## Unit Overview

**Essential Questions: **

**Lesson Plans and Seeds**

Lesson Plan A.1-3: Statistical Variability

Lesson Seed A.1: Statistical Questions

**Download Seeds, Plans, and Resources (zip)**

**Content Emphasis By Clusters in Grade 6**

**Progressions from Common Core State Standards in Mathematics**

Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.

### Unit Overview

Students in grade 6 build on and reinforce their understanding of number as they begin to develop their ability to think statistically. They recognize that a data distribution may not have a definite center, and that strategies for measuring the center – mean, median, mode – may yield different values.

**Teacher Notes:**

- Teachers should prepare students to understand the differences between and appropriate uses of mean, median, and mode when describing data.
- Teachers should model the correct usage of statistical vocabulary and terms, thereby helping students correctly integrate these new concepts into their current understanding of number.
- Teachers should provide students with opportunities to experience statistical variability using data gathered through a wide variety of authentic, student-centered scenarios.

**Enduring Understandings:**

At the completion of this unit on statistical variability, the student will understand that:

- The way that data is collected, organized and displayed influences interpretation and informs decisions..
- Data sets can be described and compared using various statistical measures, depending on which characteristics are being emphasized.
- Data is either categorical or numerical, which can be determined by describing the nature of the attribute under investigation.
- The extent to which values in a data set differ can be described using measures of variability.
- Misleading data can influence data results.

**Focus Standards (Listed as Examples of Opportunities for In-Depth Focus in the PARCC Content Framework document):
**

**Possible Student Outcomes:**

The student will be able to:

- differentiate between a statistical question and a non-statistical question.
- develop a conceptual understanding of characteristics for any data set, including its distribution, spread, measures of center, and general shape.
- identify and work with mean and median as measures of center.
- identify range as a measure of variation.
- look at a data set and estimate values for the measures of center.

**Evidence of Student Learning: **

*The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.*

**Fluency Expectations and Examples of Culminating Standards:**

**Common Misconceptions:**

Students may

- have difficulty understanding the concept of “average” and when the use of mean, median, or mode is most appropriate to identify “average.”
- use words, such as middle and most to help them recall how to determine median and mode, respectively. However, confusion about the meaning of median and mode can cause students to forget to determine the middle value AFTER all of the values in a data set have been placed in ascending or descending order; and to equate most with largest value in the data set rather than the most frequent.
- be unsure of what to do if the mean, median, and mode of the same data set all have the same values, or if more than one mode value (or none) exists in a data set.

**Interdisciplinary Connections:**

Interdisciplinary connections fall into a number of related categories:

*Literacy standards within the Maryland Common Core State Curriculum*

*Science, Technology, Engineering, and Mathematics standards*

*Instructional connections to mathematics that will be established by local school systems, and will reflect their specific grade-level coursework in other content areas, such as English language arts, reading, science, social studies, world languages, physical education, and fine arts, among others.*

**Sample Assessment Items: ***The items included in this component will be aligned to the standards in the unit and will include:*

*Items purchased from vendors*

*PARCC prototype items*

*PARCC public release items*

*Maryland Public release items*

**Interventions/Enrichments/PD: ***(Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)*

**Vocabulary/Terminology/Concepts: ***This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.*

**
Part I – Focus Cluster
Develop Understanding of Statistical Variability **

** variability: ** It is the ability to change or alter. In data, it will change or vary according to the situation.

** statistical question: ** A question that is asked about a group of data.

** distribution: ** To divide, share, or spread data in order to answer a statistical question. Distribution can be described by its center (mean or median), spread (range) and overall shape (curve).

** outliers: ** A piece of data that seems to be too far out at one end of the range is called an outlier. Outliers can affect how you interpret your data.

** measure of center: ** The mean and median are the measure of center for numerical data. They summarize the data into one number.

** measure of variation: ** The range is the distance between the highest and lowest data values.

**Part II – Instructional Connections outside the Focus Cluster**

** dot plots: ** It is sometimes called a line plot. A set of data is represented by using dots on a number line.

** histograms : ** is a form of bar graph in which the categories are consecutive equal intervals along a numerical scale. The height of each bar is determined by the number of data pieces that fall into that particular interval. Students have to be careful about using the appropriate interval for each bar width and a good scale for the height of the bars.

** box plots : ** It is sometimes called a box-and-whisker plot. It displays the data on a number line in such a way you can see the median, the quartiles and outliers of a set of data. It does not display any other specific values in a set of data.

** interquartile range : ** is the distance between the 75

^{th}percentile and the 25

^{th}percentile on a box plot. The interquartile range is the range of the middle 50% of the data.

** mean absolute deviation : ** it describes the average distance from the mean for the numbers in the data set. First you find the mean of the set of data. Then you subtract the mean from each data point and find the absolute value. Get the mean of your answers and that is your mean absolute deviation.

** deviations : ** something that departs from the norm or standard

** variability : ** “the state or characteristic of being variable” describes how spread or closely clustered a set of data is. Variability measures such things as the range, standard deviation and variance.

** distribution : ** the arrangement of numbers in a data set; a set of values that represent a variable and the frequencies of each representation.

_06_27.pdf