Math Misconceptions 6.SP.5

3 + 4 = 34 Look closely at errors in studentsâ€™ work (formative assessment) to help you reflect and make instructional decisions to suit all studentsâ€™ needs.

This standard requires students to find the mean absolute deviation, which means that students need to find the absolute value of a difference. Before introducing the definition of absolute value use both counting and subtraction strategies to develop the concept of distance between two points. Counting reinforces that subtraction is used to calculate the distance between two data points. Pick two points on a number line and ask students if it matters which point they start at to find the distance between the points. Our goal is to develop students’ conceptual understanding so they recognize 5 − 3 = 3 − 5 . Both represent a distance of 2 units away from 0; emphasize that distance is always positive.

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The measures of center (median and mean) are often taught as a rote process using only the algorithms. Without the conceptual understanding it is difficult for students to apply meaning to graphical representations and real life situations. Students often get confused when finding the median of an even number of data points because they donâ€™t know what to do with two center points. Measures of center are a way to balance data; therefore the goal is for students to realize that exactly half the data should be below the median and half above.

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When asked to find the measure of center students often only find the median or the mean. Students need to practice finding both measures of center and then discuss which one is a better representation for the given data. What does an outlier do to my data? It is especially important for students to recognize the effect an outlier has on the mean and contrast that with the effect on the median. As students work with different data points they begin to recognize that outliers affect the mean much more than the median.

MISCONCEPTION:

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Once students decide the best measure of center for their data is the mean they can start discussing how far each data point deviates from the mean and how that information will help them characterize the spread of the data. For a more in-depth discussion on this go to page 5 of the Common Core Tools Progression document.

Line graphs and bar graphs seem to be our go-to graphs for everything. They are easy to create and can fit lots of data. However, students need time to explore other graphs and to determine the best graph to be used for their data. They may find that a circle graph or a histogram or even a box plot, depending on the purpose of the data, is best. Give your students a couple different data sets and time to work together in small groups putting the data into several different graphs. Discuss which graphs worked and why and which graphs didnâ€™t work and why. The discussion from this type of a classroom activity can be very powerful. MISCONCEPTION:

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