint locates the number a/b Ability to explain, for example, on the number line. that when a is 2 and b is 4, the fraction is represented on a number line at the second tick mark from zero or when a is 3 and b is 4, the fraction is represented on a number line at the third tick mark from zero. 3.NF.A.3: Explain equivalence of Ability to use concrete An important concept when comparing fractions is to look fractions in special cases, and manipulatives and visual at the size of the parts and the number of the parts. For compare fractions by reasoning models to explain reasoning example, is smaller than because when 1 whole is cut into about their size. about fractions 8 pieces, the pieces are much smaller than when 1 whole is cut into 2 pieces. Knowledge that equivalent fractions are ways of describing Students recognize when examining fractions with the same amount by using common denominators, the wholes have been divided into different-sized fractional parts. the same number of equal parts. So the fraction with the (e.g., is the same as or or ) larger numerator has the larger number of equal parts. Ability to use a variety of models when investigating To compare fractions that have the same numerator but equivalent fractions (e.g., different denominators, students understand that each number line, Cuisenaire rods, fraction has the same number of equal parts but the size of fraction towers, fraction circles, the parts are different. They can infer that the same equivalence fraction strips) number of smaller pieces is less than the same number of bigger pieces. Ability to relate equivalency to fractions of a region or fractions of a set
endpoint locates the number a/b on the number line. Ability to explain, for example, that when a is 2 and b is 4, the fraction is represented on a number line at the second tick mark from zero or when a is 3 and b is 4, the fraction is represented on a number line at the third tick mark from zero. 3.NF.A.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Ability to use concrete manipulatives and visual models to explain reasoning about fractions Knowledge that equivalent fractions are ways of describing the same amount by using different-sized fractional parts. (e.g., is the same as or or ) Ability to use a variety of models when investigating equivalent fractions (e.g., number line, Cuisenaire rods, fraction towers, fraction circles, equivalence fraction strips) Ability to relate equivalency to fractions of a region or fractions of a set An important concept when comparing fractions is to look at the size of the parts and the number of the parts. For example, is smaller than because when 1 whole is cut into 8 pieces, the pieces are much smaller than when 1 whole is cut into 2 pieces. Students recognize when examining fractions with common denominators, the wholes have been divided into the same number of equal parts. So the fraction with the larger numerator has the larger number of equal parts. To compare fractions that have the same numerator but different denominators, students understand that each fraction has the same number of equal parts but the size of the parts are different. They can infer that the same number of smaller pieces is less than the same number of bigger pieces.