ILLINOIS TEACH & TALK

Illinois Assessment of Readiness Mathematics Evidence Tables. 

Retrieved from:  https://www.isbe.net/Documents/IAR-Grade-3-Math-Evidence-State.pdf

 

Grade 3 is the first time students are being introduced to fractions. In 3.NF.1 students are building the foundation of fraction sense and building on the idea that a fraction is part of a defined whole. 

 

Numbers and Operations- Fractions is a critical area of focus according to the Standards Document pg. 21

 

(2) Students develop an understanding of fractions, beginning with unit fractions.

Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in

a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve

comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.

 

Further clarification and discussion comes from the Progressions:

 

The meaning of fractions In Grades 1 and 2, students use fraction language to describe partitions of shapes into equal shares.2.G.3 I n Grade 3 they start to develop the idea of a fraction more formally, building on the idea of partitioning a whole into equal parts. The whole can be a shape such as a circle or rectangle, a line segment, or any one finite entity susceptible to subdivision and measurement. In Grade 4, this is extended to include wholes that are collections of objects.

 

Grade 3 students start with unit fractions (fractions with numerator 1), which are formed by partitioning a whole into equal parts and taking one part, e.g., if a whole is partitioned into 4 equal parts then each part is 1/4 of the whole, and 4 copies of that part make the whole. Next, students build fractions from unit fractions, seeing the

numerator 3 of 3/4 as saying that 3/4 is the quantity you get by putting 3 of the 1/4’s together.3.NF.1 They read any fraction this way, and in particular there is no need to introduce “proper fractions" and “improper fractions" initially; 5/3 is the quantity you get by combining 5 parts together when the whole is divided into 3 equal parts. Two

important aspects of fractions provide opportunities for the mathematical practice of attending to precision (MP6):

• Specifying the whole.

• Explaining what is meant by “equal parts.”

 

Initially, students can use an intuitive notion of congruence (“same size and same shape”) to explain why the parts are equal, e.g., when they divide a square into four equal squares or four equal rectangles.

Students come to understand a more precise meaning for “equal parts” as “parts with equal measurements.” For example, when a ruler is partitioned into halves or quarters of an inch, they see that each subdivision has the same length. In area models they reason about the area of a shaded region to decide what fraction of the whole it represents (MP3).

 

The goal is for students to see unit fractions as the basic building blocks of fractions, in the same sense that the number 1 is the basic building block of the whole numbers; just as every whole number is obtained by combining a sufficient number of 1s, every fraction is obtained by combining a sufficient number of unit fractions.