4.NOS.E: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NOS.E.11Apply understanding of a fraction c/d with d > 1 as a sum of unit fractions (c/d = 1/d + 1/d + ... + 1/d) to decompose a fraction (including fractions greater than 1) into a sum of fractions with the same denominator in more than one way, recording each decomposition as an equation. Justify decompositions using visual fraction models and equations (e.g., 3/8 = 1/8 + 1/8 + 1/8 or 3/8 = 1/8 + 2/8 or 2 1/8 = 1 + 1 + 1/8 or 2 1/8 = 8/8 + 8/8 + 1/8).4.NOS.E.12Apply and extend previous understanding of addition and subtraction of whole numbers to add and subtract fractions with like denominators. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Estimate sums and differences by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 3/4 + 3/4 will be greater than 1 because both fractions are greater than 1/2). c. Apply and extend whole number addition and subtraction strategies (e.g. counting on, making a whole, partial sums, compensation, properties of operations, the inverse relationship between addition and subtraction) to add and subtract fractions. d. Solve problems in context involving addition and subtraction of fractions using visual fraction models and equations to represent the problem.4.NOS.E.13Apply and extend previous understandings of multiplication to multiply a fraction by a whole number (b × c/d). a. Estimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 4 × 1/2 will be less than 4 because I have 4 groups of something less than 1). b. Use understanding of multiplication as equal groups to multiply a unit fraction by whole number (e.g., interpret b × 1/d as b groups of 1/d). c. Use understanding of multiplication as equal groups to multiply a fraction by whole number (e.g., interpret b × c/d as b groups of c/d when c/d is greater than or less than 1). d. Solve problems in context involving multiplication of a fraction by a whole number, using visual fraction models and equations to represent the problem.

1-on-1 AI tutoring aligned to 4.NOS.E. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →