Comparing Fractions with like and Unlike Denominators: Concrete Level

 Introduction Phase 1 Initial Acquisition of Skill Phase 2 Practice Strategies Phase 3 Evaluation Phase 4 Maintenance

Introduction

Math Skill/Concept: Comparing fractions with like and unlike denominators using concrete materials.

Prerequisite Skills:

• Identify and name fractional parts using concrete materials.
• Identify numerator and denominator and understand what they represent.

Learning Objectives:

1) Compare fractional parts with like denominators using concrete materials that represent the area/measurement model (e.g. circle pieces, fraction bars/strips, cuisenaire rods).

2.) Compare fractional parts with unlike denominators using concrete materials that represent the area/measurement model (e.g. circle pieces, fraction bars/strips, cuisenaire rods).

3) Compare fractional parts with like denominators using concrete materials that represent the sets model (e.g. sets of counting chips, beans, unifix cubes, tickets).

4) Compare fractional parts with unlike denominators using concrete materials that represent the sets model (e.g. sets of counting chips, beans, unifix cubes, tickets).

Important Ideas for Implementation:

1) Only a concrete level plan is included for this math concept because the corresponding SOL for 3rd grade speaks directly to comparing fractions with like and unlike denominators using concrete materials. Moving students to an abstract level of understanding regarding this skill would come in later grades.

2) First introduce the concepts of comparing fractions with like and unlike denominators using concrete materials that represent “areas,” such as pizza and pizza slices, circle pieces, fraction bars/strips, and Cuisenaire rods. Students who have learning problems will be able to better conceptualize the differences/sameness between fractional parts through the area model because they can visualize the parts in relationship to the whole and can also “feel” the value of each fraction by running their fingers around the area of the “whole” that a fraction comprises.

3) Teach and provide student practice for comparing fractions with like denominators before doing so for unlike denominators.

4) Emphasize the importance of the relationship of the numerator to the denominator when comparing fractional parts, particularly when comparing fractions with like denominators. Students may rely on comparing the value of the numerators only, since this strategy will be a successful one with like denominators. However, this strategy will not be successful with unlike denominators. Such a strategy also prevents students from truly understanding what a fraction actually represents, which is the proportion of the “parts” to the “whole.”