Lesson Plan: 6.SP.A.1-3 Statistical Variability(This lesson should be adapted, including instructional time, to meet the needs of your students.)

Background InformationContent/Grade Level Statistics and Probability/Grade 6

Unit/Cluster Develop understanding of statistical variability

Essential Questions/Enduring Understandings Addressed in the Lesson

What importance does statistical variability play in real-world situations?

Modeling data can help us understand patterns.

Standards Addressed in This Lesson 6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

6.SP.A.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.A.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.

It is critical that the Standards for Mathematical Practices are incorporated in ALL lesson activities throughout the unit as appropriate. It is not the expectation that all eight Mathematical Practices will be evident in every lesson. The Standards for Mathematical Practices make an excellent framework on which to plan your instruction. Look for the infusion of the Mathematical Practices throughout this unit.

Lesson Topic Statistical Variability

Relevance/Connections 6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations.

Page 1 of 17

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.

Student Outcomes Students will be able to determine the difference between a statistical and a non-statistical question. Students will be able to understand that a set of data can be described by certain characteristics

such as center, spread, and overall shape. Students will be able to determine the difference between a measure of center and a measure of

variation.Prior Knowledge Needed to Support This Learning

5.MD.B.2 Make a line plot to display a data set of measurements in fractions of

a unit ( 12 ,

14 ,

18 ). Use operations on fractions for this grade to solve

problems involving information presented in line plots.

Method for determining student readiness for the lesson

Using Think/Pair/Share, have students analyze a given line plot (Attachment #1 - Pairs of Shoes Owned by Students in Math Class). (Reference 4.MD.B.4 and 5.MD.B.2) Give students 2-3 minutes to brainstorm all they notice about the line plot. (Possible responses: general shape, most, least, greatest-smallest, no data points, the answer if data were re-distributed equally…)

Learning Experience

Component Details

Which Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

Warm Up Question Sort - Attachment #2

Page 2 of 17

Learning Experience

Component Details

Which Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

Organize students in small groups. Give each group a set of questions that have been cut and shuffled in advance. Pose the following:

Organize the given questions into categories. Create titles for your categories and be ready to explain your method of

organization. Once students have completed their sort, have students circulate from group to

group to observe the work of others. One student may want to remain with the group to share and answer questions.

Students may return and revise their sorts and titles. Teacher should lead a discussion which results in class agreement on statistical

and non-statistical questions.

Motivation Students will create a dot plot (line plot) from the information they find in an informal survey. They may survey students in the classroom or go to the internet to find information.

For example: Students can find out the number of pizza restaurants in students’ neighborhoods. They can then create a dot plot from this information. They could also go online and find the number of pizza restaurants in a given zip code and create a dot plot to show this information.

Activity 1

UDL Components Multiple Means of

Representation Multiple Means

for Action and

UDL Components: Principle I: Representation is present in the activity. Students are using a Frayer

model to represent their term in 4 different ways. Principle II: Expression is present in the activity. Students are sharing their product

with the entire class and explaining their term in their own unique way. Principle III: Engagement is present in the activity. Students are creating a product

Make sense of problems and persevere in solving them by requiring students to research to find the meanings of vocabulary related to statistical variability.

Page 3 of 17

Learning Experience

Component Details

Which Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

Expression Multiple Means

for EngagementKey QuestionsFormative AssessmentSummary

of their own choice to represent their term.

Directions:

1. Students create Frayer Model (see Attachment #3) for 1 of the following terms using a variety of resources available to your classroom (textbook, internet resources, prior knowledge, information printed by teacher in advance): Measures of Center Measures of Variation Measures of Spread (note to teacher – students should discover that measures

of spread are the same as measures of variation) Mean Median Mode Range Outliers Mean absolute deviation

2. Students create a product (mind map, song, rap, brochure, digital presentation, skit, cartoon, fairy tale/story, or infomercial) to represent their term. Real-world connection should be included.

3. Present to the class or jigsaw-style. Those students not presenting should complete a graphic organizer which organizes terms and definitions by measures of center vs. measures of variation (Attachment #4).

4. Review graphic organizers and use follow-up questions to promote class discussion:

(SMP # 1)

Construct viable arguments and critique the reasoning of others by requiring students to justify their conclusions from the product they create to represent their term.(SMP #3)

Attend to precision by making their creation precise in meaning and being able to clearly explain it to others.(SMP #6)

Page 4 of 17

Learning Experience

Component Details

Which Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

What did you notice about_____? How could you describe____? How could you describe the difference between___ and ___? Why is it helpful to know these terms? What would happen if…? In what situations would it be more helpful to use ___ rather than___?

Activity 2

UDL Components Multiple Means of

Representation Multiple Means

for Action and Expression

Multiple Means for Engagement

Key Question

UDL Components: Principle I: Representation is present in the activity.

Students are asked to critique dot plots presented in different ways. Students see dot plots online with the button activity and on charts presented by teacher. In some cases students are seeing them created online.

Principle II: Expression is present in the activity. Students can take advantage of a video, charts of information, class discussions and interactive work on an interactive computer program from Illustrative Mathematics. Students are encouraged to work independently, in pairs, or in small groups, depending on varying needs/preference for peer mentoring and support.

Principle III: Engagement is present in the activity. Students have a number of different types of learning activities to work on which will give different learners options for engagement as they work with partners, have discussions with whole group, work on an interactive computer program and use of dot plots to check for statistical questions.

Make sense of problems and persevere in solving them by requiring students to use the given information to decide if the data are statistical questions.(SMP # 1)

Attend to precision by expecting students to be able to critique dot plots from given information.(SMP #6)

Page 5 of 17

Learning Experience

Component Details

Which Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?

Directions:

Using the graphic organizer, complete the matching/memory game activity using the vocabulary from activity 1 (Attachment #5).

Closure 1. Using the web site: http://www.illustrativemathematics.org/standards/k8 . Open the web site. Choose Grade 6. Choose Statistics and Probability. Choose Show All. Choose #1, see illustrations. Open 6SP Buttons: Statistical Questions. Ask students to complete the activity on the site.

2. To apply student learning of terms learned throughout this lesson, students should answer the questions based on the given line plot and justify the chosen value using appropriate terminology.

3. Display the attached line plots. Ask students to write statistical questions that can be answered using these line plots. (Attachment # 6).

Supporting InformationInterventions/Enrichments

Students with Disabilities/Struggling Learners

Students with Disabilities/Struggling Learners and ELL:http://www.glencoe.com/sites/common_assets/mathematics/mc2/cim/interactive_labs/M2_02/M2_02_dev_100.html

Page 6 of 17

ELL Gifted and Talented

(This site allows a student to create a line plot using both whole numbers and decimals. A voice walks the student through the process and then gives her time to practice on her own.)

Word bank generated when needed.

GT extension: Create your own statistical and non-statistical questions and an answer key. Others in the class could sort. Students could also present their questions.

Materials Paper, pencils, colored pencils, markers, crayons, etc.

Technology Document camera

Resources http://www.illustrativemathematics.org/standards/k8http://learnzillion.com/student/lessons/540-recognizing-statistical-questionshttp://www.glencoe.com/sites/common_assets/mathematics/mc2/cim/interactive_labs/M2_02/M2_02_dev_100.html

Page 7 of 17

Attachment #1: Method for determining student readiness for the lesson

Pairs of Shoes Owned by Students in Math Class

x

x x

x x x

x x x

x x x x

x x x x x x

x x x x x x x x x

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Page 8 of 17

Attachment #2 Warm-up: Question Sort Activity –

How old am I? How old are the students in my school?

How many siblings does my teacher have? How many siblings does each student in my class have?

How many hours of TV do I watch in one week? How many hours of TV do each of my family members watch in a week?

How tall am I? How tall are the members of my class?

How many slices of pizza can I eat? How many slices of pizza can each of my friends and family eat at my birthday party?

How many spots on a fawn? How many spots are on a head of fawns?

How many ounces does a baby calf drink in a day? How many ounces does a baby calf drink each day in a month?

How many points did the center make in the first basketball game of the year?

How many points did the center make during each basketball game of the season?

Page 9 of 17

Frayer Model

Definition (in your own words) Facts/Characteristics

Examples Non-Examples

Page 10 of 17

Attachment #3

Page 11 of 17

Attachment #4 Activity 1 – Term/Definition Organizer

Measures of . Measures of . Other

Page 12 of 17

Attachment #5 Activity 2 – Vocabulary Match/Memory Game

Measures of Center

Summarizes the values in a numerical data set with a single

number and includes mean, median, or mode.

Measures of Spread

Describes how the values in a numerical data set vary with a single number which includes

range and mean absolute deviation.

Measures of Variation

Describes how the values in a numerical data set vary with a single number which includes range and mean absolute deviation.

Page 13 of 17

MedianThe middle number in an ordered

set of data.

Mean The average of a set of data.

Mean absolute deviation The average distance between each data value and the mean.

OutliersAn outlier is a data value that is either much greater or much less

than the median.

Range

The difference between the highest and lowest numbers in a

set of data.

Page 14 of 17

ModeThe most frequent number in a

set of data.

Page 15 of 17

Attachment #6

What is the typical size of a button in the jar?

X

X

X X

X X X

X X X X

X X X X X X

018

14

38

12

58

34

78 1

Button Diameter (inches)

What is the typical number of holes in these buttons?

X

X

X X

X X

X X

X X X

X X X

X X X

0 1 2 3 4 5

Page 16 of 17

Number of Holes in a Button

Page 17 of 17