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Lesson Plan

9. Understand differences in sample means (C)

teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards CCSS.Math.Content.7.SP.B.3 http://corestandards.org/Math/Content/7/SP/B/3
teaches Common Core State Standards CCSS.Math.Content.7.SP.B.4 http://corestandards.org/Math/Content/7/SP/B/4
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Lesson objective: Understand how to make conjectures about the differences in the two groups from a strictly visual perspective and then support comparisons with appropriate measures of center and variability.

 

Students bring prior knowledge of giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered from 6.SP.B.5c. Additionally, students bring prior knowledge of using statistics from random samples to make inferences about population characteristics from 7.SP.1. This prior knowledge is extended to measuring the difference between the centers of two numerical data distributions by expressing it as a multiple of the distributions’ measure of variability. A conceptual challenge students may encounter is informally assessing the degree of visual overlap of two numerical data distributions with similar variabilities. ​

 

The concept is developed through work with dot plots, which can help students see the differences between the centers of numerical data distributions and express this difference as a multiple of the distributions’ measure of variability. This work helps students deepen their understanding of number as they learn to use sample statistics to describe and compare data distributions.

 

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) conjecture about the differences in the means of two samples from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability.

 

Key vocabulary:

  • center

  • distribution

  • dot plot

  • MAD (mean absolute deviation)

  • population

  • population mean

  • random sample

  • range

  • sample mean

  • spread

  • sampling variability

 

Special materials needed:

  • data for Conceptual Understanding Task

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