7.NS.2-3 Misconceptions

Math Misconceptions 7.NS.2 7.NS.3

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.

When multiplying two negative integers, students may try to apply addition and subtraction rules. These students have not had enough time to explore and make generalizations. Students gain a deeper understanding when they have time to develop a pattern. Once they understand the pattern in integer multiplication, they then can begin to formalize the rules for multiplying integers.

MISCONCEPTION:

WHAT TO DO:

Students can often visualize what 3 x (-5) looks like. They are using a method they are comfortable with, repeated addition, to solve the problem. Yet, when faced with problems that require multiplying of two negative numbers they struggle to visualize what it looks like. If 3 x (-5) is repeated addition then it stands to reason that -3 x (-5) is repeated subtraction because -3 x (-5) is the opposite of 3 x (-5).

“The integer with the greater absolute value dictates the sign of the product.�

This student is again, applying the rules for addition and subtraction of integers to multiplication. It is important for this student to continue to use manipulatives, draw pictures, and explore patterns.

MISCONCEPTION:

WHAT TO DO:

* NOTE: See the screencast in the module that shows the commutative example of this problem.

Integers are defined as all whole numbers and their opposites, so a student tries to simplify the definition and say, “integers are NOT fractions.” According to this “new” definition of integers where does pi fit?

MISCONCEPTION:

According to this definition pi would be considered an integer because it is a non-terminating decimal, which means it cannot be written as a fraction.

CONSIDERATION:

Pi is somewhere between the integers 3 & 4. We don’t know an exact location for Pi because it is a non-terminating decimal, which means we cannot represent Pi as a fraction. We can only approximate that it is somewhere between 3 & 4 and closer to 3. For mathematical calculations, we commonly use 3.14 or 22/7 to approximate pi. When we apply the proper definition of an integer, pi is not a whole number and thus it is not an integer.