Access Point #: MAFS.4.NF.2.AP.3a (Archived Access Point)

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Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., 3/4 = 1/4 + 1/4+ 1/4).


Essential Understandings


  • Using fraction manipulatives, model a whole and then decompose (i.e., divide) it into equal parts to create unit fractions (i.e., fractions where 1 is the numerator). For example: 1 = 1/3 + 1/3 + 1/3 or 1 = 1/4 + 1/4 + 1/4 + 1/4.
  • Using fraction manipulatives, model a non-unit fraction (i.e., a fraction where 1 is not the numerator) and then decompose the fraction into unit fractions. For example: 2/3 = 1/3 + 1/3 or 3/4 = 1/4 + 1/4 + 1/4.
  • Understand how parts of a whole can be expressed as fractions using numbers.
  • Understand the following concepts, symbols, and vocabulary: numerator, denominator, fraction, decompose, unit fraction.

Number: MAFS.4.NF.2.AP.3a Category: Access Points
Date Adopted or Revised: 06/14 Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (Major Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Related Standards

Name Description
MAFS.4.NF.2.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
  1. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
  2. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
  3. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
  4. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Examples of Opportunities for In-Depth Focus

This standard represents an important step in the multi-grade progression for addition and subtraction of fractions. Students extend their prior understanding of addition and subtraction to add and subtract fractions with like denominators by thinking of adding or subtracting so many unit fractions.

Related Courses

Name Description
5012060: Mathematics - Grade Four
7712050: Access Mathematics Grade 4
5012065: Grade 4 Accelerated Mathematics
5012015: Foundational Skills in Mathematics 3-5

Related Resources

Element Cards

Name Description
4th Grade Math Element Cards:

Element Cards are available to assist in planning for instruction. They are designed to promote understanding of how students move toward the academic standards. Element Cards contain one or more access points, essential understandings, suggested instructional strategies and suggested supports.

Professional Development

Name Description
Fractions and Decimals Content Module :

Content Modules provide explanations and examples of the concepts contained in the academic standards that may be difficult to teach or unfamiliar to special education teachers. They promote an understanding of the concepts so that a teacher can begin to plan how to teach the concepts to students. Content Modules contain potential adaptations, modifications and ideas for Universal Design for Learning.

Teaching Idea

Name Description
Curriculum Resource Guide: Fractions and Decimals:

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