Math Misconceptions

1.NBT.4-6

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

make instructional decisions to suit all students’ needs.

As students begin to add specific numbers together using place value and properties as strategies, they often make mistakes in regards to the value of the digits. It’s difficult for students to understand that when the digit 6 is written in the ones position it holds the value of 6 ones, but when the digit 6 is written in the tens position it holds the value of 6 bundles of 10 and 60. Ask yourself, “Do students understand the value of each digit, rather than just looking at the digit in isolation?” Place value understanding needs to be solid before students begin “adding” tens and tens along with ones and ones together. MISCONCEPTION:

WHAT TO DO:

Mentally finding 10 more or 10 less than a number may be difficult for a student who does not fully understand the structure of the base-ten system. If a student has to use counting strategies to complete this mental exercise, then developmentally the student needs more experiences with concrete materials, hundreds charts, and bundling ten ones into a group of ten. Additional work with decomposing and representing numbers in different ways can also be helpful. For example, given the number 57, students can practice representing that number with an equation such as 57 + 10 = 67. MISCONCEPTION*:

* While counting on fingers isn’t really a misconception, it does demonstrate a habit of mind that shows lack of base-ten understanding.

WHAT TO DO:

When concrete materials are needed, students can also use place value mats with base ten blocks to compose and decompose values by multiples of ten

(an example of a place value mat and manipulatives is shown on the following page).

Subtracting multiples of ten with concrete models still continues to emphasize the importance of understanding the value of digits, specifically in this case, the value of the digit located in the tens place. It’s difficult for students to understand that when the digit 6 is written in the ones position it holds the value of 6 ones, but when the digit 6 is written in the tens position it holds the value of 6 bundles of 10 and 60. Ask yourself, “Do students understand the value of each digit, rather than just looking at the digit in isolation?” Place value understanding needs to be solid before students begin “subtracting” tens. MISCONCEPTION:

WHAT TO DO: