use equivalent fractions as a strategy to add and subtract fractions apply and extend previous understandings of multiplication and division to multiply and divide fractions use an understanding of fractions to help prepare the way for work with the rational number system in grades 6 and 7. Possible Organization of Unit Standards: This table identifies additional grade-level standards within a given cluster that support the over-arching unit standards from within the same cluster. The table also provides instructional connections to standards from outside the cluster. Priority Standards within the Cluster Supporting Standards within the Cluster Instructional Connections outside the Cluster 3.NF.1 Understanding decimals as numbers 3.NF.1 Understand a fraction 1/b as the quantity formed by one part when a whole is partitioned into b equal parts. 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3.NF.2a Represent a fraction 1/b on a number line diagram by the interval from 0 to 1 as the whole and partitioning it into b equal parts. 3.NF.2b Represent a fraction a/b on a a number line by marking off a lengths of 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3.NF.3 Explain equivalence of fractions, and compare fractions by reasoning about their size. 3.NF.3a Represent two fractions as equivalent if they are the same size, or the same point on a number line. 3.NF.3b Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent. 3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. 3.MD.1 Tell and write time to the nearest minute and measure time in intervals of minutes. Solve word problems involving time intervals in minutes by representing the problem on a number line diagram. 3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
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 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 table, fraction strips) Ability to relate equivalency to fractions of a region or fractions of a set Ability to use benchmarks of 0, and 1 comparing fractions Knowledge of and experience with fractional number sense to lay foundation for manipulating, comparing, finding equivalent fractions, etc. 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.
3.NF.A.3c: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Knowledge of the denominator as the number of parts that a whole is divided into in order to explain why a denominator of 1 indicates whole Knowledge that a fraction in which the numerator is equal to or larger than the denominator is labeled an improper fraction, but is still a correct representation of the value being stated. Knowledge that when appropriate, an improper fraction can be renamed as a mixed number.
4.NF.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. Knowledge of this Standard provides a foundation for the relationship between fractions and decimals. Students can use decimal blocks, Digi-Blocks, money, graph paper, and other place value models to explore the relationship between fractions with denominators of 10 and 100. Students begin to make connections to the place value chart as shown in the Clarification of 4.NF.6 below. This work in fourth grade lays the foundation for performing operations with decimal numbers in fifth grade.