Adding and Subtracting Fractions with Mixed Numbers: Abstract Level

More Teaching Plans on this topic: Concrete, Representational

Introduction

Math Skill/Concept: Addition of fractions with mixed numbers (Like denominators) using numbers and symbols.

Prerequisite Skills:

• Ability to add fractions with mixed numbers using concrete objects.
• Ability to add fractions with mixed numbers by drawing pictures.
• Familiarity with place value mats representing “ones” and “tens.”

Learning Objectives:

1) Add fractions with mixed numbers using a “fraction place value mat” and a fraction number line.

2) Solve story problems and equations involving addition of fractions with mixed numbers using the FASTDRAW Strategy without drawing.

Important Ideas for Implementation:

1) This plan describes the use of several cueing devices that will facilitate students’ transition from drawing solutions to solving problems at the abstract level. These cueing devices include a fraction place value mat and fraction number lines. Some students will move quickly from adding fractions with mixed numbers using these cues to solving such problems without using these cues. Other students will benefit from their use for longer periods of time. For these students, the process of fading the use of these cues will need to be more systematically applied. Students may periodically need to use drawings to solve problems at the abstract level as a “back-up” strategy. This should not be discouraged, especially as they initially solve problems at this level. You can help students fade their use of drawings by setting goals for decreasing the number of problems for which they use drawings. You might consider intermixing problems you know they can solve without drawing with problems they will probably need to draw solutions for.

2) This plan also describes how to solve story problems that involve addition of fractions with mixed numbers. Continuing to teach this skill using the FASTDRAW Strategy will help students with memory problems to “remember” the steps needed to solve such problems. The only difference between teaching FASTDRAW at the abstract level and the representational level is that you will teach students to apply abstract problem-solving methods during the “A” step in DRAW rather than drawing solutions.

3) At the abstract level, it is important to systematically help students fade the use of cues such as fraction place value mats, fraction number lines, and FASTDRAW Strategy Cue Sheets so that eventually they solve problems without such cueing.

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