##
* *Reflection: Real World Applications
SKILL BUILDER: How to Make a Graph - Section 1: Introduction

I've included here three examples of student graphs to better explain why I'm teaching an elementary math standard in an upper grades high school class.

The first graph was actually what motivated me to stop and devote a whole lesson to graphing. The student seems to understand the basics of graphing, but with little care to whether their graph actually *communicates* anything. It is sloppy and seems to be in service to the requirements of the assignment, not towards developing a deeper understanding of the data they'd collected.

The second graph is a little better, but aesthetically leaves a lot to be desired. I don't like that there's no real visual differentiation between the different "fish" species or the different rounds of the contest. Also, it is a poor use of space as more than half of the paper is left blank, crowding all the data together in the bottom half of the page.

Finally, the last graph was completed after the lesson. It's not the world's best graph, but it does have a few things going for it:

1. It's neat and makes good use of space.

2. The units are consistent.

3. the different colors clearly differentiate the two things being compared.

Again, it's not shockingly great, but it does do the basic job of representing quantitative information visually which, in turn, should help students observe patterns and make sense of the data.

*Real World Applications: Why spend time teaching graphs?*

# SKILL BUILDER: How to Make a Graph

Lesson 17 of 17

## Objective: Students will be able to make simple, clear graphs at appropriate scales.

## Big Idea: Graphs are an way to turn abstract quantitative data into a picture, allowing students to visualize patterns and trends in the data.

*45 minutes*

In this lesson students will take a set of data, make a simple graph, and then interpret the graph to make a statement supported by quantitative data. Since I teach in 2 hour blocks, I would usually teach this lesson in the hour prior to the data analysis lesson in the tragedy of the commons sequence. However, you may choose to teach this lesson at another time, perhaps even incorporating it into the writing a lab report lesson in the Nature of Science Unit.

**Connection to Standard:**

The basic skill of making a simple graph is supposed to be an elementary grade standard and well within the skillset of high school students. However, the reality of the situation I find myself in is that many students can not make a basic graph. One potential reason for this is that, for much of their recent schooling by the time they reach my class in the 11th or 12th grade, “making a graph” has meant plotting equations on a four quadrant plane, and so, even though they may have learned this skill in earlier grades, by the time they reach me, they are unfamiliar with making a “real world” graph with data points occurring only within the first quadrant (i.e., +x,+y).

Whatever the reason for the inability of many students to make graphs, it’s a skill worth teaching. Since graphs are such an important tool to understand trends and patterns in data, I find this lesson indispensable in preparing students for the kinds of data analysis questions they will be asked to consider as the course continues.

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#### Warm Up

*5 min*

I begin the class by doing a little bit of acting. I start holding up a simple, neat, and colorful graph and asking them what I’m holding. They quickly identify it as a graph and I continue by telling the class how much I love graphs, explaining how they solve the problem of making sense of a lot of numbers by turning them into a picture that tells a story.

Then I really get into the part of the crazy science teacher by explaining that as much as I love graphs, I go absolutely CRAZY when I grade student graphs because of some very common mistakes.

I then point to the chart on the side of the board and let them know that we are going to make a graph of the data in the chart to make “a picture that tells a story”. I then ask them to take out a sheet of lined paper and turn it sideways to a “landscape” orientation. Then I dive into my “major complaints” with student graphs in the guided practice section.

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#### Guided Practice

*25 min*

As this lesson progresses, I introduce my "major complaints" or pet peeves of badly made graphs one by one. By going over each common student mistake that I claim "drives me crazy", I am scaffolding the steps to make a decent, simple, clear and useful graph.

**Major Complaint #1: Students don’t use the paper’s space well.**

To address this issue, I have students draw a line to be their x axis along the bottom of the page, making sure to mention they leave about an inch of space to label the x axis.

I then have them label the x axis with the years represented in the chart (Month 1, Month 2, Month 3, and Month 4). I walk around looking at students graphs to make sure the months are evenly spaced along the width of their paper. For students having difficulty, I suggest they count the lines on the paper to evenly space the months. I continue to walk around the room checking student work, dramatically saying “excellent!”, “now THAT’s an X axis!”, or something like that to keep the students’ energy levels high.

The second part of using the space well involves using the y axis to set up an appropriate scale for the graph. I have students then carefully draw a vertical line on the left side of their paper, reminding them to keep about an inch of space to label the y axis with units.

I then ask the students, “if we were to make a graph of the heights of the students in this room, would we make the scale of the graph go to 100 feet? They will quickly reply no, and when I ask them why not, they will hopefully offer that no one is even close to that tall, and this would result in most of the graph being empty. I ask them, what would an appropriate scale then be? Which they will most likely say ranging from 0-7 feet. Students might also suggest that a more detailed graph, could be made by making the range even smaller to account for the fact that the actual range of heights are likely somewhere between 50 and 80 inches.

To apply this to our graph, I ask students to identify the largest number on the chart. If you use the chart I provide, then the largest number is 27. I ask them what our scale should go up to, and they will likely offer 30, as it’s a nice round number just beyond the largest value on the graph.

I then ask students to set up their y axis with a scale that places 30 somewhere near the top of their paper. I then repeat the steps of walking around checking student work, offering encouragement to those students doing well and assistance to those that need it.

**Major Complaint #2: Students don’t differentiate between variables!**

I then ask students to begin to plot points for one of the variables, in this case, ants is the first on the chart, so I have them plot those points first. I then quickly move around the room checking that students are plotting the different months’ points appropriately on both the x and y axes. When students are finished with plotting the points, I ask them to connect the points to make a line.

I have them repeat this step with the next variable from the chart (ladybugs). After they connect these points, I point out that the lines look the same and ask how we might differentiate these lines. Students aren’t unfamiliar with graphs, so they’ll probably suggest some options, with different colors likely being the more common suggestion. I then have a volunteer from each lab group approach my supplies cabinet and I give them a box of colored pencils (some students, of course, have their own colored pencils, crayons, or highlighters, and they are free to use them if they wish).

I then ask them to choose a different color for each variable (e.g., brown for ants and red for ladybugs) and to color their lines appropriately. After this, I ask them how someone looking at their graph could tell which line represented which variable. Hopefully students will know that a graph needs a key. I then have them choose an appropriate location to place the key and have them complete the key for the four different variables by naming the variable and having an appropriately colored line or box next to the name of the variable.

Once I have walked around and checked the key we briefly talk about the last complaint I have for student graphs.

**Major Complaint #3: Students make sloppy graphs!**

This one is fairly easy to approach. As I walk around checking the graphs during all the steps of this section, I let students know when they need to write neater, make their lines straighter, or provide more space between units (i.e., there’s no need to label every integer on the y axis, increments of 5 are fine). Since I have been correcting their work and trying to make it neat all along, all that is left for me to do at this point is to point out how neat their graphs look and suggest that this is due to careful planning and taking their time on their graph.

I then ask students to finish plotting the rest of the data from the chart to complete their graphs before we move on to the interpretation of the graph. If any students complete this early, I ask them to either asset other members of their group or to plot the graph on the whiteboard for the whole class to see.

Once students have had a few minutes to complete their graph, I remind them that their graph should have a title. In the case of my example, “Bugs caught by a Bug Trap”, I have them use the same title of the chart for the graph.

#### Resources

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#### Interpreting the Graph

*15 min*

Next comes the opportunity to interpret the graph, by trying to understand the story it is telling. I start by asking student volunteers to make a statement about the graph. Examples of responses could include, “the bug trap caught more flies than anything else”, or “except for ladybugs, the total number of bugs caught decreased over time”. I then ask a different student to support the first student’s statement with specific quantitative data (e.g., the trap caught 27 flies in one month and that is more than any other species).

After giving a few student volunteers the opportunity to make statements, I then switch to interpretations. In this case, I ask students to interpret the graph and suggest an explanation for the trends or patterns in the data. Responses may include, “The population of ladybugs was increasing, so more of them were caught over time”, “the ants used communication to warn each other not to go near the trap and that’s why they were caught less”, or “maybe a spider built a web near the trap and started catching more than the trap could”.

Whatever their responses, the idea here is for students to see that while graphs can supply information and help scientists identify patterns and relationships between multiple variables, they can just as often be additionally useful to scientists because they can point the way towards new questions and new avenues of inquiry.

Following this, I ask students to complete their graphs if they have not already done so and then give the following instructions:

- On the back of your paper, write two factual statements about the graph and support each statement with specific quantitative data.
- Then for each statement, write a possible explanation for the phenomenon you described.

If students finish this early, I offer extra credit to any student that would like to make a divided bar graph or pie chart of the data to show the proportion of each species caught compared with the total number of captured insects. If any student does not complete the work in class, I let them know that the assignment (and any additional graph for extra credit) is due for homework by our next meeting.

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