Graphing Made Easy - Author: Bette Rintrona - MST 3-Students will represent numerical relationships in one- and two-dimensional graphs. Students will apply reasoning strategies and justify conclusions involving simple and/or compound statements.

LEARNING EXPERIENCE
Graphing Made Easy

Learning Experience: Graphing Made Easy

Author: Bette Rintrona

School District: Town of Webb

LEARNING CONTEXT

MST 3-Students will represent numerical relationships in one- and two-dimensional graphs. Students will apply reasoning strategies and justify conclusions involving simple and/or compound statements.

This experience will fit into the 5^th, 6^th, or 7^th grade mathematics curriculum with minor adjustments. It would be a beneficial exercise to be used in conjunction with science lessons, also.

Students should have some exposure to line, bar, picto, and circle graphs. They should be familiar with the vocabulary that is needed to discuss construction and interpretation of these graphs.

PROCEDURE

This experience is set up to help students learn the appropriate way to construct and analyze bar, line, picto, and circle graphs. They will also learn to set up frequency tables and perform some statistical analysis (mean, median, and mode) on their data. The classroom teacher has transparent flow sheets for the above graphs, frequency tables, and statistical activities that she will place on the overhead. Each student will have matching copies to work with at his desk. The teacher will proceed through the steps given on each flow sheet and then demonstrate how to graph or tabulate a specific problem on the graph below the flow sheet. The students will copy these examples on their sheets, making notes and pertinent remarks. The teacher may elect to have students come to the overhead to help construct the graphs. Each student will then save his completed graphs and tables in a folder for later reference and further independent use. The teacher will spend some time discussing the situations that each graph would be most appropriate for. The teacher will also guide the students when drawing conclusions from the data that has been graphed.

INSTRUCTIONAL/ENVIRONMENTAL MODIFICATIONS

Resource room students will have modifications according to their IEPs. Remedial math students will receive help from the Title I teacher.

MATERIALS AND SUPPLIES

Students will need a folder, straight edge, colored and regular pencils, and copies of all flow sheets that the classroom teacher uses on the overhead. The teacher will need a source of problems appropriate for each type of graph and overhead copies of all flow sheets. The teacher will also need overhead markers to demonstrate the graphs.

ASSESSMENT TOOLS AND TECHNIQUES

Assessment will take place by the teacher watching students independently reproduce the various graphs with new data. Students will have rubrics to guide them in their construction and analysis of the graphs. They will be able to refer to flow sheets for added guidance. Class discussion will allow the teacher to verify the students’ analysis of the information that they graph.

TIME REQUIRED

Planning time: 45 minutes to gather appropriate graphing questions and make keys of all graphs and tables to be presented.

Implementation: 3-4 hours divided into sessions of 45 minutes each. The first two sessions are for frequency table, line, and bar graph. The last sessions are for picto, circle, and statistics.

Assessment: 1-2 hours watching students producing the six different products.

STUDENT WORK

This experience will be taught in the 1999/2000 school year.

REFLECTION

The various types of graphs give exposure to several graphing forms which should help meet the different needs that students may have.
The fact that each student will produce and keep for reference a well organized, quality example of many graphs will aid them in a better understanding of graphic representation.
A thorough understanding of graphing will transfer well to success with graphs in areas such as science and social studies.
This is a well-organized activity for both teacher and students. It gives reinforcement by covering several different graphs, and it allows for carry over by gathering all materials in a folder for future reference.

Rubric: Steps for making and interpreting a circle graph

	Element #1	Element #2	Element #3	Element #4
Elements Scale	Gathering and Organizing Data	Displays Data on Graphs	Reads Information from Graph	Interprets Graphing Information
Weights
4	Student can thoroughly organize data in a frequency table and then convert information to percentiles.	Student is able to transfer percentiles to accurate approximations of sections on a circle graph.	Student is able to consistently read information from a circle graph.	Student shows strength and insight in analyzing and interpreting graphing information.
3	Student organizes data in frequency table but makes 1 or 2 errors converting data to percentiles.	Student is able to transfer percentiles to close approximations of sections on a circle graph.	Student can read data off the graph, making minor errors.	Student is able to analyze and interpret graphing information with only 1 or 2 errors.
2	Student is not accurately converting information from frequency tables to percentiles.	Student’s data does not closely match the sections on a circle graph.	Student makes several errors about graphing information.	Student’s conclusions often are not valid, based on the data given.
1	Percentiles do not reflect information from the frequency tables.	Student makes a poor match of data to the sections of circle graph.	Student’s conclusions are not correct about the data on the graph.	Student’s conclusions are incorrect based on the data given.

Rubric: Steps for making and interpreting a line, bar, or pictograph

	Element #1	Element #2	Element #3	Element #4
Elements Scale	Gather and Organize Data	Displays Data on Graphs	Reads Information from Graphs	Interprets Graphing Information
Weights
4	Student has a thorough understanding of constructing a frequency table and accurately records all data by tally marks	Graph contains all the following elements: title, horizontal axis, vertical axis, labels, scale, equal units, and points, lines, pictures, and bars as appropriate	Student is able to consistently read information from graph even when non-standard cases are given	Shows strength and insight in analyzing and interpreting graphic data
3	Student understands how to construct a frequency table and makes one or two errors	Graph contains all but one or two of the criteria. There are only minor errors in its construction.	Student can read data off most graphs, but has some difficulty with nonstandard values.	Student is able to analyze and interpret graphs making only minor errors in analysis.
2	Student does not completely understand how to construct a frequency table and makes 3 or more errors	Graph is missing 3 or more of the criteria needed. There are several errors in construction	Student makes 1 or 2 errors reading information, even in standard cases.	Student does not truly understand how to interpret his graphs and makes some poor conclusions
1	Student attempts to construct a frequency table but does so incorrectly	Graph was attempted but contained many errors in format and construction	Student does not take information from the graph correctly	Student incorrectly analyzes information

Flow Chart For
Constructing a Bar Graph

* Main use to compare data visually
* Be extremely neat as this is a visual
tool for others to see.


			Decide on a Title

	Label Vertical Axis			Label Horizontal Axis

	Look at range of data

	Create a vertical scale			Choose horizontal spaces
	and place numbers			and place units on
	on graph			graph


		Create vertical bars by transferring
		data to your graph

		Analyze your graph and draw conclusions

Flow Chart For
Constructing a Line Graph

* Main use to show changes
over time


			Decide on a Title

	Label Vertical Axis			Label Horizontal Axis

	Look at range of data

	Create vertical scale			Create even
				horizontal spaces


		Place dots at the intersection
		of horizontal & vertical data
		Connect dots to form a line graph

		Analyze your graph and draw conclusions

Flow Chart For
Constructing a Pictograph

* Good for showing a visual
picture


			Choose a Title

	Place labels on the			Choose a key
	vertical axis			(a picture to represent your data)

	Look at data for			Place your key at
	each category			the bottom of the graph

	Draw the correct			Tell how much
	number of pictures			each picture is
	for each category			worth


		Draw conclusions about your graph

Flow Chart For
Making a Circle Graph

* Good for showing decimals
or percents that total 100%


			Establish Categories

	Find amount			Find total for
	in each category			all categories


		Express each group as a fraction of the total


			Number in category
			Number in total


		Change fraction to decimal
			(Divide top by bottom)


		Estimate size of the decimal


		Label each section with category and decimal


		Give your graph a title


		Interpret your graph and draw conclusions

Flow Chart For

Finding Statistical Averages

Mean

Median

Mode

(Average)

(Central Number)

(Most Frequent Number)

Add Numbers

Put numbers in order

Find the value that occurs

from least to greatest

most often

Divide by the

Find the middle

number of values

number

If there is no middle

number, add the "2"

middle number and

divide by 2

Example:

Test scores for the last quarter math tests were:

70, 80, 80, 90, 80, 60

Find:

Mean

Median

Mode

Range

* Range - difference between highest and lowest values

* Mean - the hardest to find (the mean teacher made me find an average)

* Median - This has the same name as "median" - central grassy section on large highways

* Mode - Sounds like "most"