6th Grade Unit 7: Data Analysis

Unit Driving Question

How can data analysis be used in real-world scenarios?

Essential Questions

1. How can we analyze data?

2. What information about a data set is gained from analyzing a visual representation for the data?

Big Ideas

1. Mean, median, and mode are measures of central tendency that provide information about the center of a data set.
2. Box and whisker plots are used to represent the distribution of a data set. 

Useful Websites

The following apps, websites, and smartboard lessons can be used throughout the unit, as needed, during small groups, lessons, to reinforce standards.  They are also useful for students who may need reinforcement, remediation, or differentiation.

1. Virtual Nerd: Virtual Nerd provides video tutorials as a supplemental resource for both students and teachers.

2. Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard so that students may study at their own pace both in and outside of the classroom.

3. Mr.Naussbaum.com: MrNussbaum.com offers interactive games specifically designed to pinpoint one or several essential concepts to make the learning process more interactive and enjoyable.

4. Interactive Sites for Education: These interactive activities work great on your interactive whiteboard, computer, laptop, or Chromebook for whole group or small group instruction or use in the computer lab or at home for individual learning. Most of these activities are Flash-based.  This means that they will NOT work on iPads unless you are running an app that allows Flash to play such as Puffin.  

5. Kahoot: Kahoots are fun, learning games best played in a group setting.  Players answer questions on individual devices (Ex: Chromebook, iPads) while games are displayed on a shared screen (Ex: Smartboard or TV).  Choose a Kahoot to match your desired skill or create your own.

6. Zapzapmath: Zapzapmath has over 150 math lessons designed to incorporate higher order thinking skills in the fields of creation, evaluation, and analysis. This is combined into a game-based system of fun math learning.

7. Mr.Anker Tests: Interactive activities and games for dozens of math skills.  Most of these activities run on Flash.

Launch Task

1 Lesson

• Numerical Data (Illuminations): In this lesson, students are asked to determine the typical height of a student in the class.  Through classroom discussion, students will decide on the best way to collect and analyze data in order to answer this question.  Terms including line plot and mean, median, and range may be suggested as ways to analyze this data because they have studied these terms in previous grades.  If time permits, this activity can be extended to compare the class’ height data to data collected about the class’ shoe sizes.  The height data collected in the lesson will be used in a later task, Comparing Mean and Median (Open Up).

Big Ideas for Development Lessons

1 - 2 Weeks (approximately 1 week per big idea)

Big Idea 1: Mean, median, and mode are measures of central tendency that provide information about the center of a

                   data set.

Key Resources

1. Interpreting Mean as Fair Share (Open Up): The Warm Up challenges students to find an expression with a value close to 4 in preparation for finding mean in later activities.  Activity 1 gives students a visual representation of the interpretation of mean being a “leveling out” of data which students learned about in fifth grade.  Activity 2 gives students the chance to find the mean for a real-world situation.  In the extension of this activity, students can investigate the effect of an extreme value on the mean of a data set.  In the Cool Down, students calculate mean for a set of temperature data in the first question. The second question gives students a mean and a data set with a missing data point and asks students to find the missing data point using the information.

2. The Median of a Data Set (Open Up): Activity 1 introduces students to the limitations of mean as a descriptor of a data set when the data set has an extreme value.  Activity 2 uses data collected by students to calculate the median of the data set and has students explain the meaning of median in terms of the data.  The Cool Down provides additional problems for students to calculate median and explain the meaning of median for those data sets.

3. Comparing Mean and Median (Open Up): The Warm Up provides two dot plots for data about the heights of presidents.  Students are asked to draw conclusions about the mean and median of the data sets using the dot plots.  The Warm Up is accessible to sixth graders because they learned about dot plot (line plots) in third grade.  Activity 1 is designed for students to discover that the mean of a data set is affected by extreme values in the data set and the median provides the most descriptive information in this situation. This activity uses the class’ height data collected in the initial task, Numerical Data.  In Activity 2, students study how the distribution of the data can affect the mean and median of a data set using dot plots. A histogram is also included in this activity.  Students will not formally study histograms until seventh grade, but they have been studying frequency tables and bar charts with intervals which is essentially a histogram since third grade.  The Cool Down asks students to estimate the mean and median of data sets and decide which measure describes the most typical data point using histograms and dot plots of the data sets.

4. Jumping Jack Math (Illuminations): In this activity, students collect class data and explore the effect of extreme values on mean, median, and mode.

5. Exploring Mean and Median (GeoGebra): This interactive activity provides students a chance to investigate how mean and median change as the data points change in a data set.

     

Big Idea Formative Assessment

• Measures of Central Tendency Probe: To learn more about how to use the OKMAP common formative assessment probes, complete the NextThought Formative Assessment Probes training module.   
• Doggie Farm Performance Assessment (does NOT cover 6.N.4.4): For access to scoring rubric and student samples, complete the NextThought PLC Common Assessment Discussion, Implementation, and Analysis training module.  

Evidence of Understanding 

Perform calculations for mean, median, and mode using real-world data.

• Use mean, median, and mode to compare data sets.

• Discuss the effects of extreme values on the mean and median of a data set.

Recognize which measure of central tendency provides the most descriptive information for a given data set.

• Make predictions about which measure of central tendency will provide the most descriptive information for a given data set.

• Discuss the advantages and disadvantages of using each measure of central tendency to analyze real-world data.

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment)

• Puppy Weights (Illustrative Mathematics): This task asks students to apply what they have learned during this unit by using the data from the Warm Up of Box Plots (Open Up) to make a graph to display the data, describe the distribution of the data, and find the typical value of the data set using what they know about measures of central tendency.