Math Misconceptions 6.NS.5 6.NS.6 6.NS.7 6.NS.8
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.
A common misconception for students when first introduced to negative numbers is to believe that negative numbers work the same as positive numbers. A student might believe that “-2 is smaller than -5� because 2 is smaller than 5. Drawing number lines and plotting points on them helps students recognize that points are arranged from least to greatest as they read left to right. It also helps them begin to realize that the farther left or down they move on a number line the farther away from zero they get and the values decrease. This repeated practice also helps students understand absolute value.
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There may be a couple of misconceptions students develop when graphing in coordinate grids. They may switch the order when plotting the coordinate pair, (y, x), they may get confused when an ordered pair includes a zero, or they may plot points in the spaces rather than the intersections. Having students first plot points on both vertical and horizontal number lines helps students transfer graphing to coordinate planes. Students in 5th grade are only familiar with quadrant I; students in 6th grade are introduced to graphing in the other quadrants. Repeated practice graphing points and comparing points helps students dispel these misconceptions.
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Standards 6.NS.7 and 6.NS.8 introduce absolute value to students. The misconception that often occurs is students believe absolute value is the opposite of a number. Reminding students that absolute value is the distance from zero and that it is always expressed as a positive number helps, but often it isnâ&#x20AC;&#x2122;t enough. Absolute value needs to be discussed in real-life context to help solidify understanding. One diver goes to a depth of 2000 meters another diver goes to a depth of 4000 meters. Which one is greater? Students have no trouble saying 4000 > 2000. However, mathematically this should be written as 4000 < -2000 when comparing numbers. Itâ&#x20AC;&#x2122;s easy to see why they get confused. In real-life the absolute value can be used to show magnitude. 4000 feet below sea level is a greater depth than 2000 feet below sea level because it is farther from sea level or zero. Absolute value is a distance, not a direction like negative or positive.
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