The symmetry and   duplication in bee hives and ant colonies will be compared to tiling the   plane in TI-84

McCarty, Thomas

Patric, Amy

Peters, David

English

The College at Brockport, State University of New York: Digital Commons @Brockport

The College at Brockport: State University of New York
Digital Commons @Brockport
Lesson Plans CMST Institute
8-10-2004
Symmetry and Duplication
Amy Patric
The College at Brockport
David Peters
The College at Brockport
Thomas McCarty
The College at Brockport
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Patric, Amy; Peters, David; and McCarty, Thomas, "Symmetry and Duplication" (2004). Lesson Plans. 30.
http://digitalcommons.brockport.edu/cmst_lessonplans/30
Amy Patric, David (Mike) Peters, Thomas McCarty 
NAS 501 
Final Project – Integrated Lesson Plan – Science Component 
 
Grade level/Subject taught:  11th and 12th Grade Local Chemistry, Math 
Objectives:  After using the models that we have constructed in Interactive Physics, and 
using the TI84+ Silver Edition graphing calculator, students will have a greater 
understanding of the concept of balancing equations. 
 
Key Idea taught: 
Balancing Equations of all types, particularly the ones found in Chemistry and Math 
class.  (This is a required component of each curriculum.) 
 
We have built two different models using Interactive Physics – one is a science scale, and 
one is of a math scale.  The models actually represent the equation that is being balanced.  
This lesson plan will focus solely on the Science scale. 
 
In the science scale model, there is a balance with two weighing pans – one has two 
blocks, the other only has one block.  The pan with two blocks is supposed to represent 
two different elements.  The red block represents Element X, and the yellow block 
represents Element Y.  On the other pan, there is an orange block, and that is supposed to 
represent the combination of Elements X and Y to make Compound XY. 
 
The model looks like this: 
 
 
 
The sliders are used to adjust the mass of Element X, Element Y, and Compound XY.  In 
the directions, it shows the students how the scale works, and gives a simple example. 
 
Before I would use this model in class, I would show the students several examples of 
unbalanced equations, and see if they could figure out what was wrong.  I would have 
them do this as a journal entry for the day – a warm-up to the class.  After approximately 
ten minutes, I would have the students come back together as a class, and we would go 
over the equations, and work through balancing them properly.  This would take another 
ten minutes or so.  I would then ask the students if they would like a better way to picture 
balancing equations.  I assume that they will all want to see this.  I will then project the 
model on the screen using the LCD projector.  I would start the model out using zero for 
all of the values.  (This way it will balance!)  When I run the model, the scale will not 
move.  I would then change all of the values and run the model again.  This time, the 
scale will not balance, and it will fall to the heavier side, like this: 
 
 
 
My challenge to the students would then be to list the same chemical formulas on the 
board, and have them work through this using the actual masses of all of the elements.  It 
will be interesting to see the students work through the model using different values.  I 
think that this will really help to solidify this concept. 
 
Over the next few classes, I would plan to review balancing equations, and then branch 
into more complex equations.  This would be a good way to move into the concept of 
Stoichiometry without scaring the students.  (Most get scared when they hear the name, 
not to mention that it deals with equations and conversions!)  
 
My rubric to grade this particular activity would be as follows: 
 
Target Acceptable Unacceptable 
Student accurately obtains 
data for interpretation 
All data correlates to in-
class model 
Data does not correlate to 
in-class model 
Student shows 
understanding of the 
concept of balancing 
equations. 
Student is able to correctly 
balance the equations 
provided in the worksheet. 
Student is not able to 
correctly balance the 
equations provided in the 
worksheet. 
Student shows 
understanding of computer 
model. 
Student accurately identifies 
ways to modify and 
improve the current model. 
Student is unable to identify 
any possible changes to the 
current model. 
Student expresses their 
thoughts and can apply 
knowledge gained in the 
virtual lab activity 
Conclusion and analysis 
questions are well written, 
accurate, concise, and grade 
level appropriate 
Conclusion and analysis 
questions are not well 
written, accurate, concise, 
or grade level appropriate 
 
Balancing Equations Lab     Name:  _________________ 
 
Today we will be practicing balancing equations using a computer model that I have built 
in Interactive Physics. 
 
To begin, you should see a screen that looks like this: 
 
 
 
As you can see, there is a scale, and three different blocks. 
 
What do the different blocks represent? 
 Red: 
 
 
 Yellow: 
 
 
 Orange: 
 
 
What is the purpose of the slider bars? 
 
 
 
Why does this accurately represent balancing equations? 
 
Our first equation to be balanced is the combination of Hydrogen and Oxygen to make 
Water.  This equation looks like this: 
 
________ H2 + ________ O2   ________ H2O 
 
Why do we write H2 and O2?  (Hint:  What is a diatomic element?) 
 
 
What is the hint for remembering diatomic elements? 
 
 
 
What are the masses of the elements/compounds in our model? 
 H2: 
 O2: 
 H2O: 
 
Try to balance the equation above.  Now let’s try modeling our ideas using the scale. 
 
How did that work? 
 
 
 
 
Are there any weaknesses with this model?  What would you do to improve the model? 
 
 
 
 
 
Let’s try modeling other equations: 
 
1. ________ + ________  ________ 
 
 
2. ________ + ________  ________ 
 
 
3. ________ + ________  ________ 
 
 
4. ________ + ________  ________ 
 
 
5. ________ + ________  ________ 
 
 
 
 
 
Analysis 
 
What have you learned about balancing equations after today’s class? 
 
 
 
 
 
 
Do you find it easier to picture balancing equations after seeing this model? 
 
 
 
 
 
 
 
Do you think that you could use this model in math class?  How? 
 
 
 
 
 
 
Why is it so important for equations to be balanced? 
 
 
 
 
 
 
What might happen if equations were NOT balanced? 
 
 
 
 
 
 
CMST SCOLLARCITY second tool Lesson Plan using a second choice of 
modeling software, (Due Tuesday, August 10th).  
 
Submit as hard copy AND electronically through ANGEL 
 
Name:Tom McCarthy  
Grade level(s)/Subject taught Geometry  10th  Grade: 
Objectives: (Remember…How will the modeling tool help the student better learn the 
objective?)Math-Science concepts to be integrated: The concept in nature of 
symmetry 
and duplication as in the hives of certain bees, the colonies of various ants or the 
formation of coral in the oceans. This will be compared with Tiling the Plane with the 
TI-84+. The class will begin with a brief review about selecting and drawing regular 
pentagons using the TI-84+ calculators. The team leaders of the different groups will 
demonstrate the necessary steps that will allow  the groups to draw their original 
polygon that will be used to mimic nature. The group activity would last about 10 
minutes(or less) 
followed by a short video depicting the symmetry seen in certain bee hives, ant nests 
and coral found in certain oceans and seas. He last stage will be for groups to each 
choose their own polygon to tessellate with the TI-84+ calculators. 
 
Prompts: Using the TI-84+ calculators I plan on having my students mimic Nature by 
using tessellation(Tiling the Plane) on their calculators. The clas will begin with a brief 
review by the teacher of the way to draw  regular polygons. After entering GeoMaster 
bu using the APPS,ALPHA,TAN keys they will push ENTER twice to bing up the 
MENU window and GRAPH, WINDOW 7  to bring RegPolygon to the screen. 
Pushing ENTER twice will anchor the center and pushing the > key once will bring up 
the fault #(6) and the + or – keys will allow the groups to choose their polygon 
according to the number of sides(3-12). By keeping x=0 and y= a small even # they 
can keep their polygons at a small reasonable size which will keep more of the 
tessellations on the view screen. Once the Group leaders have their team ready the 
class will view Nature’s attempts to show symmetry.    
 
 
 
 
Items to include in your second tool lesson plan: 
 
For the math teacher: 
1. Write the Mathematical Concept or “key idea” that your second modeling tool will 
be used to teach: (e.g. Students use mathematical modeling/ multiple representation to provide a means of 
presenting, interpreting, communicating, and connecting mathematical information and relationships)  
 
The key idea will be to use the TI-84+ calculators to mimic  the symmetry of Nature 
by using the tessellation function to show Symmetry by Tiling the Plane.  
 
 
 
 
 
 
and/or… 
For the Science teacher: 
1b.  Write the Science Concept or “key idea” that your second modeling tool will be 
used to teach: (e.g. Organisms maintain a dynamic equilibrium that sustains life). 
 
 
 
 
 
 
 
 
For you second tool lesson, please describe how you plan on using one of the 
remaining modeling software packages with your students (Stella, AS, GSP, or IP).  
You might describe what a visitor might see walking into your classroom during this 
lesson.  You might also describe the role of the student during the entire lesson and 
your role as the teacher.  Please try to be specific as possible. Also, construct a 
tentative rubric that you might use with your students. ** see example page 5 Thhe class will 
see a 10-15 minute video that exhibits the symmetry of Nature. The inside of beehives and insect 
tunnels or homes will be shown along with the growth of certain Pacific corals that tend to duplicate 
their structures. The concept of exact duplication(no two snowflakes are exactly equal) can be 
mentioned but the main focus will will demonstrate how nature can reflect symmetry. Once the 
symmetry of Nature is observed the groups will reunite to learn the skill of Tiling the Plane. 
 
Each group leader(having already been shown the necessary steps) will guide their group through the 
following steps. By pressing GRAPH, TRACE  5  the window will indicate that they are in the Symmetry 
window and by pressing ENTER the choice 1: Point  2  and  2: RegPolygon 0  will appear. By muving 
the  v  key once to the RegPolygon  0 
Section and pressing ENTER twice the tessellation will take place and a duplicate of the polygon will 
appear at your chosen point. By using the ^, v, >, < keys the group will move to other points, press 
ENTER once bringing up the 1: Point   8  an  2: RegPolygon 0 they can move the v  key to the 
RegPolygon 0, press ENTER twice and another tessellation will occur This can be repeated to mimic 
natures changes which show symmetry. 
 
While the different groups are Tiling the Plane the teacher will observe each group, ask certain 
questions, but the groups and the Group Leaders will do almost all the work. An observer would see the 
use of the TI-84+ to integrate Mat-Scinc without notable  
Input from the teacher. The Target students will be group leaders the Acceptable students will be able to draw 
regular polygons, and perform at least two tessellations.  The Unacceptable level would be students who couldn’t 
draw regular polygons and tessellate at least one figure. Hopefully the Unacceptable students will be few if any. 
 
   
 


Symmetry and Duplication

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