Using the CRA Method to Teach Comparing Fractions
When differentiating practice for students, start with the Concrete-Representational-Abstract (CRA) method. It's a powerful teaching framework that helps students understand mathematical concepts step by step.
This approach allows students to build a solid understanding by starting with tangible, hands-on manipulatives before moving toward more abstract reasoning. Below, we’ll walk through how to apply the CRA method for comparing fractions, complete with examples aligned to our "Comparing Fractions Task Cards."
Concrete: Hands-On Exploration
The concrete stage begins with students using physical manipulatives like fraction bars (our fave!), counters, or fraction circles. These tools help students develop a sense of the size of different fractions and how they relate to one another. For example:
Using Fraction Bars: Have students compare two fractions, such as 2/3 and 3/4, by physically aligning fraction bars to see which is longer. They’ll observe that 3/4 covers more space than 2/3.
Building with Fraction Circles: Students can stack pieces of fraction circles to visually compare fractions with the same numerator or denominator.
Begin by having students compare fractions with either the same numerator or denominator, ensuring they build confidence through hands-on experience.
Representational: Visual Models
In the representational stage, students transition from physical tools to drawings, diagrams, and number lines. This stage helps students visualize fractions and make comparisons without the need for manipulatives. Here’s how to implement this stage:
Drawing Bar Models: Have students draw bar models for fractions like 1/2 and 2/5. By dividing and shading their drawings, they’ll see which fraction represents the greater amount.
Using Number Lines: Guide students to plot fractions on a number line. For instance, students can plot 3/4 and 2/3 to compare their positions and see that 3/4 is closer to 1.
Begin with giving students labeled models, but move to including unlabeled fraction models and number lines. This step challenges students to interpret and draw their own representations to solve comparison problems.
Abstract: Comparing Fractions with Symbols
The abstract stage involves reasoning about fractions without visual aids. At this level, students rely on their understanding of numerators, denominators, and benchmark fractions to make comparisons. For example:
Using Benchmark Fractions: Ask students to determine which fraction is closer to 1/2 or 1. For instance, they’ll notice that 2/5 is smaller than 1/2 because it has fewer parts of the same size.
Applying Rules for Same Numerator/Denominator: Teach students to compare fractions by reasoning about their parts. For example, when comparing 3/5 and 3/7, they’ll recognize that 3/5 is larger because fifths are bigger than sevenths.
Assign students word problems that require students to compare fractions without visual aids, encouraging them to apply reasoning and mathematical symbols (<, >, =).
Why CRA Works for Comparing Fractions
The CRA method provides students with multiple entry points to understanding fractions. It ensures they develop a strong conceptual foundation before transitioning to abstract reasoning. By engaging with fractions at different levels, students gain confidence and flexibility in their math skills.
To make this process even easier, check out our Comparing Fractions Task Cards!
These leveled, no-prep cards offer differentiated practice for students at every stage of learning to meet your students' needs whether they are on-, below-, or above-level as follows:
→ Level 1 - Compare two fractions with either the same numerator or denominator using labeled pictures, fraction bars, or number lines.
→ Level 2 - Use unlabeled pictures, fraction bars, or number lines to solve word problems comparing two fractions with either the same numerator or denominator.
→ Level 3 - Solve word problems that require comparisons of two fractions with either the same numerator or denominator.
With hands-on activities, visual models, and word problems, they’re perfect for math centers, small groups, or independent practice. Grab your set today and watch your students master comparing fractions with ease!
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