Case Study On Unit Fractions

UNIT OVERVIEW
INTRODUCTION TIME: 8 weeks
In this unit, students extend and deepen second grade practice with “equal shares” to understand fractions as equal partitions of a whole (2.G.A.3). Their knowledge becomes more formal as they work with area models and the number line.

Topic A opens Unit 5 with students actively partitioning different models of wholes into equal parts (e.g., concrete models, fraction strips, drawn pictorial area models on paper). They identify and count equal parts as 1 half, 1 fourth, 1 third, 1 sixth, and 1 eighth in unit form before an introduction to the unit fraction (3.NF.A.1).

In Topic B, students compare unit fractions and learn to build non‐unit fractions with unit fractions as basic building blocks (3.NF.A.3d). This parallels the understanding that the number 1 is the basic building block of whole numbers.

In Topic C, students practice comparing unit fractions with fraction strips, specifying the whole and labeling fractions in relation to the number of equal parts in that whole (3.NF.A.3d).

In Topic D, students transfer their work to the number line. They begin by using the interval from 0 to 1 as the whole. Continuing beyond the first interval, they partition, place, count, and compare fractions on the number line (3.NF.A.2a, 3.NF.A.2b, 3.NF.A.3d).

In Topic E, they notice that some fractions with different units are placed at the exact same point on the number line, and therefore are equal (3.NF.A.3a). For example, , , and are equivalent fractions (3.NF.A.3b). Students recognize that whole numbers can be written as fractions, as exemplified on the number lines below (3.NF.A.3c). Topic F concludes the unit with comparing fractions that have the same numerators. As they compare fractions by reasoning about their size, students understand that fractions with the same numerator and a larger denominator are actually smaller pieces of the whole (3.NF.A.3d). Topic F leaves students with a new method for precisely partitioning a number line into unit fractions of any size without using a ruler.

A note on standard alignment: In this unit, students work with a variety of fractional units. These fractional units include halves, thirds, fourths, sixths, and eighths, which are specified in the Grade 3 standards, as well as additional fractional units such as fifths, ninths, tenths, and twelfths. These additional fractional units are not part of the Grade 3 standards. Their inclusion in this module combats rigid thinking, encouraging students to see any number as a fractional unit. This bridges to content in Grades 4 and 5 (4.NF.1-7 and 5.NF.1-7). Unit 5 assessments do not test the additional fractions.
COMMON CORE CONTENT STANDARDS - FOCUS GRADE LEVEL STANDARDS
Develop understanding of fractions as numbers
3.NF.A.1 – Number and Operations – Fractions
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.
3.NF.A.2 – Number and Operations – Fractions
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a) 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.
b) 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.
3.NF.A.3 – Number and Operations - Fractions Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same

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