The mathematical purpose of this lesson is for students to understand that measures of center can be more or less representative of a data set based on the data distribution shape. Previously, students learned names used to describe typical shapes of data distributions and how to interpret data based on the shape. Students have also learned how to find the mean and median and use them to represent typical values in a data set. In the associated Algebra lesson, students will explore the effect of extreme values on these two measures of center. This lesson will continue to build on the understanding that the median is the preferred measure of center for skewed data for upcoming lessons. Students reason abstractly and quantitatively (MP2) when they make a connection between balance point and mean as well as when they decide which measure of center more accurately represents what is typical of a data set.
The Balance Point activity in this lesson works best when each student has access to the digital applet, because they can experiment with many examples of data sets to see how the shape of the distribution affects the mean.
Lesson overview
- 10.1 Warm-up: Estimation: Lamp Post (5 minutes)
- 10.2 Activity: Balance Point (20 minutes)
- 10.3 Activity: Mean vs. Median (15 minutes)
Learning goals:
- Understand the relationship between the measures of center and the shape of data.
Learning goals (student facing):
- Let’s explore the relationship between measures of center and the shape of data.
Required materials:
- Meter sticks
- Pennies
Required preparation:
- The digital version is recommended for all classes over the paper and pencil version.
- If using the digital version, acquire computers or tablets that can run the applet, one for every 1–2 students.
- If technology is not available, there is a paper and pencil alternative.
Standards:
- This lesson builds on the standard: CCSS.6.SP.B.5.dMS.6.SP.5dMO.6.DSP.B.5d
- This lesson builds towards the standard: CCSS.HSS-ID.A.3MS.S-ID.3MO.A1.DS.A.3
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