Learn · Illustrative Mathematics · Grade 6 · Unit 8
Short lessons you can play with. Ask questions that data can answer, build dot plots and histograms, find the mean by sharing fairly and by balancing, measure spread, find the median and quartiles, and read box plots, then check yourself. When you’re ready, practice in Data Detectives.
Nine chapters follow the unit’s lessons in order. Each step shows one idea with something to change, then a quick check. A wrong answer names the likely mistake and gives one more try. Fraction answers can be typed as 3/20 or as a decimal.
The GAISE II framework (American Statistical Association and NCTM, 2020) builds all of statistics on a cycle: ask a statistical question, collect data, analyze it, and interpret the results, with variability at the center. The first chapter is about telling a statistical question (“How many pets do our classmates have?”) from one with a single answer, and every display after that answers a question in context.
Researchers Arthur Bakker and Koeno Gravemeijer describe a key shift: from seeing data as separate values to seeing a distribution with a shape, a center, and a spread. The widgets keep asking two questions together: what’s typical, and how spread out are the values?
Children hold several ideas of “average” (Mokros and Russell, 1995), and the balance point is the one that shows real understanding. Following IM, the mean appears first as leveling out bars, then as the point where a dot plot balances, and only then as add-and-divide. The mean absolute deviation is built the same way: each dot’s distance to the mean is drawn, then averaged.
Studies find that most students, even in college, mix up histograms and bar graphs, read a histogram’s bottom axis as counts, and think a flat histogram has less variability (Kaplan and others, 2014). With box plots, many read a longer part as holding more data (Lem and others, 2013). These pages build histograms from dot plots and draw box plots over their own dots, so the bars and parts always stand for data, and the quick checks name these mistakes.
For a roughly symmetric distribution, the mean and MAD describe it well; when it’s skewed or has a far-off value, the median and IQR do better. One widget drags a single value far away and shows the mean moving while the median stays put. Groups are compared with both a center and a spread, never one value.
Each chapter ends with a link to the matching station in Data Detectives, the practice game for this unit. Progress is saved on this device.
Collecting and studying a class’s own data (Lessons 1 and 18) works better in class.