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Preparing Students for Algebra with Fractions
Did you know that fractions knowledge in grade 5 uniquely predicts students’ math achievement in high school?
In a major study analyzing multi-year data from a nationally representative sample of students, fractions knowledge at age 10 was the strongest predictor for math achievement at age 16 (Siegler et al., 2012). This was true even after controlling for other variables that commonly impact math performance, including general intellectual ability, working memory, and family income and education levels.
Setting the foundation for algebra with fractions
Fractions are students’ first exposure to abstraction in math, and proficiency is crucial for foundational algebraic thinking used in advanced math courses (National Council of Teachers of Mathematics). Since “fraction knowledge and algebraic thinking share important conceptual underpinnings,” rational number sense is crucial for future work with algebraic concepts (Rodrigues et al., 2016, p. 135). Unfortunately, many students’ limited conceptual understanding of fractions remains the key “missing pillar,” resulting in a widespread lack of algebra readiness (National Math Advisory Panel, 2008).
Understanding fractions as numbers
A specific aspect of fractions knowledge that impacts subsequent algebra learning is fraction magnitude (size). Students with a stronger understanding of fraction magnitude when starting algebra “learn more of the algebra content than peers who start with weaker fraction magnitude understanding” (Booth, Newton & Twiss-Garrity, 2014, as cited in Rodrigues et al., 2016).
Fraction magnitude knowledge begins with seeing fractions as numbers – understanding how the numerator and denominator work together to create a single value. Number line activities can support magnitude understanding by allowing students to recognize how the relationship between a numerator and a denominator impacts fraction size; however, the abstract nature of this representation can be challenging for students who have math difficulties (Rodrigues et al., 2016).
When students meet fractions, they are required to manipulate numbers instead of simply “finding answers” for the first time in their math careers. Students who develop a strong fraction number sense (understanding that fractions are numbers that can be rewritten in different forms) will be much better prepared for the abstraction of algebra.
Let’s compare two students, one who is well-versed in fractions concepts and skills and another who relies heavily on memorized procedures.
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Strong fractions instruction, which helps students understand fractions as numbers that can be rewritten, can actually prepare students well for the abstraction of algebra. Jessica’s familiarity with the magnitude of fractions greater than one allowed her to convert 20/9 in a flexible and efficient manner. An algebra teacher would point out that Jessica’s reasoning is exactly like the abstract manipulation at the heart of algebra. With an underlying conceptual framework in place due to her fractions knowledge, Jessica will be better prepared to understand and manipulate coefficients and variables in the future.
Any algebra teacher will agree that simply “knowing the steps” for a problem is disadvantageous for students. In algebra, there are many different types of problems; steps can get forgotten, working memory issues cause confusion, or students might forget which algorithm to use with a certain problem. If a student isn’t already used to the idea that certain things in math can be rewritten to make things easier, algebra will be a hard pill to swallow. On the other hand, if students come to algebra already familiar with that notion thanks to a strong foundation in fractions, things fall into place very easily!
Preparing students for algebra with Frax
ExploreLearning Frax helps grade 3+ students master foundational fractions through research-driven methods and interactive games in an out-of-this-world galaxy setting.
- Frax introduces fractions as numbers first to build a strong conceptual understanding of fractions. Frax tackles length models from the very first lesson, helping students develop a robust sense of fraction magnitude from day one.
- Frax builds on intuitive visual representations (like length models) to introduce the number line representation of a fraction. Students work heavily with number lines as they build a strong understanding of fraction magnitude, which is essential to later success in algebra.
- Frax meets students at their own level with frequent rewards, just-in-time instruction, and game-based fun.
- Frax supports teachers with student reporting, pre-made offline resources, professional development, and community with other educators. The program can supplement any core math curriculum.