Chapter 11
Adrienne, Darrin & Katie
Gathering Data
• There should be a purpose to collecting data
o To answer questions
o Add information to our world
o Compare things or groups
• The data being collected should be of interest and meaning
to the collectors
• Data can be classified or sorted in different ways
• Data is gathered from a sample of the population
How to Gather Data
• Pose questions that have meaning to the students
o Favorites
o Numbers
o Measures
• What are some questions you can come up with that would
be good data gathering questions?
• Involve the students personally, as it is a great way for the
class to get to know each other better and for the students to
feel a sense of individuality
• Integrate the community into your data collection
How to Gather Data cont'd
• This is a great way to involve cross-curricular materials with
science and even social studies
o Do you have any ideas of how you can do this in your
classroom?
• Involve the students as much as possible when deciding on
the data to be gathered and the questions to be asked
• When there is an abundance of possible answers try and
limit the amount so analyzing and graphing the data will be
more valuable
What is the purpose for graphs?
A graph clearly shows you the data.
In class teachers should have the students create their own
graphs that help them see the information.
Informal approach: When the students collect their own data
and create the graphs the data is more meaningful for them.
*Just don't let students get caught in the details of the graph too
much.
Most Important part of constructing a
graph?
• The discussion that comes from the graph is the most
important part.
o Factual
o Inferences
• Have the students interact with different graphs in case they
struggle with a certain type and they can see how the
information is conveyed differently
Cluster graphs
• Here you classify items, or sort items into different
categories.
• This is more of a table than a graph
• Why is it good for kids to learn Cluster graphs/tables/charts?
http://jmathpage.com/JIMSStatisticspage.html (simple graphs)
Bar Graphs and Pictographs
• Bar graph is one of the 1st ways students learn to graph
data. Why do you think that is?
• There needs to be countable parts like squares or objects,
or tallies.
http://nlvm.usu.edu/en/nav/frames_asid_190_g_1_t_1.html
• Different types of Bar graphs:
1) Real graph: real objects
2)Pictograph:
K-3 http://www.mhschool.com/math/2003/student/
Continuous Data Graphs
• Line plots: great because they show you where every piece
of data is.
http://www.ixl.com/math/practice/grade-2-create-line-plots
• Histograms: Like a bar graph, but in equal intervals along
numeric scale. Book says it is not used because it confuses
kids. What scale should they use? Ex.
http://www.ixl.com/math/practice/grade-5-create-histograms
• Line graphs: "Used when there is a numeric value
associated with equally spaced points along a continuous
scale" (Lovin & Van de Walle).
http://www.mathgoodies.com/lessons/graphs/line.html
Which graph do you think is useful for the kids? Why?
Circle Graphs
• K-3 they use circle graphs which have data points, not
percentages.
• The circle graphs can show fractional ideas.
• Let's create a Human Pie Chart!
• What are you favorite Thanksgiving Dishes?
• Human Circle Graph Activity.
Graph changes for grades 3-5
• Bar graphs: become double bar graphs.
• Pictographs now represent more than 1. This starts slightly
in 2nd grade but more so in 3rd to 5th.
http://www.ixl.com/math/practice/grade-3-pictographs
• Continuous data Graphs: Book says histograms are still
skipped unles state standards requires teachers to cover
these graphs.
• Circle Graphs: In grades 3-5, these graphs still show
fractional ideas, but now they also show percentage.
http://nces.ed.gov/nceskids/createagraph/
More Graph Changes
• Also Coordinate Graph is introduced, slightly in 2nd grade
but more so during the 3rd-5th grades.
http://www.ixl.com/math/practice/grade-3-coordinate-graphs
Which of these graphs do you think, will help the kids?
• Stem and Leaf Plots: "A form of bar graph in which numeric
data are plotted by using actual numerals in data to form the
graph" (Lovin & Van de Walle p. 332).
• 2 Stem and Leaf plot
• Stem and Leaf plot activity
The Classification of Data
• Data Classification - The way in which data gets
categorized, an activity fundamental to data analysis
• Attribute Materials - Sets of objects that lend themselves to
being sorted and classified in different ways
o Unstructured
o Structured
• Classification Exercises
o (three-loop activity demonstration)
o ("guess my rule" class activity)
• For the early grades data classification lays the foundation
for later data analysis, and fosters logical reasoning
Data Analysis - Statistics
Statistics - numbers that describe data, and give insight to the
relevance of described data
• Mean, median and mode - all specific types of averages, or
measures of central tendency
o http://jmathpage.com/JIMSStatisticspage.html
o (Leveling the Bars Activity --- The Leveling Concept of
Mean)
o (Balance Point Demonstration --- The Balance Point
Concept of Mean)
• (bowling activity data gathering/sharing)
Data Analysis --- Bowling Activity
• Exploring the Data gathered during this activity
Mean --- Thought of as the "average" of a set of numbers
Median --- The middle-value in an ordered set of numbers
Mode --- The value that occurs most frequently in a set
Range ---The distance between the highest and lowest
data values in a set
o Variance --- How dispersed the data are within the range
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References
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Johnnie's Math Page. (2010). Sort the fruit. [Electronic graphing website]. Retrieved
from http://jmathpage.com/JIMSStatisticspage.html
IXL. (2010). 2nd grade math. [Electronic graphing website]. Retrieved from
http://www.ixl.com/math/practice/grade-2-create-line-plots
IXL. (2010). 3rd grade math. [Electronic graphing website]. Retrieved
from http://www.ixl.com/math/practice/grade-3-pictographs
IXL. (2010). 3rd grade math. [Electronic graphing website]. Retrieved from
http://www.ixl.com/math/practice/grade-3-coordinate-graphs
IXL. (2010). 5th grade math. [Electronic graphing website]. Retrieved from
http://www.ixl.com/math/practice/grade-5-create-histograms
Lovin, L. and Van De Walle, J. (2006) Teaching student-centered mathematics grades k-3. Boston:
Pearson.
Lovin, L. and Van De Walle, J. (2006) Teaching student-centered mathematics grades 3-5 Boston:
Pearson.
Macmillan-McGraw Hill. (2009). Math tool chest. [Electronic graphing website]. Retrieved from
http://www.mhschool.com/math/mathtoolchest/mtc_online/
Math goodies. (2010). Mrs. glosser's math goodies. [Electronic graphing website]. Retrieved from
http://www.mathgoodies.com/lessons/graphs/line.html
NCES. (n.d.). Create a Graph. [Electronic graphing website]. Retrieved from
http://nces.ed.gov/nceskids/createagraph/
NLVM. (2010). Bar chart-nlvm. [Electronic graphing website]. Retrieved from
http://nlvm.usu.edu/en/nav/frames_asid_190_g_1_t_1.html.
Johnnie's Math Page. (2010). Mean Runners. [Electronic graphing website]. Retrieved from
http://jmathpage.com/JIMSStatisticspage.html