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Home Up Scale and Mapping Invasion rates Quadrat sampling Graphing 1 Graphing 2

Effective Graphing:  Using Graphs to Present Data (Part 2)

 Grade Level: 6-8Cartoon showing coloured 3D pie chart

Time Frame: 40-45 minutes

Subject:  Math

Introduction to Lesson:  Almost all scientific and technical reports, as well as more "mainstream" media like newspapers and magazines, contain tables and figures. The purpose of these tables and figures is to display data and illustrate ideas and concepts in an organized fashion, so that it is easier for others to understand. There are many different types of graphs. Depending on the nature of the data, some graphs are more appropriate than others.  Knowing the appropriate type of graph to use to illustrate a given data set is a crucial skill that students need to master.  This and the subsequent lesson in the sequence will work with students to review / learn how to pick the appropriate kind of graph to display different kinds of data sets.  Students then will practice creating different kinds of graphs using the data on the Phragmites  invasion that they’ve collected in previous classes.

New Jersey Core Curriculum Content Standards

STANDARD 4.1 (Number and numerical operations) All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.

A. Number Sense

·          Use real-life experiences, physical materials, and technology to construct meanings for numbers 

·          Explore the use of ratios and proportions in a variety of situations.

C.  Estimation

·          Use a variety of strategies for estimating both quantities and the results of computations.

·          Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.

·          Determine the reasonableness of an answer by estimating the result of operations.

·          Determine whether a given estimate is an overestimate or an underestimate.

STANDARD 4.2 (Geometry and measurement) All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

D. Units of Measurement

·          Use measurements and estimates to describe and compare phenomena

E. Measuring Geometric Objects

·          Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot).

STANDARD 4.3 (Patterns and algebra) All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

C. Modeling

·          Draw freehand sketches of graphs that model real phenomena and use such graphs to predict and interpret events.

·          Changes over time

·          Relations between quantities

·          Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)

STANDARD 4.4 (Data analysis, probability, and discrete mathematics) All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.

A. Data Analysis (or Statistics)

·          Collect, generate, organize, and display data.

·          Read, interpret, select, construct, analyze, generate questions about, and draw inferences from displays of data.

o        Bar graph, line graph, circle graph, table, histogram

o         Range, median, and mean

o        Calculators and computers used to record and process information

·          Respond to questions about data, generate their own questions and hypotheses, and formulate strategies for answering their questions and testing their hypotheses.

STANDARD 3.1 (Reading) All students will understand and apply the knowledge of sounds, letters, and words in written English to become independent and fluent readers, and will read a variety of materials and texts with fluency and comprehension.

A. Concepts About Print/Text

·          Use a … glossary independently and appropriately.

C. Decoding and Word Recognition

·          Apply knowledge of new words correctly

STANDARD 1.2 (Creation and Performance) All students will utilize those skills, media, methods, and technologies appropriate to each art form in the creation, performance, and presentation of dance, music, theater, and visual art.

D. Visual Art

·          Individually or collaboratively create two and three-dimensional works of art employing the elements and principles of art.

·          Recognize and use various media and materials to create different works of art.

Objectives:  

bulletStudents will continue to practice their graphing skills through creation of a variety of different graphs based on the results of exercises in previous lessons
bulletStudents will practice interpreting patterns displayed in the graphs that they create.

Materials and Resources:

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Data from previous classes

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Worksheet

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Computers running excel or similar software, or graph paper, rulers and pencils (if bar charts are to be made by hand) and compasses and protractors (if pie charts are to be made by hand)

Sequence Instruction:

1.      You have been asked to graph changes in number of types of species (biodiversity) of over time. What will be the X variable and what will be the Y variable in each of these graphs?  Why?

2.      What is the nature of the X axis variable? (i.e. is it discrete or continuous?)

3.      Are you trying to show a trends or a relationship?

4.      What does that mean for the type of graph that you need to use to represent this data correctly?

5.      Create those graphs using the data that you calculated in the quadrat exercise (Q15).  Be sure to label the axes appropriately and to give your graph a good title.

6.      You have been asked to graph changes in mean abundance of the four most common native species over time. What will be the X variable and what will be the Y variable in each of these graphs?  Why?

7.      What is the nature of the X axis variable? (i.e. is it discrete or continuous?)

8.      Are you trying to show a trends or a relationship?

9.      What does that mean for the type of graph that you need to use to represent this data correctly?

10.  Create those graphs using the data that you calculated in the quadrat exercise (Q18).  Be sure to label the axes appropriately and to give your graph a good title.

11.  You also want to graph changes in mean abundance of Phragmites in the model marsh over time. What will be the X variable and what will be the Y variable in each of these graphs?  Why?

12.  Create a graph using the data that you calculated in the quadrat exercise (Q18).  Be sure to label the axes appropriately and to give your graph a good title.

13.  You suspect that there’s a relationship between average Phragmites densities and the average biodiversity found within a marsh.  When making this sort of graph, the variable that you think is CAUSING an effect goes on the X axis, and the values for whatever is responding to that variable are plotted on the Y axis.  What does that mean for which variable should be the X and what should be the Y in this case?

14.  What is the nature of the X axis variable? (i.e. is it discrete or continuous?)

15.  Are you trying to show a trends or a relationship?

16.  What does that mean for the type of graph that you need to use to represent this data correctly?

17.  Fill in the following table using the data that you calculated in the quadrat exercise

 

Average Density of Invasive Phragmites

Average biodiversity in quadrats within the marsh

Time 1

 

 

Time 2

 

 

Time 3

 

 

Time 4

 

 

18.        Use the data from the table to create the graph.  Be sure to label the axes appropriately and to give your graph a good title.

19.        Does it seem like there’s a relationship between the density of invasive Phragmites and the biodiversity in the marsh?  If so, is it a positive relationship (the more invasive Phragmites there is, more the biodiversity in the marsh) or is it negative?

20.         You want to know if there is there a relationship between the density of invasive Phragmites and the density of one or more of the native species in the marsh.

21.         The teacher will assign you a species from the marsh.  Tabulate the data you will need for your graph in the table below

 

Average Density of Invasive  Phragmites

Average density of assigned  species (fill in its name below) in quadrats within the marsh

(__________________________________________________)

Time 1

 

 

Time 2

 

 

Time 3

 

 

Time 4

 

 

 

22.  Create a graph showing the relationship between the density of invasive Phragmites and that of your assigned species using the data from your table.  Be sure to label the axes appropriately and to give your graph a good title.

23.  Does it seem like there’s a relationship between the density of Phragmites and the density of your assigned species in the marsh?  If so, is it a positive relationship (the more Phragmites there is, more the abundant it is in the marsh) or is it negative?

 

Accommodations and Modification:                                                                        

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Group students into groups such that each has a mix of students with different learning styles and strengths.

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 Provide students with visual impairment with alternative visual media (printouts of PowerPoint slides) to allow them to participate in the games

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If needed, pair students so that one student can read directions orally to another

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If needed, provide written instructions / closed captioning for students who are hard of hearing.

Assessment / Homework / Anchor Activity (if lesson goes shorter than planned)

Provide students with additional data sets and ask them

  1. What is the appropriate graph format for data of that type and why?
  2. Create the graph for each data set using the format that you’ve identified.

Closure   

Have students complete any two of the following to write about

bulletThe most interesting thing I learned about making graphs today was….
bulletWhat I learned about the effect of Phragmites on other species in a marsh from the graphs I made in this class was….
bulletOne thing I learned today that I never knew before was….
bulletI would still like to know more about…
bulletI am still confused about…
bulletThis lesson was valuable because…
 

If there’s time, go around the room and ask each student to share one of their answers with the group.

 

TEACHER FEEDBACK REQUEST:  We are always to working to improve these lesson plans. If you use this lesson plan, we'd love to hear from you with your thoughts, comments and suggestions for future improvements.  Please take the time to fill in our survey at http://www.zoomerang.com/Survey/?p=WEB229JA3BEWBD .  Thanks!

 

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© 2009. Louise Wootton  Edited by Claire Gallagher

 Although the information in this document has been funded wholly or in part by the United States Environmental Protection Agency under assistance agreement NE97262206  to Georgian Court   University, it has not gone through the Agency's publications review process and, therefore, may not necessarily reflect the views of the Agency and no official endorsement should be inferred.

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