Math Misconceptions 4.NBT.1-3
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
When students come to 4th grade, they have already had experiences with place value, and misconceptions may be present. Additionally, 4th grade is where students build solid understanding of the relationships between the place values. Much of the instructional focus is given to the names of each of the places (such as ones, tens, hundreds) or the value of a digit that is in that place (the digit 3 in the tens place has a value of 30). But specific attention is needed with the relationships between the place values. One way to illustrate this point is to have students manipulate a digit from one place to another, verbalizing and writing down the multiplication or division operation that is taking place (move a 7 from the ones place to the tens place verbalizing that multiplying 7 by10 or 7 bundles of 10 creates 70, and multiplying by another 10 or 70 bundles of ten results in 700). Emphasizing the relationships between the places is the key to 4th grade place value. MISCONCEPTION*: * While this student has the correct answer, this explanation demonstrates application of a rule and a lack of understanding of why it works.
WHAT TO DO:
The success of comparing multi-digit numbers depends on students realizing that it is the digits with the highest place value that contribute the most to the value of a number. For example, students might say that 1,576 is greater than 742 because it contains more digits. This strategy will provide correct answers for whole numbers, but lack of understanding is likely to lead to misconceptions when comparing decimal numbers or numbers with the same amount of digits. If students are not asked to explain their thinking or to construct a viable argument for why one number is greater than another, the teacher may overestimate a student’s understanding of comparing numbers in various situations. MISCONCEPTION:
WHAT TO DO:
Also use expanded form to compare number values. 1000 + 500 + 70 + 6
700 + 40 + 2
Rounding misconceptions occur when students place an emphasis on applying a series of steps, procedures, or rules to round to a specific place, 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 it took you 57 minutes to cook dinner last night, you might say that it took you about an hour to cook dinner. 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 concept. MISCONCEPTION:
WHAT TO DO: