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### Chapter 11

Adrienne, Darrin & Katie

Gathering Data

- There should be a purpose to collecting data
- To answer questions
- Add information to our world
- 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
- Favorites
- Numbers
- 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
- 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.
- Factual
- 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
- Unstructured
- Structured

- Classification Exercises
- (three-loop activity demonstration)
- ("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
- http://jmathpage.com/JIMSStatisticspage.html
- (Leveling the Bars Activity --- The Leveling Concept of Mean)
- (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
- Variance --- How dispersed the data are within the range

References

- 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

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