Math Misconceptions
3.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.
Rounding misconceptions occur when teachers and students place an emphasis on applying a series of steps, procedures, or rules to round to a specific place. Such steps do not reinforce strong number sense and may lead students to not understand 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 concepts. MISCONCEPTION:
WHAT TO DO:
When looking at the properties of operations, students often have several misconceptions. Students discover that addition is commutative because they are presented with the idea that 307+576 and 576+307 are related expressions. However, some students do not understand why addition is commutative. Addition is the sum of two or more groups and the order does not change the result. This is important to understanding the addition operation. Without an understanding of why addition is commutative, students overgeneralize and begin thinking that subtraction is also commutative. It’s important for students to understand that subtraction is finding the difference or distance between two quantities. MISCONCEPTION:
WHAT TO DO: Addition is commutative. 576 + 307 = 307 + 576 800 (8 flats) + 70 (7 rods) + 13 (units) = 883
Subtraction is not commutative.
* Remember to not say, “You can’t subtract 500 from 300.” In years to come, students will subtract these values when they begin their work with negative numbers.
Students may have misconceptions when working with large numbers. For example, when given 5 x 60, students shut down or simply guess by recalling basic facts and /or not paying attention to place value In order to work with larger numbers (multiples of ten), students must represent them with models, and apply strategies based on place value and the understanding of multiplication. Students in 3rd grade will begin working with the properties of operations and look for the patterns that occur when multiplying by ten. The goal of the multiplication standard in this cluster is to expand number sense so that numbers are understood in a variety of ways. For example, the number 80 can also be understood as 4 groups of 20.The goal of including multiplication in this cluster allows students to apply their understanding of multiplication (from the Operations and Algebraic Thinking Domain) while extending place value understanding and the properties of operations. MISCONCEPTION:
WHAT TO DO: 30 groups of 10 5 groups of 60 (5 x 6) x 10 60 + 60 + 60 + 60 + 60 (6 + 6 + 6 + 6 + 6) x 10 Skip Counting: 6, 12, 18, 24, 30 (multiplied by 10)