Grade 6 Mathematics Seminar
Unit 5: Survey Analysis
Unit Overview
In this unit of study, students will apply their understanding of statistics and probability to
display and analyze data. Students will develop a survey question of interest and a data
collection tool. They will display data in various forms and analyze results using different
measures. They will develop statistical skills that they can apply to solve real world problems.
This unit is expected to take 5 weeks (approximately 25 days).
Common Core Content Standards
6.SP
Develop understanding of statistical variability.
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.
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.
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.
Summarize and describe distribution.
4. Display numerical data in plots on a number line, including dot plots, histograms,
and box plots.
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.
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Grade 6 Mathematics Seminar
Unit Guide
Week
Focus
1
Categorical vs. numerical data:
developing a survey question and data
collection method.
Displaying data using a box plot,
histogram, and dot plot; describing
data by analyzing shape, center, and
spread.
Displaying data using a box plot,
histogram, and dot plot; describing
data by analyzing shape, center, and
spread.
Data analysis and making predictions
based on larger samples.
Analyzing and presenting data results.
2
3
4
5
Content
Standard(s)
6.SP.1
6.SP.2
6.SP.3
S.SP.4
6.SP.2
6.SP.3
6.SP.4
6.SP.5
6.SP.4
6.SP.5
6.SP.5
Additional Resources for Teachers
A quick reference on the difference between numerical (quantitative) and categorical data
(Week 1): http://www.usablestats.com/lessons/datatypes
For additional resources on good vs. bad questions, visit these sites by copying and pasting into
your browser:
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&ved=0CFsQFjAE&url
=http%3A%2F%2Fwww.wku.edu%2F~holli.drummond%2Ffirst%2520page%2Fclasses%2Fstra
tegies%2520of%2520social%2520research%2Fexample%2520of%2520bad%2520survey%2520
questions.pdf&ei=Af3qT8KRGcjJ6gGt1v2qBQ&usg=AFQjCNH9NV2xVpBYmVWdg5fVpx7
RkwxJmA
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CFMQFjAA&u
rl=http%3A%2F%2Fcontemporarycommunication.com%2FNarration%2F1_Surveys%2FDocum
ents%2FBad%2520Questions%2520Lecture%2520Examples.doc&ei=Af3qT8KRGcjJ6gGt1v2q
BQ&usg=AFQjCNFqk09ZykVIba9NjGk5PLy_E2-9SA
Video describing different aspects of 6.SP.3-5 (Week 2):
http://player.discoveryeducation.com/index.cfm?guidAssetId=282F02AE-43F8-4A65-B2E182F2785143DE&blnFromSearch=1&productcode=US
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Grade 6 Mathematics Seminar
Resources on Displays of Data (Week 2):
Histograms:
http://stattrek.com/statistics/charts/histogram.aspx (video and info)
http://illuminations.nctm.org/ActivityDetail.aspx?ID=78 (online creator)
http://easycalculation.com/graphs/create-histogram.php (online creator)
http://www.stat.wmich.edu/s216/basics/basics.html (How to do on graphing calculator)
Box Plots:
http://stattrek.com/statistics/charts/boxplot.aspx (video and info)
http://www.mathwarehouse.com/charts/box-and-whisker-plot-maker.php (online creator)
http://www.shodor.org/interactivate/activities/BoxPlot/ (online creator)
http://www.stat.wmich.edu/s216/basics/basics.html (how to do box plots on a graphing
calculator)
Dot Plot:
http://stattrek.com/statistics/charts/dot-plot.aspx (video and info)
http://www.vertex42.com/ExcelArticles/dot-plot.html (dot plot on Excel)
ETA Cuisenaire. (2008) Hands- On Standards, Deluxe Edition The First Source from
Introducing Math Manipulatives (Grades 5-6) Vernon Hills, IL: ETA Cuisenaire. (p. 171)
Facilitator Notes – Week 1
Day 1: Categorical vs. Numerical Data
1. Have students answer Warm-Up Questions. Display the words ‘numerical data’ and
categorical data’. Discuss: “What does the word category mean? What does the word
numerical mean? When you completed your warm-up, what did you notice? Which
questions do you think are categorical and which are numerical?” Discuss the
definitions of ‘numerical data’ and ‘categorical data,’ and as a class determine which of
the warm-up questions is numerical.
2. Assign students to small groups and distribute a set of Categorical vs. Numerical
Sorting Activity cut into strips. Have groups sort questions into the appropriate
category. Discuss answers as a class. Ask, “Are there questions that could go into either
category depending on how the question is asked?” (Note: “How respected do you feel at
school?” could be numerical if students are given a rating scale.)
3. Have students develop 3-5 questions that would elicit numerical data and 3-5 questions
that would elicit categorical data. Consider having students search online to find survey
questions. Have students exchange papers, and sort their partner’s questions by using a
‘c’ or ‘n.’ Questions can also be read aloud for categorical and numerical classification,
and the class can respond with a thumbs up or down. Collect questions.
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Days 2 - 4: Writing a Good Question
1. Have students select a station from those listed below to learn more about questioning.
When finished, have students form triads and report to each other on what they learned.
(Note: If all students choose the video, then watch it as a class, discuss it, and then have
two stations for the articles.)
 Station A: Question Types. This YouTube video provides a comical way to look
at many different types of questions. Have students watch the video, then discuss
components of a good question. Re-watch the video and discuss which of the
questions were good and which were not good. Ask, “How can the bad questions
be improved?” www.youtube.com/watch?v=DsuCGE9N8L4
 Station B: Creating a Good Survey. This article illustrates the attributes of a
good survey. http://www.accesscable.net/~infopoll/tips.htm
 Station C: The Importance of Asking the Right Question. This article
provides a story about why asking the right question is important in order to
receive the right answer. It also has a good list of data-collecting tips.
http://www.realinnovation.com/content/c100215a.asp
2. Have students analyze the Bad Questions vs. Good Questions, using one of the
following strategies:
 Read each question out loud and ask students to think-pair-share whether the
question is good or not. Attempt to re-phrase the ‘bad’ questions so they would
be considered good questions.
 Post the questions around the room and ask students to walk around individually
or with partners recording which questions are good or bad. Come back as a
whole group to debrief and correct the bad questions.
 Assign each pair 1-2 questions and ask them to briefly act out the delivery of
these questions. In their skit, have students discuss why their question is good or
not good. Have them rephrase any question they consider to be poorly written.
3. As a class, summarize the key ideas about good and bad questions. Have the class list the
characteristics of good questions.
4. Share that the next 5 weeks will consist of students determining an issue/question pairing.
They will collect and analyze the data. Discuss with students the elements of a good
question for this project by providing some guidelines, such as:
 The question should be of interest to them and should address an issue that affects
kids their age.
 The question should elicit numerical data.
 Data should be able to be collected daily.
5. Have students complete a think-pair-share and complete a chart similar to the one below.
Have students share their answers as a group. Consider also providing the examples
below if they were not already discussed.
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Grade 6 Mathematics Seminar
Issue
Question
Kids spend too much time on their
cell phones.
How many text messages do I send every
day?
Kids are tired during the school day.
How many hours of sleep do I get every
night?
Obesity is a problem for many
children.
How much time do I spend outside every
day?
Kids do not spend enough time doing
physical activity.
How much time do I spend watching TV
every day?
Kids are not getting their homework
done.
How much time do I spend playing video
games every day?
Kids do not get to play outside
enough.
How much time do I spend on homework
every day?
6. Group students into twos or threes for this project. Once they have determined and
developed their question, have them share out with the class. Using a “thumbs up or
thumbs down” method, have students determine whether or not they would classify the
question as a ‘good question.’
7. Have students complete Checkpoint Questions. Collect and use information to plan for
Day 5 Skill Review.
Instructional Note: Data collection will take place over the next 5-7 days and there should be 1
piece of data for each day. Each student in the class will respond to each group’s survey every
day. Groups should spend time developing a data collection tool. Begin by asking if they or
their families have ever been surveyed. Discuss the different survey formats (mail, phone, email,
etc.). Consider allowing students to do this on paper or through an online tool such as a Google
survey. Data collection will be done through the math seminar class only for this first round of
data collection.
Day 5: Skill Review/Pre-Assessment
Skill Review lessons are opportunities to offer targeted, differentiated support for students based
on their current understanding of content standards. Prior to this lesson, review the Checkpoint
Questions to determine the instructional needs of your students. Plan a differentiated lesson
using strategies that meet the needs of the class (strategic grouping, stations, two-group model,
all pupil response, etc.).
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
Grade 6 Mathematics Seminar
For ideas for creating and responding to formative assessment data, visit:
http://letthedatabeyourguide.wikispaces.com/
For differentiation strategies, visit:
http://daretodifferentiate.wikispaces.com/
http://media.hcpss.org/newcode/strategies/strategies.php
For ideas for teaching/re-teaching creating good questions and classifying numerical and
categorical data, refer to Elementary and Middle School Mathematics: Teaching
Developmentally by John Van de Walle (p. 439-440).
1. Ask students to complete a gallery walk to pre-assess their knowledge of the following
skills:
a. Box Plots, Dot Plots, Histograms
b. Mean, Median, Mode, Range, IQ Range, Absolute Mean Deviation
2. Consider using chart paper and keeping their work posted. As topics are reviewed during
Week 2, add or remove ideas from the paper.
Facilitator Notes – Week 2
Instructional Note: Allow students time each day to record their survey data. Encourage
students to do this at home, especially over weekends, but expect to set aside some time each day
for those students who may forget.
Day 1-3: Teacher Data Display
1. Review dot plots, box plots, and histograms using a set of numerical data that students
recognize. Connect their learning back to their own personal data. For example, if you
say,“As we learn how to use box plots, think about how you could include this type of
plot in your data analysis,” some examples may include test grades, homework
completion, sports related statistics, temperature, and birthdates. As a class generate a set
of numerical data to use for each of the displays.
2. Have students work in small groups to display the data using a dot plot, box plot, and
histogram. As each graph is created, be sure to discuss the center (mean/median), spread
(range/mean absolute deviation/IQ Range), and overall shape of each graph, as outlined
below:
 Mean: Discuss the reasonableness of answers and what the ‘mean’ actually
stands for. If all data was shared equally among each person, how much would
they each have?
 Median: Explain that the median is the halfway point. Exactly 50% of the class
has the median # of siblings or less and exactly 50% of the class has the median #
of siblings or more. Be sure to include the median value. Median cannot be
found on a histogram, but an approximate median can be determined.
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Grade 6 Mathematics Seminar


Shape: The mode shows itself in a dot plot as a large hump in the graph, a hump
can also appear on a histogram and can be discussed. However, if the x-axis is a
range of values, this hump cannot be identified as a mode. You can identify it as
an approximate mode. The shape of a graph can be symmetrical (if you were to
fold it in half on the median, the sides look similar).
Spread: Range is the most common way to describe the spread of the data. The
IQ range describes the range where the middle 50% of the data is grouped.
Consider having students watch this short video clip for a description and purpose
behind Absolute Mean Deviation:
http://www.youtube.com/watch?v=z9AJk7TvdpQ
Sample Discussion Points: Difference between histograms and bar graphs:
Bar Graphs
Histograms
Graph title and labeled
axes
Graph title and labeled axes
Bars do not touch
Bars touch
Vertical scale is
frequency
Vertical scale is frequency
Categorical Data
Numerical Data
x-axis represents
categories
x-axis represents numerical data and can be labeled as
a range
3. Discuss any unusual aspects of each graph such as outliers and (in dot plots and
histograms) humps in the graph (mode or approx. mode). Discuss which measures of
central tendency can be found using each graphical representation.
4. Have students complete Checkpoint Questions. Collect and use information to plan for
Day 5 Skill Review.
Day 4: Skill Review and Data Organization
Part I: Skill Review
Skill Review lessons are opportunities to offer targeted, differentiated support for students based
on their current understanding of content standards. Prior to this lesson, review the Checkpoint
Questions to determine the instructional needs of your students. Plan a differentiated lesson
using strategies that meet the needs of the class (strategic grouping, stations, two-group model,
all pupil response, etc.).
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
Grade 6 Mathematics Seminar
For ideas for creating and responding to formative assessment data, visit:
http://letthedatabeyourguide.wikispaces.com/
For differentiation strategies, visit:
http://daretodifferentiate.wikispaces.com/
http://media.hcpss.org/newcode/strategies/strategies.php
For ideas for teaching/re-teaching creating the shape of data refer to Elementary and Middle
School Mathematics: Teaching Developmentally by John Van de Walle (p. 438-439).
For ideas for teaching/re-teaching, use the following Moving with Math (MH1) Lessons:
 Measures of Central Tendency (p. 55)
 Modeling situations with graphs (p. 62, p. 71)
For ideas for teaching/re-teaching measures of central tendency, refer to More Good Questions:
Great Ways to Differentiate Secondary Mathematics Instruction by Marian Small (p. 160, 176,
181).
For ideas for teaching/re-teaching measures of central tendency, refer to Good Questions: Great
Ways to Differentiate Mathematics Instruction by Marian Small (p. 161, 170, 175).
Part II: Data Organization
1. Have students turn in survey data (there should be 6 days worth of data)
2. Have students begin organizing their data in preparation for displaying it. Consider
allowing them to use Excel and its filter feature so their data is organized from least to
greatest more efficiently. This could also be done for them as they are answering the
checkpoint questions.
Day 5: Student Data Display
1. Ask students to display their data using the three graphs that have been discussed.
Graphs should be done both by hand and using a computer (see above resources from
Week 2, Day 1 - 3) Although all data may not be best represented using all three graphs
(ex: some data makes more sense for a histogram, some should be displayed using a dot
plot, but all the data should be able to be represented well using a box plot), consider
having students still complete all 3 and have a discussion on which graphs they did not
feel were useful in representing data. Sample responses include:
 A histogram would be useful for data that need to be represented using
ranges/intervals. For example: the number of text messages sent in a given day
could range anywhere from 0 - 200. This data that is best displayed in ranges 010, 11-20 and so on.
 A dot plot is useful for sets of data with a compact range and a limited number of
unique results. For example: hours of sleep ranging from 5-10 where the results
are given to the nearest hour or half hour.
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Grade 6 Mathematics Seminar
Facilitator Notes – Week 3
Day 1: Student Data Display
1. Allow students to continue their work with organizing and displaying their data.
2. Circulate to monitor progress and ask guiding questions to make sure students are on
track.
Day 2: Skill Review Day
Instruction Note: If necessary, allow students time to finish data display.
Skill Review lessons are opportunities to offer targeted, differentiated support for students based
on their current understanding of content standards. Plan a differentiated lesson using strategies
that meet the needs of the class (strategic grouping, stations, two-group model, all pupil
response, etc.).
For ideas for creating and responding to formative assessment data, visit:
http://letthedatabeyourguide.wikispaces.com/
For differentiation strategies, visit:
http://daretodifferentiate.wikispaces.com/
http://media.hcpss.org/newcode/strategies/strategies.php
For ideas for teaching/re-teaching, use the following Moving with Math (MH1) Lesson:
Measures of Central Tendency (p. 55).
For ideas for teaching/re-teaching measures of central tendency, refer to:
 More Good Questions: Great Ways to Differentiate Secondary Mathematics
Instruction by Marian Small (p. 160, 176, 181).
 Good Questions: Great Ways to Differentiate Mathematics Instruction by Marian
Small (p. 161, 170, 175).
Vocabulary Review Activity: Below is a list of possible activities to help students review the
data analysis vocabulary from Week 2 and to reviewmean, median, mode, range, IQ range, and
absolute mean deviation.
 Ask students to line up according to how many siblings each student has. For
mode, ask the students to “stack themselves” like a dot plot if they have the same
number of siblings as someone else.
 Give each student a large amount of Katie Kubes and ask them to stack as many
as possible in 10 seconds.
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

Ask students to do as many jumping jacks as they can in 15 seconds. Give
students an equal number of paper clips and have them time each other for how
long it takes to link them together.
Using one of the data sets from above, determine an appropriate interval and ask
students to group themselves in corners of the room (This is a great way to show
how histogram data is grouped into ‘bins’). For example, say, “If you stacked
between 3 and 8 Katie Kubes, go to this corner of the room. From here you can
discuss whether a mode, range, median, or mean can be found or if they can only
approximate these measures.”
“I have, who has” Vocabulary Activity (This can be done on Day 3 as a Warm Up if time does
not permit this to be done as an exit ticket on Day 2. Consider doing it both days if possible).
Day 3: Finish Vocabulary Review, Begin Student Data Analysis
1. Complete the “I have, who has” Vocabulary Activity from Day 2 as a Warm Up.
2. Have students complete the Checkpoint Questions in order to guide them through
analyzing their data. They should use their graphs as well as the data they collected to
find each value. Collect and use information to plan for the next Skill Review Day.
Day 4: Student Data Analysis
1. Have students continue working on their data analysis checkpoint questions.
Day 5: Student data analysis/Debrief
1. Allow time for students to finish working on data analysis if necessary.
2. Strategically pair students to peer review each other’s work.
3. Discuss the data students analyzed.
 Did the results turn out the way they expected?
 Were any of the results surprising?
 How could this survey be improved?
4. At some point during this discussion, students should recognize that surveying a larger
group of people would allow the population to be better represented. Ask students to
plan a way to involve a larger group of students and determine a quick and efficient way
to collect the data. For example, each student could select 2-3 random teachers and ask
them to survey their 3rd period class. Each teacher would only receive one ballot and
students would quickly give their responses. The actual survey should take no more than
5 minutes of class time. (Note: Get participating teachers’ approval beforehand; ask
them to return results in two days.)
5. Have students create a ballot to give to teachers and describe the process of collecting
survey results.
6. Have students review the checkpoint questions they have answered so far. Explain that
by the end of next week they will be developing a presentation displaying the results of
both surveys, how the results compare to each other, and drawing a conclusion to their
original question. Ask students to create a checklist/rubric of the topics they should
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address during their presentation and how they will be assessed. For guidance, refer to
the bulleted list under Week 5, Day 1’s that list of the proposed objectives for the
presentation. If time does not allow, complete this sometime during Week 4.
7. Have students complete a brief pre-assessment on writing fractions as percents and
proportional relationships (6.RP.3 Standard).
Facilitator Notes – Week 4
Day 1: Skill Review Day: Review of Finding Percents and Making Predictions (6.RP.3)
Skill Review lessons are opportunities to offer targeted, differentiated support for students based
on their current understanding of content standards. Prior to this lesson, review the preassessment given on Week 3, Day 5 to determine the instructional needs of your students. Plan a
differentiated lesson using strategies that meet the needs of the class (strategic grouping, stations,
two-group model, all pupil response, etc.).
For ideas for creating and responding to formative assessment data, visit:
http://letthedatabeyourguide.wikispaces.com/
For differentiation strategies, visit:
http://daretodifferentiate.wikispaces.com/
http://media.hcpss.org/newcode/strategies/strategies.php
For ideas for teaching/re-teaching percents and proportional reasoning to Elementary and Middle
School Mathematics: Teaching Developmentally by John Van de Walle Pages 337-340 and 363364
For ideas for re-teaching proportional reasoning, use the following Teaching Student-Centered
Mathematics Grades 5-8 by John Van de Walle and LouAnn H. Lovin (p.169-176).
For ideas for teaching/re-teaching, use the following Moving with Math resources:
 Ratios and Percents Lesson Plan (MH4) (p. 27)
 Ratio and Proportions Lesson Plan (MH2) (p. 37-38)
 Estimating Reasonable Answers Lesson Plans (MH2) (p. 71-74)
Other Instructional Strategies:
1. Using the Fraction Circle in Hundredths activity sheet on p. 171 of Hands-On Standards
(grade 5-6), lead the students through completing the chart and the corresponding circle
graph to represent their results.
2. Extension 1:
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 How would the numerator change if you change the denominator assuming the
data is proportional?
 How would the circle graph change if the denominator and numerator change
proportionally?
3. Extension 2:
 Have the students complete a quick survey of their classmates (number of kids
wearing sneakers, their favorite class, etc.).
 Create a circle graph to represent this data in percentages.
 Discuss whether or not the students feel that their sample demographic represents
the school’s demographic as a whole.
 Is it reasonable to expect that the proportions that they found for their sample
would remain the same if we extended the same survey to the entire school?
 If so, what is the chance that if I randomly chose a student in the hallway, they
would (insert one of the categories from the survey the kids completed)?
Day 2: Find Percents from Dot Plots or Histograms and Make Predictions Based on a
Larger Sample
1. Using either their dot plots or their histograms, have students find the percent of the data
pieces that resulted in each value or range of values.
2. As a visual aid, consider having students use the hundreds disk (an example can be found
on the bottom of the page http://www.aimathtools.com/plastigraphs11.html) or create a
representation using an online circle grapher, which will allow them to check their
percentages for accuracy since they are calculated for them.
 http://illuminations.nctm.org/ActivityDetail.aspx?ID=204
 http://nlvm.usu.edu/en/nav/frames_asid_183_g_1_t_5.html?open=activities&hide
panel=true&from=vlibrary.html
3. Discuss whether or not the new sample represents the same population that the original
sample did. Why is it better to survey a larger sample?
4. Have students make predictions based on the number of people in the new survey (approx
25 students per class) Ask students to record the number of people they believe will
respond similarly to their survey during the second round of data collection. Compare
possible strategies and have students share their answers.
Day 3-5: Data Analysis and Display (Round 2)
1. Ask students to display and analyze this new data the same way they displayed and
analyzed the first. Consider having them decide whether a dot plot or a histogram would
be more reasonable to use. Require all students to create a box plot. Consider using
Excel to organize the data from least to greatest for them so they may focus on the more
important tasks.
2. Ask students to answer the analysis questions inCheckpoint Questions for this new set
of data. Collect and use information to plan for any additional skill review needed next
week.
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Grade 6 Mathematics Seminar
Facilitator Notes – Week 5
Day 1-3: Work on Presentations
1. In their presentations, students will:
 Describe their question and its importance
 Describe their data collection tool
 Display the results of the first survey and describe the results
 Display the results of the second survey and describe the results
 Discuss differences and similarities between the results of the two surveys
 Determine a possible conclusion based on the findings from the survey
2. The presentations can be in any format, but should be visual. Offer choices if possible.
Examples: Power Point, storyboard, iMovie, Flip Cam, etc. Consider allowing students
who are really committed to their cause to create a public service announcement for the
school news program. Remind students to consider their audience when designing their
presentations.
Days 4-5: Presentations and Debrief
1. Have groups take turns presenting their findings. Consider having audience members fill
out the rubric/checklist they developed during week 3 or 4 to keep them focused on the
presentations.
2. Discuss:
 Should we expect these results to hold true for all 6th graders at the school? All
students at our school? All students in Howard County? All students in Maryland?
etc.
 How far can you expect similar results to reach? Why?
 What questions should you be asking when you read or are told about the results
of a survey? For example, as an educated statistician what questions should you
ask when you are told that on average the U.S. home has its TV on for 7 hours
and 12 minutes a day (available at http://soundvision.com/Info/teens/stat.asp
adapted from BJK&E Media report, The New York Times, December 30, 1997)?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.