6SP-Summarize+and+describe+distributions

6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5.Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. 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. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standards**===
 * Reason abstractly and quantitatively.
 * Model with mathematics.
 * Use appropriate tools strategically.
 * Attend to precision.
 * Look for and make use of structure.
 * Construct viable arguments and critique the reasoning of others. ||
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking: Summarize, Relationships**=== ||

Students display data graphically using number lines. Dot plots, histograms and box plots are three graphs to be used. Students are expected to determine the appropriate graph as well as read data from graphs generated by others.

Students summarize numerical data by providing background information about the attribute being measured, methods and unit of measurement, the context of data collection activities (addressing random sampling), the number of observations, and summary statistics. Summary statistics include quantitative measures of center (median and median) and variability (interquartile range and mean absolute deviation) including extreme values (minimum and maximum), mean, median, mode, range, and quartiles.

Students record the number of observations. Using histograms, students determine the number of values between specified intervals. Given a box plot and the total number of data values, students identify the number of data points that are represented by the box. Reporting of the number of observations must consider the attribute of the data sets, including units (when applicable).

Given a set of data values, students summarize the measure of center with the median or mean

Students develop these understandings of what the mean represents by redistributing data sets to be level or fair (equal distribution) and by observing that the total distance of the data values above the mean is equal to the total distance of the data values below the mean (balancing point).

Students use the concept of mean to solve problems. Given a data set represented in a frequency table, students calculate the mean. Students find a missing value in a data set to produce a specific average.

Students find the IQR from a data set by finding the upper and lower quartiles and taking the difference or from reading a box plot.

Students understand how the measures of center and measures of variability are represented by graphical displays.

Students describe the context of the data, using the shape of the data and are able to use this information to determine an appropriate measure of center and measure of variability.

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...**Summarize and describe data in a variety of graphs.

 * I can recognize the measures of central tendency.
 * I can recognize variances for a set of data.
 * I can display numerical data using a variety of graphs.
 * I can order, display, and describe data in tables and graphs.
 * I can calculate measures of variances.
 * I can identify the effect of outliers.

box plots, dot plots, histograms, frequency tables, cluster, peak, gap, mean, median, interquartile range, measures of center, measures of variability, data, Mean Absolute Deviation (M.A.D.), quartiles, lower quartile (1st quartile or Q1), upper quartile (3rd quartile or Q3), symmetrical, skewed, summary statistics, outlier

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

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**
Teaching the Common Core Math Standards with Hands-On Activities: Creating Data Displays (page 72) Teaching the Common Core Math Standards with Hands-On Activities: Summarizing Data (page 75)

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**

 * Quantiles 1**
 * Quantiles 2**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Enrichment:**

Fund Raising p.84: Navigating through Algebra Pledge Plans p.83: Navigating Through Algebra Popular People p.159: Navigating Through Problem Solving and Reasoning How Do the Dollars Stack Up p.161: Navigating Through Problem Solving and Reasoning

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources:**===

Mathematics Station Activities for Common Core State Standards Grade 6 (pages 120, 127,and 150) Carnegie Learning: Lesson 15.3, Lesson 15.4, Lesson 16.5, Lesson 15.5, Lesson 16.1, Lesson 16.2, Lesson 16.3

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