Math Misconceptions 8.NS.1 & 8.NS.2
3 + 4 = 34 Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
Some students assume that all fractions are classified as rational numbers. These students do not have a complete understanding of rational numbers. They recognize a rational number is any number that can be written as a fraction, but misunderstand that the fraction must be able to be written as the ratio of two integers where the denominator cannot equal zero. When divided out, this ratio will turn out to be either a terminating or a repeating decimal. Student confusion happens in part because they learn to manipulate symbols and numbers without meaning. Teachers need to provide contexts in which students develop the why behind what they are doing. The student below has missed the details of the definition. He has missed the requirement that both the numerator and denominator need to be integers.
MISCONCEPTION:
WHAT TO DO:
Students should recognize the difference between the 10 and the
16 . The
10 is not an integer because it is a non-terminating, non-repeating decimal. But the 16 is an integer because it can be simplified to a terminating decimal (in this case a whole number). Note: This example also corrects the misconception that all square roots are irrational.
Students may see a radical sign and automatically classify it irrational. Students may reinforce this misconception when working with an expression involving radical signs and immediately assume they will result in an irrational number. Remind students to use the properties (commutative, associative, or distributive) to help simplify an expression before classifying it as rational or irrational.
MISCONCEPTION:
WHAT TO DO:
Many students get confused between “repeating” and “non-terminating” numbers making it difficult for students to classify numbers as rational or irrational. Sometimes their confusion is from not understanding what the symbols mean and sometimes it is from misunderstanding the definitions of “repeating” and/or “non-terminating.” A good way to describe it to students might be, “all repeating numbers are non-terminating, but all non-terminating numbers are not necessarily repeating.”
MISCONCEPTION:
WHAT TO DO: