Math Misconceptions

5.NBT.1-4

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

make instructional decisions to suit all students’ needs.

Students form misconceptions about place value relationships when they focus on the face value of the digits in each place rather than the place values themselves. They may focus in on a 2 in the tenths place and a 2 in the hundredths place and see them as the same value. Students need to focus in on the places themselves and not only the digits. The structure of the base-ten number system is essentially multiplicative, as it involves counts of different sized groups that are powers of 10. The relationship between any adjacent place value units is always the same; one unit of higher place value can be decomposed into ten units of the next lower place value. For example, 1,000 can be decomposed into ten 100’s. One way to show this relationship is to compose and decompose various models such as base-ten blocks or nonstandard paper strips (cut apart and taped together) that are not associated with a face value of a digit. MISCONCEPTION:

WHAT TO DO:

When students try to explain patterns in the number of zeros when powers of ten are multiplied or divided, they often conclude that zeros are just either “added on” or “crossed off” to find an answer or that the decimal point magically moves to the right or to the left. While this procedure can work if applied correctly, this standard calls for students to explain the patterns. Students need repeated experiences with place value relationships and the meanings of multiplication and division by ten in order to explain or model their understanding about the zeros and why the decimal point is placed in a specific location. Additionally, relationships can be examined by asking questions such as, “What number would be 10 times greater?” or “What number would be 1/10 of the value?” Students must have repeated opportunities to work flexibly with these powers of ten. MISCONCEPTION:

WHAT TO DO:

3.67 + 3.67 + 3.67 + 3.67 + 3.67 + 3.67 + 3.67 + 3.67 + 3.67 + 3.67 = 36.7

When students compare two decimal numbers up to the thousandths, they may confuse place value terms such as “hundreds” and “hundredths” or think that more digits mean a larger number, which is an incorrect application of whole number comparisons. Students should compare numbers concretely with representative models, showing the values of the abstract numbers. By keeping the focus on the value of the digits (which can also be recorded using expanded form), the numbers can be directly compared. MISCONCEPTION:

WHAT TO DO:

Rounding misconceptions occur when students place an emphasis on applying a series of steps, procedures, or rules to round to a given number. Furthermore, if students can only complete rounding when they are given a specific place to round to, such as round to the hundreds place, then that would suggest that they are not understanding why someone would round numbers to begin with. Context of a situation can help this. For example, if you purchased items at a store for $9.75, you might say that you need about $10.00. The use of a number line diagram, labeled in different ways, helps students determine the halfway point between two numbers, which is a more effective way to work with rounding concepts. MISCONCEPTION:

WHAT TO DO: