Math Misconceptions

6.SP.2 6.SP.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.

There are two types of data: categorical and numerical. Each type should be displayed and summarized using different methods. Students need to recognize the difference between categorical and numerical data and how to represent each type of data. CATEGORICAL DATA: Students are most familiar with bar graphs and often want to graph everything using a bar graph. Bar graphs should be used to summarize categorical data like types of pets or favorite flavors of ice cream. Circle graphs can also be used to represent categorical data but should be linked to percent.

• Categorical data should be summarized using frequency counts. For example, 6 students have a cat, 3 have a snake, 10 have a dog, and 1 has a horse.

• Categorical data does not have a shape because if the order is changed, the shape also changes.

• The mode is a meaningful representation of the data because in this case 10 students have a dog, which means most of the students have a dog for a pet.

• The mean and median are not meaningful representations of the data because finding an average or the middle doesn’t tell us anything about the data.

NUMERICAL DATA: Numerical data should be summarized using histograms, stem and leaf plots, dot plots (line plots), circle graphs, and box plots (box and whisker plots). It’s important for students to know what type of data they are working with and how to represent that data.

• Numerical data should be organized numerically and thus it has a fixed shape.

• The overall shape, the measure of variation, the measure of center (mean and median), can also be used to summarize numerical data. Discussions about outliers and how they affect the overall shape and measures of center help students understand data trends.

• The mode may be an interesting topic for conversation because it may give meaning to the data, but it may not. For example, in the examples below the mode for the African Elephant Ear Weight is 106 pounds. Does that tell us anything? Most African elephants have ears that weigh 106 pounds but is that a good representation of ALL African elephants?

Statistics help us make informed decisions using data.

Statistical tools help bring insight and clarity to data.