
Unit 4, Exploring Generalization, amplifies the theme of mathematical generalization: How do statistics behave when new samples are considered? If teachers have not already done so, one investigation considers the effects of measuring a length, such as an arm span, with a more precise tool, such as a meter stick or tape measure. Measuring an arm span with a meter stick typically does not substantially alter the center of the distribution, but it does reduce the variability of the measurements. Do the statistics of center and variability (precision) capture what stays the same and what changes when the measurement process is altered by the use of the better tool? Unit 4 introduces new contexts of production. In Toothpick Factory, students produce packages of toothpicks and use center statistics to infer the target value (i.e., how many toothpicks per package). Statistics of variability measure the consistency of production (the tendency to pack the same number of toothpicks in each package), Students use these statistics to compare two different methods of producing toothpick packages. In Rate Walk, students walk 10 meters at different target rates (0.5 m/sec, 1 m/sec, and 5 m/sec.). They use statistics of center and variability to decide at which rate they performed best. Other production process contexts are available on the website, including Candy Factory and Fantasy Football.
Additional Materials
Teacher's Corner
Performances
COS1A: Use visual qualities of the data to summarize the distribution.
COS2A: Calculate statistics indicating central tendency.
COS2B: Calculate statistics indicating variability.
COS3C: Generalize the use of a statistic beyond its original context of application or invention.
COS3E: Predict the effect on a statistic of a change in the process generating the sample.
COS3F: Choose/Evaluate statistic by considering qualities of one or more samples.
COS4A: Predict that a statistic’s value will change from sample to sample.