Math Misconceptions

4.NF.1-2

Look closely at errors in students’ work (formative assessment) to help you reflect

and make instructional decisions to suit all students’ needs.

Students can form misconceptions about equivalent fractions, their values, and their meanings when they only work with a set of procedures for generating them. If they are instructed to just “times the numerator and the denominator by the same number”, they are not getting the foundation for what is happing when finding equivalents. Repartitioning fractions is a great way to build understanding of generating equivalents. Fraction strips that can be folded in new ways provide a tangible way of demonstrating this point. Also, use methods of covering, laying fraction pieces on top of one another to discover equivalents and begin to make conjectures that build a logical progression of statements to explore the truth about their thinking (Standard for Mathematical Practice). MISCONCEPTION:

WHAT TO DO:

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When students compare fraction values, they fall back on what they know and understand about whole numbers. In this example, 8 has more than 4, and the drawings are shown to match that thinking. The first misconception is students often fail to recognize that fraction comparisons are only valid when they refer to the same whole. Additionally, students need to learn many strategies for fraction comparisons, such as creating common denominators, creating common numerators, and using benchmark fractions to reason and justify their conclusions. With the use of visual models, manipulatives, and number line diagrams, students can deepen their understanding, rather than relying on a checklist of steps that have no context or transfer to addition fraction skills. MISCONCEPTION:

WHAT TO DO: