Building Understanding of Fractions

Primary Standards:

MAFS.3.NF.1.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

MAFS.3.NF.1.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram.

  1. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
  2. Represent a fraction a/b on a number line diagram by marking off a lengths 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.

MAFS.3.G.1.2: Partition shapes into parts with equal areas.  Express the area of each part as a unit fraction of the whole.  For, example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

MAFS.3.NF.1.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

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.

Content Knowledge:

The focus of this Unit is on understanding fractions and fraction notation.  In prior grades, students explored partitioning shapes into equal halves, thirds, and fourths but did not use notation () to designate these equal parts.

Through explorations with a variety of fraction models (area and linear), students work towards understanding what fractions are.  They connect the visuals to the notation of numerator over denominator and develop an understanding of what each number represents.  They also recognize that fractions can be thought of as a collection of unit fractions, i.e.  can be thought of as three  sections.

Explorations, discussions and problem solving at this level are designed to nurture a strong understanding of fractions that provide the foundation for the fraction computation skills that follow in the next few years.


GCG 1 – Learning Goal: As a mathematician, I will be able to use strategies to fluently multiply by 6

  • Step 1: Explore and connect the distributive property with known facts (e.g., double x3 facts, x5 fact plus one)
  • Step 2: Decide when to apply the commutative property and other known facts for efficiency (e.g., students already know 10×6, they wouldn’t need to use the x5 plus one strategy)

GCG 2 – Learning Goal: As a mathematician, I will be able to use models to create and iterate fractions

  • Step 1: Partition concrete or pictorial shapes into 2, 3, 4, 6, and 8 equal parts and naming them based on the number of parts (e.g. thirds, fourths, eighths, etc.)
  • Step 2: Identify that one part of a whole is a unit fraction, name the fraction, and write it in fraction notation
  • Step 3: Identify a fraction as a collection of unit fractions. Write fractions in fractional notation (including fractions equivalent to whole numbers)

GCG 3 – Learning Goal: As a mathematician, I will be able to use number line models to create & iterate fractions

  • Step 1: Partition number lines into 2, 3, 4, 6, and 8 equal parts (relate to partitioning bar/ rectangular models)
  • Step 2: Identify and write fractions on a number line using fractional notation (including fractions equivalent to whole numbers)

GCG 4 – Learning Goal:  As a mathematician, I will be able to use models to represent whole numbers and fractions greater than one

  • Step 1: Use unit fractions to build and write fractions greater than one (with area/bar models)
  • Step 2: Use partitioned distances on a number line to identify and name fractions greater than one
  • Step 3: Recognize and model equivalent fractions as whole numbers (greater than 1)
Share this Story
Share this Story