1.
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Can my students determine what
data is necessary to answer a question and how to gather that
data? Can my students
ask relevant questions about the data?
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Example Grade K-3:
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The
questions posed for or by young children should come from their
interest in their immediate environment.
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III-1.1, 3.5
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Do
more children in our room wear shoes that tie or shoes that fasten
with velcro?
How
do the children in our class get to school?
How
many people are in your family?
Do
you live in a house, an apartment, or a mobile home?
What
kind of pet do you have?
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After
the data have been gathered, organized, and displayed, various
questions can be asked that help the children focus on the
relationships revealed by the graph, chart, or table.
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Descriptive
questions
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How
many children have dogs?
How
many children have goldfish?
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Comparative
questions
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Are
there more children who have dogs or more children who have cats?
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It
is important to get children thinking beyond the specific
information presented on the graph to other ideas or implications.
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We
did a graph last week to answer the question, “Do you live in a
house, an apartment, or a mobile home?”
Does that have anything to do with whether or not you have
a pet or what type of pet you own?
Do the people who have goldfish live in a house or an
apartment? Do more
people who live in houses have dogs than people who live in
apartments?
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Example Grade 3-4:
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How
many of you were born in Michigan?
If you were born in this state, is it likely that your
parents were too? What
about your grandparents? Would
the same be true if we asked students from another state?
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III-1.1, 2.5
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Example Grade 5-6:
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Students
can find answers to complex questions such as, “Do we need a
safety patrol in front of our school?”
by asking many related questions:
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III-1.1, 3.5
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What
percentage of our students walk to school?
How
many come on the bus?
How
many come in cars?
Are
there certain periods of time when the traffic is heaviest?
Have
there been any accidents or near accidents?
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Example Grade 7-8:
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Consider
the question “What is the best brand of ice cream?”
What does the term “best” mean? Does it mean best
according to the opinion of the class?
Or does it mean best selling in the town? Or the best deal
for the money? Or
best for your health in terms of being lowest in cholesterol?
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III-1.1, 2.5
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2.
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Do my students know how to
gather data about a population by using a representative sample?
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Example Grade K-3:
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Can
you tell what is in this bag if you don’t get to look inside and
see everything in it? What
if you could reach in and pull a few things out?
Can you tell what is in the bag if you reached in several
times and each time pulled out a red crayon?
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III-2.5
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Example Grade 3-4:
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How
many pages in a book need to be analyzed to determine the average
number of words per page in the book?
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III-2.5
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Example Grade 5-6:
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What
if I only have time to interview five fifth graders about their
favorite food? What
is a fair way to insure that everyone has an equal opportunity to
be interviewed?
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III-2.5
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Example Grade 7-8:
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Would
a sample be adequate for ordering class T-shirts of different
sizes? Would a sample be adequate for ordering the kinds of pizza
for a class picnic?
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III-2.5
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3.
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Can my students collect,
organize, summarize, and display data using different formats?
(Including mean, median, range, stem-and-leaf graphs, box and
whisker plots, and dot plots.)
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Example Grade K-3:
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The
data gathered in response to the question “What pets do we
have?”, can be displayed in the following ways.
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III-1.3
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What
kind of information do you get from the first graph that is not
available from the second graph?
What information is more obvious from the second graph?
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Example Grade 3-4:
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The
data gathered in response to the question “What pets do we
have?” Can be displayed in the following ways.
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III-1.3
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What
kind of information do you get from the first graph that is not
available from the second graph?
What information is more obvious from the second graph?
Display the data in a bar graph.
How else can the data be displayed?
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Example Grade 5-6:
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In
response to the question, “How long does it take you to get to
school?” the
children in the class reported times ranging from
six minutes to one hour and four minutes.
The teacher displayed the information on a frequency table:
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III-1.3
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1
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11
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1
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21
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31
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41
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51
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61
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2
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12
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22
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1
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32
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1
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42
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52
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62
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3
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13
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1
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23
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1
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33
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43
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53
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63
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4
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14
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1
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24
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34
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1
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44
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54
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64
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1
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5
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15
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3
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25
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2
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35
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45
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1
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55
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65
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6
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1
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16
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26
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36
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46
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56
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66
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7
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17
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1
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27
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1
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37
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1
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47
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57
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67
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8
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1
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18
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1
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28
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1
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38
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1
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48
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58
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68
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9
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19
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29
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1
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39
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1
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49
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59
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69
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10
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20
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30
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40
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50
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1
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60
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70
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How
can we display this information so that we can easily see about
how long most students take to get to school?
How big should the intervals be?
How would the information look if we used five minute
intervals? Ten minute intervals?
Thirty minute intervals?
Which would produce a flat graph?
Which would show best
where the most common times cluster together?
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After
the graph has been constructed, students should be able to answer
the following questions.
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What
is the most common time (the mode) that it takes students in our
class to get to school?
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If
we added up all the times and divided them by number of students,
we could find the average time (the mean) it takes students in our
class to get to school. How
does that time compare to the most common time?
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