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NAME OF COURSE / CLASS: This can be a component of Algebra 1 (using the optional
restaurant as a variable), Geometry (using trig to check accuracy of the shortest distances) or
Prob/Statistics (make the restaurant a uniform requirement and look for deviations in the results).
UNIT TITLE: Applications of Variables/Trig/Deviations/Representing Real World Data
LESSON TITLE: Using ImageJ for Measurement in Satellite Images
ANTICIPATED INSTRUCTIONAL TIME: 70 minutes (including intro to software and
actual lesson)
ENDURING UNDERSTANDING: Students will have introductory knowledge of the analysis
features in ImageJ and an appreciation for technology tools to help them solve real-world
problems.
RATIONALE: As the world continues to make technological advances, today’s students need
to be comfortable using a variety of tools to solve problems relevant to their lives and work. The
lesson will use methods of demonstration, walkthrough, and a small individual project to meet its
objectives, as these methods are highly effective in our environment where everyone can
participate, and be engaged in using the software, at their own workstation.
GOALS OF THE LESSON:
G.1.1: To become comfortable with a new software application.
G.1.2: To use multiple tools to solve real-world problems.
G.1.3: To draw conclusions from a set of data.
G.1.4: To evaluate the accuracy, precision, and reasonableness of results.
G.1.5: To apply mathematics in other contexts and appreciate its purpose in other contexts.
MATHEMATICAL OBJECTIVES OF THE LESSON:
O.1.1: Students will follow the provided walkthrough to become comfortable with ImageJ.
O.1.2: Students will use a mapping service in combination with ImageJ to model a real-world
situation and take measurements.
O.1.3: Students will determine what paths they will take in a vacation scenario and which ones
they should take by bus.
O.1.4: Students will reflect (in writing) on the accuracy and precision of the results, and also
evaluate the benefits of the tools they use (specifically ImageJ, and an online mapping service).
MULTIPLE REPRESENTATIONAL TOOLS: An online mapping service will be used to
acquire maps of sidewalks and city streets. ImageJ will be used to take measurements directly
from screenshots of the maps. Measurements taken in ImageJ will be exported to a spreadsheet.
RESEARCH & BEST PRACTICES:
Measuring digital images in math and science classrooms. (See Appendix B for link.)
SUMMARY: This article gives a brief introduction to digital images and the ImageJ software.
Then it describes three lessons which use the software for measurement.
SD K-12 CONTENT STANDARDS:
Standard Description
MATH
Students are able to choose appropriate unit label, scale, and
9-12.M.1.1
precision.
Students are able to add, subtract, multiply, and divide real
9-12.N.2.1
numbers including integral exponents.
Students are able to use estimation strategies in problem
9-12.N.3.1 situations to predict results and to check the reasonableness of
results.
Students are able to select alternative computational strategies
9-12.N.3.2
and explain the chosen strategy.
9-12.S.1.1 Students are able to draw conclusions from a set of data.
Students are able to use dimensional analysis to check answers
9-12.M.1.1A
and determine units of a problem solution.
SCIENCE
Students are able to manipulate multiple variables with repeated
9-12.N.2.1A
trials.
Students are able to use statistical analysis of data to evaluate the
9-12.N.2.2A
validity of results.
Students are able to demonstrate correct precision in
9-12.N.2.3A
measurements and calculations.
GEOGRAPHY/SOCIAL SCIENCE
Students are able to use resources, data services, and geographic
9-12.G.1.1
tools that generate and interpret information.
Students are able to interpret geographic representations when
9-12.G.1.2
given information about places and events.
Students are able to evaluate and select resources, data services,
9-12.G.1.1A
and geographic tools that generate and interpret information.
NCTM EXPECTATIONS:
Topic Expectation
• develop fluency in operations with real numbers, vectors,
and matrices, using mental computation or paper-and-pencil
calculations for simple cases and technology for more-
Number and Operation
complicated cases.
• judge the reasonableness of numerical computations and
their results
• draw reasonable conclusions about a situation being
Algebra
modeled
• use geometric models to gain insights into, and answer
questions in, other areas of mathematics;
Geometry • use geometric ideas to solve problems in, and gain
insights into, other disciplines and other areas of interest such as
art and architecture
• make decisions about units and scales that are appropriate
for problem situations involving measurement.
Measurement
• analyze precision, accuracy, and approximate error in
measurement situations
• solve problems that arise in mathematics and in other
contexts;
• apply and adapt a variety of appropriate strategies to solve
Problem Solving
problems;
• monitor and reflect on the process of mathematical
problem solving
• organize and consolidate their mathematical thinking
through communication;
• communicate their mathematical thinking coherently and
Communication
clearly to peers, teachers, and others;
• use the language of mathematics to express mathematical
ideas precisely
• recognize and apply mathematics in contexts outside of
Connections
mathematics.
• select, apply, and translate among mathematical
representations to solve problems;
Representation
• use representations to model and interpret physical, social,
and mathematical phenomena
SESSION-RELATED QUESTIONS:
Since the software does not use a traditional installation, students may ask questions
about the installation process, permissions for installing on campus, etc.
Since one major purpose of the lesson (particularly for SEED418 students) is to be
comfortable with the software and using multiple tools, there may be lots of “how-do-I-
…?” questions, so we the teachers need to be very familiar and comfortable with the
features and how they are used in the activity.
The assignment questions are fairly open-ended and may result in students asking about
which specific details to include. We want them to experiment with the software, reflect
on their experience, and draw their own conclusions, so when they ask, we will say,
“write whatever you think it takes to answer the question.” We can also encourage
students to discuss their individual results to help each other draw conclusions.
IMBEDDED / FORMATIVE ASSESSMENT OPPORTUNITIES: We have the incredible
benefit of cooperative teaching with two instructors—during the demonstration and walkthrough,
one teacher can provide the examples with the projection system while the other keeps a close
eye on the students as they perform the tasks. Having the students following closely to the
demonstration while the other teacher supervises the work will be the best way to catch errors
and misunderstandings as they happen. A homework assignment provides a summative
assessment that can begin as embedded if there is time to start it at the end of the lesson.
INSTRUCTOR MATERIALS: Computer without ImageJ (we will install it as part of the
lesson) and with MS Excel, MS Word, and a Web browser (e.g. Internet Explorer or Firefox),
projector, Internet access. The download location of the ImageJ ZIP file is
http://rsbweb.nih.gov/ij/download/zips/ij142.zip.
PARTICIPANT MATERIALS: Computer without ImageJ (we will install it as part of the
lesson) and with MS Excel, MS Word, and a Web browser (e.g. Internet Explorer or Firefox),
projector, Internet access. The download location of the ImageJ ZIP file is
http://rsbweb.nih.gov/ij/download/zips/ij142.zip. Also, provide the students with the URL for the
assignment details and submission (http://abbysdoor.com/portfolio/tech_upload.php).
TEACHING NOTES / LESSON SCRIPT / PROCEDURES:
The lesson begins with a note that we will be using software with which we are unfamiliar to do
some measuring satellite images.
Then the teacher walks through the installation of the software. Students follow along, installing
the software to their Z drives.
Each student then goes to the Web site of their favorite mapping service to acquire satellite
images of campus.
The teacher walks them through preparing the image for measurement and then actually taking
the measurements.
The lesson ends with exporting the results to a spreadsheet and giving the assignment.
ASSESSMENT / HOMEWORK: See http://abbysdoor.com/portfolio/tech_upload.php
ACCOMMODATIONS: If a student doesn’t handle verbal instructions with multiple steps, we
could write up a detailed handout on using the features of the software. Students who are very
slow at typing may need help with arriving at the Web pages—another classmate or the teacher
can do this.
EXTENSIONS: As we noted above there are extensions in many other areas of math, and also
other fields. This can be tailored for a specific group of students and their interests.
REFLECTION / REVISION: This section will not be used until you teach the lesson. "To
continue working effectively at a challenging task (that is to prevent intellectual downshifting, or
reverting to earlier learned, lower cognitive level behaviors) requires significant amounts of
reflection." (Kellough & Carjuzaa, 2006, p. 160)
REFERENCES: ImageJ Web site (download page: http://rsbweb.nih.gov/ij/download.html and
concepts page: http://rsbweb.nih.gov/ij/docs/concepts.html), SD Standards, NCTM Standards,
Google Maps (http://maps.google.com)
APPENDIX A: LESSON SCRIPT (LONG VERSION)
For SEED418, the class will begin with an overview of ImageJ’s features. The students do not
need their tablets at this stage—they need only pay attention. The list of features to be covered is
located at http://abbysdoor.com/portfolio/seed418uploads/imagejfeatures.docx.
Teacher: Good morning, class. Today you will need the tablets out of the cart. If you don’t have
one ready, please get one now. (As any stragglers boot up and log in, continue: ) Today we will
be taking measurements on satellite images using software called ImageJ. Most of you are
probably not familiar with the software, so we will begin with step-by-step installation. I have a
question for anyone who can answer: What is a problem we might have here on campus with
installing software?
Students should be able to respond that we need special permission from Information
Technology Services office, maybe even someone to come install it for us, since our login
credentials do not have installation privileges.
Teacher: Right. However, this software is special. It is in a class of software that runs without a
traditional installation. You simply put the files in place and run them. So what we are going to
do is download the ZIP file and unzip its contents to each of our Z drives. Then we can run it
straight from our Z drive on any computer on campus. Who can tell me what they know about
ZIP files and the unzipping process?
Students should be able to respond that ZIP files are a collection of one or more files compressed
into a single file. Windows itself or special software can “unzip” these files to their original state.
Teacher: Yes, so let’s go back and I will walk you through the download and unzipping. You
will need to go to this Web site to download ImageJ. (At demonstration machine, type
http://rsbweb.nih.gov/ij/download.html into a Web browser—if students cannot see it clearly,
write the address on a whiteboard or some other method for easy seeing. Give students a moment
to arrive at the Web page.) There are several options for downloading the software. However, the
one we want is called “Platform Independent” and is the first one. There is a blue link for the ZIP
file. Now listen carefully, what you want to do is click on that link and choose “Save.” When
you choose Save it will ask where you want to save it. I recommend straight to your Z drive.
(Demonstrate, and wait a moment for students to catch up. While waiting, perhaps ask: ) Earlier I
mentioned one of the benefits of putting it on your Z drive. (Name of Student who is Clearly
Caught Up), what was that benefit?
Student should be able to recall that the program can then be run from anywhere on campus or
off that they have access to their network drive.
Teacher: Exactly. So, now that the ZIP file has downloaded, we have to find it and unzip it.
From your experiences on campus I am sure you know how to get to your Z drive, but for
anyone who doesn’t (demonstrate as you explain: ) Open My Computer and select your Z drive
from the list. If you do not see your Z drive in My Computer, let me know and I can help you
mount it. Now that everyone is at their Z drive, find the file called ij142.zip. Do NOT double-
click this file. Instead, RIGHT-click and find “extract here” in the context menu. The option
“extract here” will do exactly what you expect—it unzips the file into the folder we are currently
in. That means you should now have a folder called ImageJ on your Z drive.
Stop here to make sure all students have ImageJ installed.
Teacher: Now you can find the file ImageJ.exe in that folder. This is the file your double-click
whenever you want to run ImageJ. Go ahead and run ImageJ by clicking on this file. You will
notice that it runs nice and fast, and it is a compact little program. However, we don’t yet have
any images to open with ImageJ! So let’s do a small experiment together. We want to measure
how much walking we do around campus, specifically going from the Ed School to the Library,
having to go around the construction area earlier this semester. How can we find a picture of
campus to measure?
Students may have a few ideas, including asking various offices on campus if they have a photo.
The answer we are looking for is using the satellite image from a mapping service, and since we
mention satellite images earlier, someone is bound to remember.
Teacher: These are all good ideas, and what we will do today is use a mapping service. I like
Google Maps, but you can use MapQuest or something else if you like-as long as it has a scale
on the map. So let’s go back to our Web browser and open a new tab to do our mapping.
(Demonstrate as you continue: ) I am going to maps.google.com, but you can go to whichever
service you like to use. In the search box I am typing “Vermillion, SD” to find our town. Then I
am going to pan and zoom in nice and close to campus so I can see the sidewalks.
This is something the teacher should practice so that the demonstration goes very quickly. Then
the teacher can walk around to make sure everyone is caught up and help out people who are
struggling with finding the right image. The features of mapping software should be very
intuitive, but students who have not done it previously may need a lot more help than others.
Teacher: Great. Now that we have the right image, we need to get it into ImageJ. There are a
number of ways to do this. Does anyone know a good one?
There are a few possible solutions, but the one we are looking for is taking a screen shot.
Teacher: A screen shot. ImageJ provides a way to do a screen shot, but screen shots are
something you can always do, no matter what program you are using. It’s really easy. Just get the
screen to look exactly how you want it, and then press the “Print Screen” button on your
keyboard. This copies an image of the whole screen and puts in on the system clipboard, so you
can paste it anywhere that you can paste a picture. So, (demonstrate as you continue: ) I press the
Print Screen button and then I go back to ImageJ. Then all I have to do is go to the File menu,
highlight “New,” and then choose System Clipboard. Then it should appear in ImageJ.
Here is another place where you may want to stop and make sure everyone is caught up. They
really can’t continue without having an image. Here is a screen shot of how to paste the screen
shot into a new ImageJ window.
Teacher: Good. Now we are ready to work with our image. First we want to only have the part
of the screen with the map, so we need to crop the image. Cropping is taking just the portion of
the image we want and throwing away what’s outside that portion. It is very easy to crop in
ImageJ. (Demonstrate as you continue: ) Make sure your rectangular selection tool is
highlighted. Then draw a box around the map—make sure you include all of the scale—we are
going to need that! After you draw your box, go to the Image menu and click Crop. Then your
image is cropped and ready for analysis.
1. Rectangular Selection Tool
3. Choose Crop from
the Image Menu
2. Draw a rectangle around the
portion you want. It will be yellow.
Teacher: Before taking any measurements we have to set the scale. Tell me, what is the scale on
our map?
Students should be able to identify the scale in the bottom left corner and describe how it defines
the actual distance of a portion of the image.
Teacher: To set the scale we draw a line along the scale and then choose Set Scale from the
Analyze Menu. (Demonstrate)
This is another good place to stop and make sure everyone is caught up, since we are about to
take our first measurements!
1. Line Selection Tool
3. Find Set Scale in the Analyze menu
4. Fill in known distance and
unit of length. The program fills
in pixels for you. Then click OK.
2. Draw line over scale. Hold shift
to make a perfectly straight line.
Teacher: Next we have to decide what we are measuring. In the Analyze menu, select Set
Measurements. We just want to know the distances we walk, so which measurement do we
need?
Provide adequate wait time here. “Distance” is not an option. Some may use dimensional
analysis and say that “Perimeter” would get us results, which is true. However…
Teacher: OK, so this was a bit of a trick question. One of the few things I don’t like about
ImageJ is that when you measure a line, it automatically gives you the length without any of
these checked. So let’s just deselect all of them and click OK. Now we are finally ready to start
measuring! So, we want to travel a complicated path around these sidewalks, and a straight line
is not going to do it for us. Just right-click on your line selection tool, then choose Segmented
Line Tool. Click on a starting point, and then also at every point you want to turn. When you get
to the ending point, do a right-click. I am going to follow the path that we had to take around the
courtyard construction from the Ed school to the library entrance. Then go to the Analyze menu
and click Measure.
1. Right-click in order to choose
the segmented line tool.
3. Click “Measure” in
the Analyze Menu and
the Results window will
appear.
2. Click on the path
as described above.
Teacher: With the results still open, I will now do the same with just cutting across the
courtyard. This will help me determine how much more distance I had to walk when the
courtyard sidewalks were under construction. 611.699 minus 388.914 is 222.785 extra feet of
walking.
At this point it is another good time to stop and make sure everyone is able to highlight paths and
take multiple measurements in the same results window. This will be required in the final
assignment.
2. Click “Measure” in the Analyze
menu to add the new path to the
results window.
1. Highlight the next path.
Teacher: Just one more thing before we give you the assignment, and this is how you will create
one of the files you have to submit. In the Results window, go to the File Menu and select Save
As. You are probably familiar with the Save As dialog from other software applications. Find a
good place in your Z drive to save the results. You will probably want to choose a filename that
is more descriptive, like “Paths Around Campus.” Click Save, and it will save the results table as
a MS Excel spreadsheet. You can now go to your Z drive and open the .xls file that was created.
Double-clicking on it should open it in MS Excel.
NOTE: This is in the RESULTS window,
and NOT the main ImageJ window.
Teacher: Now you have all the tools you need to complete the assignment. Go to your Web
browser and type in the address http://abbysdoor.com/portfolio/tech_upload.php. This page has
the description of the assignment, questions to answer, and a form for uploading your results.
These uploads are due in by class time on Tuesday. The setup for this assignment is a fabulous
vacation to downtown Chicago. You are going to hoof it—it’s far too crazy and expensive to
drive around downtown—but you do have a little cash for the bus, so you are going to measure
your walking paths and decide for which two stretches you will take the bus instead.
Remaining class time can be used to have students get started on the homework. If they cannot
complete it during class tell them they can use the same install procedure on a computer at home,
or they can now use any computer on campus by running it from their Z drives.
APPENDIX B: RESEARCH ARTICLES INFORMING THE LESSON
Measuring digital images in math and science classrooms.
http://abbysdoor.com/portfolio/seed418uploads/article1.htm
