6SP-Develop+understanding+of+statistical+variability

6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. //For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.// 6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**===
 * ===**Common Core Standards**===
 * Make sense of problems and persevere in solving them.
 * Construct viable arguments and critique the reasoning of others.
 * Attend to precision.
 * Reason abstractly and quantitatively.
 * Model with mathematics.
 * Use appropriate tools strategically.
 * Look for and make use of structure. ||
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking:**===

**Justify, Discuss**
|| ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===

Students differentiate between statistical questions and those that are not. A statistical question is one that collects information that addresses differences in a population. The question is framed so that the responses will allow for the differences. For example, the question, “How tall am I?” is not a statistical question because there is only one response; however, the question, “How tall are the students in my class?” is a statistical question since the responses anticipates variability by providing a variety of possible anticipated responses that have numerical answers. Questions can result in a narrow or wide range of numerical values.

The distribution is the arrangement of the values of a data set. Distribution can be described using center (median or mean), and spread. Data collected can be represented on graphs, which will show the shape of the distribution of the data. Students examine the distribution of a data set and discuss the center, spread and overall shape with dot plots, histograms and box plots.

Data sets contain many numerical values that can be summarized by one number such as a measure of center. The measure of center gives a numerical value to represent the center of the data (ie. midpoint of an ordered list or the balancing point). Another characteristic of a data set is the variability (or spread) of the values. Measures of variability are used to describe this characteristic

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...**Develop an understanding of how data and statistics vary.

 * I can recognize that data varies.
 * I can identify statistical questions.I can identify the distribution of data by using its center, spread, and shape.
 * I can recognize variances for a set of data.
 * I can calculate measures of variances.

statistics, data, variability, distribution, dot plot, histograms, box plots, median, mean

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Sample Assessments**
Thinkgate
 * Daily Spiral Review**
 * Signaling**
 * Questioning**
 * Teacher Observation**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**
Teaching the Common Core Math Standards with Hands-On Activities: Statistical Questions Versus Nonstatistical Questions (page 65) Teaching the Common Core Math Standards with Hands-On Activities: And the Answer Is (page 67) Teaching the Common Core Math Standards with Hands-On Activities: Measure of Center Versus Measure of Variation (page 69)

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**

 * Quantile 1**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Enrichment:**
Activities will be used from Instructional Resources List ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources:**===

Mathematics Station Activities for Common Core State Standards Grade 6 (pages 113, 135, and 143) Carnegie Learning: Lesson 15.1, Lesson 16.1 Unit Notes Grab a Handful Box Plots Activity Minute to Win it Games Minute to Win it Games Box Plots Recording Sheet ===Box and Whisker Plot Directions=== Notes/Examples Practice 1 Practice 2

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===