| Day |
1 |
| Student Skills |
Identify real-world problem associated with
standards-based concept(s) |
| Develop background skills and knowledge
- Perform background research
- Develop content understanding of key variables
- Conduct investigations (labs) to gather data
|
|
|
|
Instructional Strategies |
- Review homework on net force and Newton's
Second Law calculations (handed out and
collected prior to the start of the module)
- Teacher introduces and poses problem,
referencing prior knowledge.
- What factors related to the hailstone make it
hazardous?
- Teacher uses module with projector and
computer for introduction.
|
| Probing Questions |
- What is meant by hazardous?
- Do all hailstones fall from similar heights?
- How large must a hailstone get before it becomes
hazardous?
|
- What are the factors affecting the motion of a
falling object
|
|
|
|
Assessment Process |
Student Product or Behavior |
- Students answer probing questions posed by
teacher in whole-class setting
- Small-group discussions to draw upon prior
knowledge and brainstorm list of factors
- Start Coffee Filter Drop Lab
|
|
Feedback |
Based on student responses, teacher provides
additional content reading or homework questions if
needed to help students develop a fuller
understanding of the real-world problem |
|
| Day |
2 |
| Student Skills |
Develop background skills and knowledge
- Perform background research
- Develop content understanding of key
variables
- Conduct investigations (labs) to gather
data)
|
| Instructional Strategies |
- Students investigate some of these
factors via lab activities (i.e. coffee
filter drop)
- Students identify factors affecting the
motion of a falling object, in particular
hailstones, using website and other
resources.
|
|
Probing Questions |
- What are the factors affecting the
motion of a falling object?
- What implications do your results have
for hailstones?
- Do all hailstones have a constant
acceleration?
- Do all hailstones hit the "ground" with
the same velocity?
- What measure of the hailstone is the
best indicator of the potential for
damage?
|
Assessment Process
|
Student Product or Behavior |
- Individual reports on coffee filter lab
- Individual identification of variables
and completeness of research
|
|
Homework |
Questions on the lab
Discussion Paragraph |
|
| Feedback |
- Check for accuracy and understanding
|
| Day |
3 |
| Student Skills |
Develop background skills and knowledge
- Perform background research
- Develop content understanding of key variables
- Conduct investigations (labs) to gather data
- Learn to use a modeling tool (e.g., STELLA)
|
|
Instructional Strategies |
- Paragraph sharing and assessment
|
|
Probing Questions |
- How do you build a model using STELLA?
What can you do with STELLA that you can't
figure out on paper?
- What do the different symbols in STELLA
mean?
- Do your models behave as you would report?
|
Assessment Process
|
Student Product or Behavior |
- Completed constant velocity and constant
acceleration models
- Completed Kinetic Energy of baseball worksheet
- Self and peer assessment of coffee lab using
rubric
- Rewrite of report based on feedback for
homework
- Completed homework on net force and
calculations of acceleration
|
|
Homework |
Complete Newton's Second Law worksheet
Review assessment and rewrite discussion |
|
| Feedback |
- Check for accuracy and understanding
- Using rubric, peer feedback on data, report, and conclusions
- Oral comments on model structure and function
|
| Day |
4 |
Student Skills
|
Simplify real-world problem
- Determine applicable principles/laws/procedures
|
|
Identify variables and interrelationships
- Make a diagram or graphic organizer connecting ideas from research
|
|
| Instructional Strategies
|
- Teacher illustrates limitations of modeling and
students determine assumptions of their model
- Review of Newton's second law of motion, free
body diagrams, kinetic energy and net force.
|
- Students create simple graphic organizer showing effects of each variable on kinetic energy (as a
measure of damage potential)
- Factor » influence on net force » influence on mass » influence on acceleration » overall effect on
kinetic energy as the object falls
|
|
|
Probing Questions
|
- Is it possible to create a model that accurately
predicts real-world outcomes? Why or why not?
- What are the assumptions we have to make (that
is, what do we have to leave out)?
- How do we determine what we leave in and what
we leave out?
- What is constant? What is changing?
|
- Which variables will you use? Why did you choose these?
- How can you graphically display the relationship between these variables and kinetic energy on
impact?
- What do your graphics mean?
- Have you thought about x and y and their effects on kinetic energy?
|
|
| Assessment Process
|
Student Product or Behavior |
- Groups produce assumptions list for use when
building model
- Participation in review of homework on
Newton's Second Law problems
|
- Graphic organizer with narrative explaining relationships
|
|
|
Homework |
Take Home Quiz
Review teacher assessment of lab discussion |
|
Feedback
|
- Guidance on making assumptions
- Oral comments on parts that are solvable with STELLA
- Student response to probing teacher-posed questions
- Oral comments from teacher on relationships in graphic organizer
|
| Day |
5 |
Student Skills
|
Defend the identified relationships and assumptions
- Present and defend in groups
|
- Represent relationships in terms of mathematical equations
- Use diagrams and relationships to Derive mathematical equations
- Determine theoretical numbers in absence of real figures
|
|
| Instructional Strategies
|
- Students organize research information and
graphic organizers and present to another group.
The Groups will switch roles and exchange
feedback
- Teacher circulates among groups
|
- In small groups, students write equations based on their research
- Teacher facilitates equation writing process
|
|
|
Probing Questions
|
- Why did you make the connections in this way?
- How did you derive those relationships from
your research?
- Are any changes needed based on feedback from
other groups?
|
- What is the math that underlies your graphical representation?
- How would you state these relationships in mathematical language?
- What does this math mean? What predictions can we make based upon this math?
|
|
|
Assessment Process
|
Student Product or Behavior |
- Groups make presentation of variables and
graphic organizer using flip chart and markers or
whiteboards and markers
|
- Participation by working with graphic organizer and research in pairs.
- Handwritten equations based upon graphic organizer and research
- Students create graphic organizers for homework for acceleration of an automobile
|
|
|
Homework |
Create an assumptions list and graphic organizer
that could be used to model the motion of a car as it
speeds up from rest.
Include reading assignment
Include narrative |
|
| Feedback |
- Students give feedback to presenting group on assumptions and graphic organizer.
- Teacher addresses student questions
- Oral comments from teacher based on presentations and individual group questions
|
| Day |
6 |
| Student Skills |
Translate variables and relationships into
computational model:
- Translate model into computational process
- Explore range of validity
|
| Instructional Strategies |
- In groups of two, students build STELLA model
using researched variables and mathematical
relationships from Day 5
- Students run their model, review their
mathematical relationships, explore results, look
for range of validity and run check cases
- Students switch computers and critique peer
models
- Students run expert models and compare results
|
|
Probing Questions |
- Which symbols in STELLA represent your
mathematical functions?
- What do the results look like? Is that what you
expected? Why or why not?
- Did you construct the model to reflect your
mathematical relationships?
- Is there a mistake in your model? How can you
fix it?
- Does your model work for all numbers, or do
some numbers make your model behave
erratically?
- What happens if you make this number bigger,
or this number smaller? Did you expect that
result? Why or why not?
|
| Assessment Process |
Student Product or Behavior |
- Students complete STELLA model on computer
- Changes made to model when necessary
- Demonstrate viability of model by performing
check cases and evaluating output
- Description of what data will be acquired using
the model to explore the factors that make
hailstones hazardous
|
|
Homework |
Create description of how the model will be used to
address the problem (specific--What data will you
get?). |
|
| Feedback |
- Formative evaluation of model (does it work? Do the results look like what was expected? What
needs to be changed?)
- Oral feedback from peer groups
- Yes/no approval of changes made to model
- Monitor participation in peer review
- Teacher checks model output after test cases are performed
|
| Day |
7 |
| Student Skills |
Interpret findings
|
|
Communicate findings
- Presentation, letter, essay, etc.
|
|
|
Instructional Strategies
|
- Students use model to explore the factors related
to the hailstone that make it hazardous.
- Students gather, organize, and evaluate data.
- In small groups, students generate conclusions
about which factors contribute to hailstone
damage potential (as measured by kinetic
energy)
|
- Students will present findings in written form.
|
|
| Probing Questions |
- Were there any surprises?
- How confident do you feel about the accuracy of
your results?
- Is there a better way to do the investigation?
- What are the sources of error?
- Who would be interested in the results of your
model? And why?
|
|
Assessment Process
|
Student Product or Behavior |
- Responses to teacher-posed questions references
to the data
|
- Answers to teacher and student-posed questions
|
|
|
Homework |
Discussion of results
Self-evaluation of module objectives |
|
| Feedback |
- Informal evaluation of student responses
- Check if students can properly reference data in drawing conclusions
- Rubric scoring of student discussion
|