4NF34 Math Misconceptions

Math Misconceptions 4.NF.3-4

Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.

Common misconceptions with fractions happen when students overgeneralize the meaning of fractions and their values. This is evident when students add or subtract straight across the numerators and denominators without considering the fraction as an entire quantity.

Teachers should plan for multiple experiences separating fractions into parts as related to the same whole. Use models to record the decompositions and record these decompositions as equations. By treating this group of standards more as composing and decomposing, rather than just adding or subtracting fractions, students will build stronger fraction sense.

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In appropriate contexts, students will need to find equivalent fractions that are represented as mixed numbers or improper fractions. Often a set of steps is taught to convert from mixed to improper or vice versa, and students typically follow these steps with little understanding, only to use but confuse these steps over time. Rather than complicating the process of finding equivalent fractions with these arbitrary procedures, students need to be working with decomposing and composing fractions to represent these equivalencies. Have students model using manipulatives or partitioned number line diagrams to figure out many representations of equivalent fractions.

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The concept of learning multiples of whole numbers has been common in classrooms, especially when first learning multiplication. Students need to understand that 1 group of 3 is 3, and 2 groups of 3 is 6, and so on. But what happens when students apply the concept of multiples to fractions? A common mistake for students to conclude is that the numerator and denominator each change values to reflect the multiple of the original fraction. Use manipulatives to first model the groups of unit fractions to help clear up this misconception.

Record those equations that show the repeated addition of what’s been modeled and the products of what’s been modeled. Once students are confident with multiples involving unit fractions, then extend the experiences to using the concept of multiples in order to multiply a fraction by a whole number.

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