This lesson reinforces students' understanding of simple random sampling
using real data from the Hubble Deep Fields (HDFs). The Hubble Deep Fields
- one looking north (HDF-N) and the other south (HDF-S) - are the deepest,
sharpest, multi-color images of the faintest universe in visible light.
A unique feature of the lesson is its reliance on the statistical analysis
of real data. This data can be easily accessed from the Internet, independent
of the lesson. Students will pick a sample of galaxies from one of the Deep
Fields. They will determine if their sample data is valid by investigating
bias in sampling techniques and the role of sample variability in determining
the optimal sample size. A second sampling, from the second Deep Field,
offers the chance to put improved sampling techniques to use. Comparisons
between the students' valid data and the astronomers' results lead to a
determination of whether the two Deep Fields are similar. The lesson concludes
with an invitation to consider whether the distant universe of the Deep
Fields is similar to the local universe.
How to Prepare for an “Online Exploration”
Decide if the activity meets your needs.
- Check out the activity ahead of time by working through it as your students
will. As you go through the activity, pay attention to the following:
Check out the “Teaching Tips” for the following information.
- How to navigate from one place to another.
- The ability level. Can students work this activity successfully?
- Natural breaks within the activity. Is there enough flexibility that
students can complete all or selected parts within the time restraints
of the daily schedule?
- Overview: Serves as a broad, comprehensive summary of the
activity, including a description, the concepts covered, prerequisites,
and the target audience.
- Science Background: Provides information about the science
behind the activity. It clarifies important concepts used in the activity
and contains a message from the scientist who worked with the team
to develop it.
- Lesson Plan: Addresses specific recommendations for using
the activities, including learning outcomes, new vocabulary, misconceptions,
engagement activities (under the heading procedure/directions), and
follow-up activities. Includes suggestions for using the activity in
one-computer classrooms and those without computers.
- National Standards: Provides alignment between the activity
and the National Science Education Standards, the National Council
of Teachers of Mathematics Curriculum and Evaluation Standards, and
the Project 2061 Benchmarks for Scientific Literacy Standards. Many
state and local standards were developed from these so it should be
easy to check for correlations.
- Grab Bag: Provides resources for educators who wish to
customize the activity. Includes images from the activity, which can
be used to develop your own interactive lesson. Also identifies resources
used in the activity and others related to the topic, which can be
used by students and educators to do further research.
Before using the activities...
- Check out your computers.
Determine a strategy for organizing your students. Options include the
- Review the Computer Needs section of the activity.
- Reserve a time to use the computer lab.
- Bookmark the activity on the Web browser (Netscape Navigator or Microsoft
Explorer) of each student computer.
Think about how this online activity matches up with teaching materials
that are already available to you. These might include:
- Use a whole-class approach with one computer.
- Use a team approach in a computer lab, with different students having
specific responsibilities during the activity (such as “mouse user,” “note
taker,” and “oral reader”).
- Use a one-computer-per-student approach.
- Curriculum guides
- Share the objectives and the key vocabulary words used in the activity.
- Use a large monitor, LCD, or transparencies to give a preview of the
activity and to demonstrate how to navigate within it.
- Give your students a computer/Web pre-assessment to determine their
computer experience and/or competence.
- Organize your students in such a way that more experienced users are
matched up with less experienced ones.
- Try one of the Suggested Engagement Activities, which can be found under
Procedure/Directions in the Lesson Plan section of the activity’s
While students are doing an activity…
- Help individual students navigate through the activity.
- Provide options for those who finish the activity early:
- Have them review the activity again to define key vocabulary words.
- Have them visit related Web links to conduct additional research.
- Have them completing some type of assessment activity. A number
of these can be found under Follow-up Activities/Extensions in the
Lesson Plan section of the activity’s Teaching Tips.
Using the activities without an Internet connection
- Order a CD of the activities.
- For activity-specific suggestions, consult the Classrooms Without Computers
section (in the Lesson Plan section of the activity’s Teaching Tips).
- Print the information provided in the Science Background, which might
be useful for content reading.
- Download the activity in advance from the Amazing Space Web site. Instructions
are in the Computer Needs section accessed from the activity’s title
- Go to the activity’s Grab Bag section and select text, student
activities, or other Internet links that direct you to related topics.
Statistics - This lesson addresses bias, in the section
labeled "Bias," and variability and sample size, in the sections
labeled "Sample Size" and "HDF-N vs. HDF-S."
Astronomy - This lesson addresses the frequency of galaxy
types in the local vs. the distant universe in the sections labeled "Start
Safari" and "Last Stop."
- Bias in selecting a sample invalidates the sample.
- Optimal sample size can be established from the variability of the data
as sample size increases.
- The similarity of the HDFs is consistent with the supposition that the
universe looks the same in all directions.
- Comparison of the most common type of galaxy in the HDFs with that in
the local universe illustrates that the universe does not look the same
at different depths.
Before attempting to complete this lesson, the student should:
- be able to construct and interpret frequency tables
- demonstrate knowledge of simple random samples
- be able to define range, mean and median as they apply to statistics
- demonstrate knowledge of min/max plots
Process Skills Acquired:
- Analyzing data
- Inferring relationships
- Interpreting graphs
Target Audience/Grade Levels:
- · Grades 10 - 12: Elementary (Introductory) Statistics or AP Statistics
- Time necessary to download computer software to support the lesson (Netscape
- Time necessary to become familiar with the lesson.
Execution Time by Module:
The following are approximate times depending on your school's Internet location
(e.g., classroom, library, computer lab), the number of computers available
with Internet access, and the number of students in the class.
- Start Safari 10-15 minutes
- Bias 10-15 minutes
- Sample Size 15-20 minutes
- HDF-N vs. HDF-S 10-15 minutes
- Last Stop 5-10 minutes
January 8, 2004
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