Foundations for Fractions in the Primary Grades

Author: Fredric Noriega, Secondary Mathematics Specialist

Tags: Math, fractions, STAAR

One math concept that is often feared by both students and teachers is fractions. Everything about fractions seems to be difficult: how to write a fraction, reduce a fraction, compare fractions and perform operations with fractions.  These are just a few of the skills that students will need to learn and demonstrate mastery of on the STAAR assessment from Grades 3-8 and Algebra 1.

With the implementation of the revised standards in mathematics, beginning with the 2014-2015 academic year, students across Texas will begin to work with fractions earlier and at a more rigorous level than with our current standards. In order to set up students for success, instructors in the early grades need to ensure that they use concrete and visual models to teach this very abstract concept.  Teachers need to create a bridge for their students. This will help students move from concrete models of fractions to visual models, and in the later grades, students will be able to work with more abstract fraction concepts.

At times educators might be resistant to the idea of having students use manipulatives in the classroom; “They can’t use manipulatives on the test” is a common statement. This is true, but if teachers can build a foundation of fractions using concrete objects they can then transition students into visual representations of fractions. Students are able to create and draw their own visual models on assessments. To better support students, teachers can expose them to a variety of concrete and pictorial models; this way a student can select and use the model(s) that they understand.

Below are examples of linear models that can be used to model fractions. Students can begin by using Cuisenaire® Rods (concrete model); with these students can easily see that a whole is being partitioned into equal parts. Students can also use a strip diagram and a number line to model fractions.


Below are 3 examples of using the area model to represent fractions. The circle model is a very popular visual to use when teaching students fractions. In addition to the circle model, students should also be able to model a fraction using the grid model and paper folding.



Teachers should also expose their students to set models. Set models are different from length and area models. A set model contains a set of objects, and the whole is the total number of objects in the set. When working with students, it is important to emphasize that the set of counters is considered 1 whole and not 8, as in the example below.



By using models and visuals to create a strong foundation of mathematics, students will be more prepared to build on their knowledge of fractions and be able to compare fractions, generate equivalent fractions, and perform operations with fractions.

These diagrams were taken from “Click on TEKS: A simple approach to understanding the Texas Essential Knowledge and Skills- Third Grade”. The resource can be found by visiting

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