Lesson Title:
Is a Sample Ample?
Designer:
Mary Beth Cook
Grade Level:
5
Big Idea:
Data Analysis and Probability
Essential Question: When is a sample better than counting?
How can you estimate the whole set without counting every
piece of a larger set?
Content Standards:
M.O.5.5.2
Students will construct, read, and interpret tables, charts,
and graphs including stem and leaf plots to draw reasonable
inferences or verify predictions.
M.O.5.1.6
Students will model and write equivalencies of fractions,
decimals, percents and ratios.
M.O.5.5.3
Students will collect and organize real-world data to
construct a circle graph (with and without technology),
present data and draw conclusions.
Learning Skills:
21C.O.5-8.3.LS.1
Student manages emotions and behaviors, engages in
collaborative work assignments requiring compromise, and
demonstrates flexibility by assuming different roles and
responsibilities within various team structures.
Technology Tools:
21C.O.5-8.1.TT.1 Student accesses server and/or network resources.
Vocabulary:
survey, data, sample, random, random sample, circle graph, percents, tally
marks, fractions, decimals, estimate, population, set (Vocabulary will be
reviewed and discussed during the lesson.)
Launch/Introduction:
15 min.
1. Post the essential question and draw students’ attention to it.
 Ask students to reflect about how they would answer this question.
 Tell them they will discuss their responses at the end of the class.
2. Post the target vocabulary words and read them with the class.
 Activate prior knowledge by asking students to explain what they
know about each word and how they have previously used the
word.
3. Pose this situation to the class.
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Taking a random sample of a large population is one way to get
important information when time, money and other factors do not allow
for every single person to be surveyed.
Tell students that today they will practice taking a random sample of a
larger population or set, but not from people, from…confetti! (toss a
small amount of confetti in the air)
4. Using a document camera and LCD projector (or overhead) show a
sample of each shape/design in the confetti.
 Tell students these are sample confetti pieces from a larger bag
with thousands of pieces and a variety of shapes. Have students
identify and name each shape. (see Teacher Notes).
5. Challenge students with a brief discussion:
 A survey could be conducted to find out about how many there are
of each shape, but it would be time consuming to sort and count
every piece. What could we do to get a reasonable idea of about
how many of each shape are in the bag? (take a random sample)
 How can we organize and present the data from the sample so it is
easy to read and interpret? (tally chart, bar graph, circle graph)
 How can we compare data sets of different sizes? (percents, circle
graphs)
 How do we know if our sample accurately reflects the composition
of the whole data set?
Investigate/Explore
30-40 min.
1. Students work in assigned pairs to complete the investigation activity.
Each pair will:
 Choose a reasonable method for taking the random sample
(i.e. take a large pinch of confetti from the bag or randomly
divide the contents into several piles and use one pile, etc.)
 Sort the confetti pieces into like piles by shape attributes.
 Count the pieces of confetti in each shape sorted pile.
 Organize and record the data on the Is a Sample Ample?
recording sheet.
 Convert the raw data to fractions, decimals and percents in
order to construct and label a circle graph.
2. Students organize their data sets into a circle graph using a template and
colored pencils, or a web based data program, i.e.
http://nces.ed.gov/nceskids/createagraph/
3. As pairs complete the activity they post their graphic organizers in a
prepared space (front chalkboard or marker board).
4. Students will combine the results of the smaller data sets into
a larger class chart. This visual will be helpful as students reflect and
respond to the Essential Question during the Summarize/Debrief portion
of the lesson, i.e. the larger the sample size, the more likely it is to reflect
the composition of the whole set.
Summarize/Debrief the Lesson:
30-35 min.
1. Gather students for lesson closure. Use questions and discussion to
assess students’ understanding.
 What method did you use to gather your sample and why?
 Was your random sample representative of the larger set?
How do you know?
 Did the method you used to take the sample significantly affect
the results? Explain.
 Did your sample size affect the accuracy of your prediction
about the larger set? Explain.
 How could/would a bias affect a random sample?
 How did you decide to collect and organize your data results?
 How does your random sample reflect the “whole” or population
we used to begin the survey?
2. Refer back to the Essential Question. Discuss students’ reflections.
Materials for each pair of students:
 ½ oz. packets of party/seasonal confetti placed in zip lock baggies
OR
 each student pair may scoop a small sample from a larger container
which represents the “whole” or survey population
 clipboards, circle graph template, graph paper, pencils, colored pencils
 computer and printer
Teacher Notes
 I used large seasonal or party theme confetti pieces with shapes that are
easy to recognize, sort and handle.
 It is important for the students to see the “whole” or confetti population in
one place before they take their random sample, i.e. in a jar or bowl.
 I assigned student partners/pairs for this activity.
 You could choose to extend the lesson by guiding students to
compare, contrast and analyze the results of the posted data sets and ask
questions like:
o What conclusions can we draw by comparing each of the data
sets?
o What conclusions can we draw by contrasting each of the data
sets?
 If the target vocabulary words are unfamiliar, pre-assign students to look
up words in a math glossary or student dictionary and share them with the
class.
 During the investigation part of the lesson I rotated in the classroom
observing student work, questioning processes and guiding pairs to check
their work for reasonableness and accuracy.
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It was helpful and important for my students to have ground rules for using
the confetti during the student Explore Activity. The confetti was to be a
tool, not a toy.
My students have had prior experience using tally charts and other
graphic sources referred to in the lesson. If your students have not, that
would be an important prerequisite skill.
There are two versions of the recording sheet. The first one can be printed
for students to use. The second one has some formatting and formulas
built in, so that students can enter data on the spreadsheet and the
numbers will be converted to fractions, decimals, and percents
automatically. This is meant to be an introduction to some of the things a
spreadsheet can do. Students are not expected to master using the format
and formula features at this time.
If students are using Excel to enter the data, they can display their data as
a circle graph showing percents. Sample data and a sample circle graph
are included with the Is a Sample Ample? worksheet.