3 Graph Literacy Lessons



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3 Graph Literacy Lessons
This module contains four lessons that can be taught independently or as a unit. The lessons are intended to help students analyze and explain graphs and are not intended to help students make their own graphs.
Resource Page Review and background information and sources for the teacher.
Lesson 1Using Graphs to Inferring Relationships between Variables
Goal: To infer the relationships between variables by analyzing the slope of a graph.
Lesson 2 - Common Mistakes or Intentional Distortions in Graphs
Goal: To compare and contrast graphs in order to identify graphs that have errors and have been distorted in order to misrepresent the relationship between variables.
Lesson 3 - Interpreting a Graph and Writing a Narrative Summary
Goal: To locate, read and interpret data from a line graph, bar graph or pie chart; identify pattern; deduce relationships and formulate generalizations. To form a logical argument that is supported by the graph or chart and to clearly and concisely express it in their written conclusion.

Background – Graphs are increasingly being used in written communication and oral presentations and writers and speakers expect readers to understand them. Fundamental to comprehending or reading graphs is knowing the different parts of a graph and what they can tell you. In the following lessons we will teach you how to read and explain a line graph, pie chart and bar graph. We will also show you how to identify common mistakes or distortions that are made when graphing that can lead to misunderstanding of the data.


Resource Page

Review and background information and sources for the teacher
Parts of a Graph


  1. title

  2. x-axis label

  3. x-axis units

  4. y-axis label

  5. y-axis units

  6. trend

  7. scale of x-axis

  8. scale of y-axis

  9. line label

  10. source





Each type of graph has characteristics that make it useful in certain situations.


Line graphs are used as a way of communicating the relationship between two variables over time. The vertical axis should be the dependent variable (recorded numerically) and the horizontal axis should be time.




Scatter plots which require a line of best fit between separate points in order to find the correlation between the two variables should not be confused with line graphs. The graphs can look very similar because of the line between points.




Bar graphs are used to compare products, populations or trials in one area of interest. The horizontal axis is a list of constants, and the vertical axis is the dependant variable which is recorded numerically.





Pie charts are best used for comparing the parts to the whole. They parts are often shown as percentages of the whole and should add up to 100%. Multiple pie charts can be used to compare populations to each other.


Sources for Reviewing Types of Graphs and Their Parts and Uses
Parts of the bar graph

http://cstl.syr.edu/fipse/tabbar/revbar/revbar.htm
Parts of a line graph

http://www.kipbs.org/new_kipbs/fsi/Files/GraphingTips.pdf
Understanding pie charts

http://eagereyes.org/techniques/pie-charts

Lesson 1 - Using Graphs to Infer Relationships between Variables

Goal: To infer the relationships between variables by analyzing the slope of a graph.
Background:
In addition to drawing graphs, it is also important that you be able to interpret data that is represented in graph form. The following activity is designed to help you develop the ability to read information shown on a graph.
Activity:


  1. For each group of students copy and cut apart the following page of graphs and their descriptions.




  1. Have students match the graph to its description.



  1. Show students the key after most of the class is done and then have them draw a series of graphs on the blank page that tell a story. Note the following example.


Identify the graph that matches each of the following stories:



  1. I had just left home when I realized I had forgotten my books so I went back to pick them up.




  1. Things went fine until I had a flat tire.




  1. I started out calmly, but sped up when I realized I was going to be late.


Graphs

Stories


This graph compares the amount of time students spend in front of an electronic screen to the amount of sleep they get.




This graph compares the population growth in Europe from 400 BC to 2000 AD (remember the Black Plague).





This graph compares locker number to grades.





This graph compares height to age in years.


This graph shows the distribution of height in a population.





This graph compares percent body fat to weight.





Graphs

Stories



































Lesson 2 - Common Mistakes or Intentional Distortions in Graphs

Goal: To compare and contrast graphs in order to identify graphs that have errors and have been distorted in order to misrepresent the relationship between variables.

Common Mistakes or Intentional Distortions in Graphs

  1. No title on graph

  2. Axis or parts are not labeled
  3. Units are not included


  4. Source of data not given

  5. Lines not identified on a multiple line graph

  6. No scale is indicated

  7. Scales are interrupted without notation

  8. Scales are not uniform - Numbers on either axis are not equally spaced

  9. Scale is selected to produce desired result

  10. Pie chart does not add up to whole (100%)

Activity:
Next to each graph list the numbers of the mistakes (above) that correspond to the errors you see in the graph or chart. See example below.



Errors
1; 3; 4; 10;

Errors ______________________ Errors _____________________


Compare and contrast the above graphs.

Errors
______________________



Lesson 3 - Interpreting a Graph and Writing a Narrative Summary
Goal:
The student is able to locate, read and interpret data from a line graph, bar graph or pie chart; identify pattern; deduce relationships and formulate generalizations.

The student is able to form a logical argument that is supported by the graph or chart and to clearly and concisely express it in their written conclusion.

Instructions:
Review the following graphs and fill in the blanks.

Use the information you have recorded to write a short summary of what is being shown by the graph, and what you think is important to notice about the information.



Remember, all statements must be supported by the data on the graph.


Subject of the graph _______________________________________________________________________

x – axis variable _________________________ y – axis variable and units _________________________

Highest bar _______________________________ Lowest bar _____________________________________

Range of the data ______________________________________ Source of data _______________________

Are there any patterns? ______________________________________________________________________

Summary of the graph ______________________________________________________________________

__________________________________________________________________________________________________________________________________________________________________________________

_________________________________________________________________________________________


____________________________________________________________________________

Main Subject ___________________________________________

What is the source of the data? _____________________________ Do the parts add up to 100% of the whole? ___________________

Which part of the chart is the largest? _______________________

Is there a significant difference between the parts? _____________

______________________________________________________

How do the parts compare to the whole? _____________________

______________________________________________________

What do you think is the most important information the chart shows? _______________________________________________

Write a short summary about the information in the chart and what might be important about how the parts compare to each other and the whole? ______________________

_____________________________________________________________________________________

__________________________________________________________________________________________________________________________________________________________________________

Subject of the graph _________________________

Source of data ______________________________

x – axis variable and units _____________________

y – axis variable and units _____________________

Highest data point ___________________________

Lowest data point ____________________________

Range of the data ____________________________


Trend of the line _______________________________________________________________________

Relationship of the two variables _________________________________________________________

Summary of the graph ___________________________________________________________________

______________________________________________________________________________________

______________________________________________________________________________________

______________________________________________________________________________________



Graph Summary Scoring Guide






Insufficient

Limited

Proficient

Excellent

Data Selection

Student does not understand the concept of data selection.

Data selection is haphazard and inappropriate to the task.

Data selection is almost always appropriate for analysis.


Student consistently selects appropriate and best data for reading and interpretation.

Graph Interpretation and Summary

Supportable patterns and relationships in the data are not identified. Illogical conclusions or generalization are drawn from the data.

There are many errors in reading and interpreting data. Ability to detect patterns and relationships in the data is limited,

Incomplete or incorrect conclusions are drawn from the graph, and a limitation of the data is not noted.



There are occasional and isolated errors may occur in the interpretation of the graph. Awareness of pattern and relationship within the data set is noted but not clearly written. Conclusions are less perceptive and awareness of the limitations of the data is unclear.

The analysis of graph is complete and precise with respect to labeling and scaling axis. Student recognizes patterns and relationships within data and clearly describes them in their writing. Supportable conclusions are drawn while recognizing that there are limitations to the data.


Clarity of Communication

Student did not express their understanding of the data in coherent manner.

Student’s ability to express their understanding of the graph is limited and their written interpretation includes many errors.

Student’s presentation is less focused and organized and their understanding is less clear. Their written interpretation is poorly edited and contains a few errors in writing conventions and/or vocabulary.

Student clearly and fully articulates their understanding of the data, including patterns, relationships and generalizations drawn from the data. Math terms are correctly used and language is clear and concise. Writing conventions are correct in written interpretation.

Notes to student:






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