Georgian Court University 

Effective Graphing: Using Graphs to Present Data (Part 2)Grade Level: 68 Time Frame: 4045 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 reallife 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. · 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 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 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 threedimensional works of art employing the elements and principles of art. · Recognize and use various media and materials to create different works of art. Objectives:
Materials and Resources:
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
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
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:
Assessment / Homework / Anchor Activity (if lesson goes shorter than planned) Provide students with additional data sets and ask them
Closure Have students complete any two of the following to write about
If there’s time, go around the room and ask each student to share one of their answers with the group.
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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.
