Math Misconceptions

7.NS.1

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.

Every integer has an opposite? Zero is an integer, so does it have an opposite? An opposite is defined as an equal distance from zero on a number line. Four and -4 are four spaces from zero so they are opposites. But what is the opposite of zero? Some research says that zero is simply zero and cannot have an opposite. Other research says that zero is the opposite of zero. CONSIDERATION:

Is a negative sign the same as a subtraction sign? No. A negative sign applies to one number; it is a position on a number line relative to zero. A negative sign is called the additive inverse and is defined by a + (-a)= 0. The additive inverse of a is the number you can add to a to get zero. A subtraction sign is an operation telling us what to do with two numbers. It is defined as meaning addition of the additive inverse or a – b = a + (-b). When using a number line we might say, “walk left on the number line the given distance.” (See the Walk the Number Line activity on page 4 of this module.) They have the same symbol because they are closely related. Modeling a problem on a number line helps students see the difference between a negative sign and a subtraction sign and it also let’s them see the connection. MISCONCEPTION:

WHAT TO DO: To model this problem on a number line, start at zero. The signs before the numbers tells us what direction to move. Negative six tells us to move left six units. The addition sign tells us to add a distance or a movement. Negative four tells us to move four more spaces to the left.

Students can model subtraction problems like -6 – 4 by rewriting the problem as an addition problem, -6 + (-4).

Students develop the idea that smaller numbers are closer to zero because most of their experiences with numbers have involved only positive numbers. Negative numbers are formally introduced in sixth grade. When students are given opportunities to think about numbers in terms of temperature, money, or floors of a building with a basement they start to gain a better understanding of the concept. MISCONCEPTION: WHAT TO DO: