Math Misconceptions 5.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.
Some students may not find equivalent fractions with common denominators before adding or subtracting fractions with unlike denominators. These students may add the numerators, and then add the denominators. While adding or subtracting unlike denominators is possible in the correct context (see the NCTM article “The Sweetest Chocolate Milk” on the first page of the BLAST module), students in 5th grade should be using equivalent fractions to determine a common denominator and complete the operations. One way to have students find their own errors is to use manipulatives, visual models, and number line diagrams to prove their thinking and solutions. These representations help students make sense of problems and persevere in solving them (Standard for Mathematical Practice.) If students ask themselves, “Does this make sense?” in the context of the problem below, they would conclude that 3 2 is less than . 7 3 MISCONCEPTION:
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When students work with adding and subtracting mixed numbers, they often apply whole number operation procedures that they have memorized. For example, this misconception shows how a student may try to “regroup/borrow” the whole number by combining it with the numerator. This would show that the student does not understand fractional values. By decomposing the mixed number into parts, it’s easier to create the improper fraction and move to finding equivalents from there. Do not rely to heavily on the procedure (algorithm) for adding and subtracting fractions with unlike denominators. Rather, use visual models, manipulatives, and number line diagrams in the context of word problems and real-world situations. 1 3 Word Problem: A cornbread recipe calls for 1 cup of milk. Sara only has cup of milk. 4 6 How much more milk does Sara need for her recipe? MISCONCEPTION:
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