Physicalpptk2

Model Eliciting Activities
Collaborative
Learning
Peer
Tutoring
Cooperative
Learning
Model-Eliciting
Activities
Problem-Based
Learning
Active
Learning
Peer-Assisted
Learning
Deborah Kozdras Christine Angel Danger

Designed as “thought-revealing activities” for students (Lesh, et al, 2000)
“The problems that we face in our ever-changing increasingly global
society are multidisciplinary, and many require the integration of multiple
STEM concepts to solve them.” (Roehrig, Moore, Wang, & Park, 2012)

“The resultant student products reveal students’ thinking and provide both
teachers and researchers with a powerful lens for viewing students’
reasoning and concept development (Carlson, Larson, & Lesh,2003)

The models created include procedures for doing things and, more importantly, metaphors for
seeing or interpreting things (Mousoulides & English, 2011).

The activities are such that student teams of three to four express their mathematical model,
test it using sample data under the possible engineering constraints, and revise their
procedure to meet the needs of their client (Lesh and Doerr, 2003; Mousoulides et al. 2008).

Reading - Key Ideas and Details: Read closely
to determine what the text says explicitly and
to make logical inferences from it; . .
Reading - Integration of Knowledge and
Ideas: Integrate and evaluate information
presented in diverse media. . .
Speaking and Listening -
Comprehension and Collaboration:
Prepare for and participate effectively
in a range of conversations and
collaborations . . .
Speaking and Listening - Comprehension and Collaboration:
Integrate and evaluate information presented in diverse media and
formats . . .
Speaking and Listening - Comprehension and
Collaboration: Evaluate a speaker’s point of
view, use of evidence . . .
Speaking and Listening – Presentation of Knowledge and
Ideas: Present information, findings, and supporting
evidence such that listeners can follow the line of reasoning .
. .
Speaking and Listening – Presentation of
Knowledge and Ideas: Make strategic use of
digital media and visual displays of data to
express information and enhance
understanding of presentations.

Pancake Syrup Syrup!
A Model Eliciting Activity for Grades K-2

Reading Passage 1
Dear Students,
Moose Maple Syrup Company has created some new pancake
toppings. These toppings are made from pure maple syrup with treats
such as fruit, nuts, or chocolate in it. We want to learn what kids like
on their pancakes so that we can decide which toppings to sell in
stores. Stores will only order three flavors, so we need to figure out
which three flavors kids want the most.
Please look at the information on the data table and help us choose
which toppings to sell. Please let us know how you decided so that
when we add new toppings we can use the same procedure as you to
decide which toppings to sell next.
Thank you for your help,
Mr. Moose

Dear Mr. Moose,
Here is how we decided which three pancake toppings
you should sell:
The three we think you should sell are:
1.
2.
3.

Reading Passage 2
Dear Students,
Thank you for your help to choose three toppings to sell.
I received a letter from some kids who told me that they do not
like it when the treats in the jar of topping sink to the bottom because
it makes it hard to get them out of the jar and they wind up with plain
syrup on their pancakes. Please look at the pictures to find out which
treats sink. Was that one on your list? If it was should we take it off?
While I was waiting for your answer stores ordered some toppings.
I am sending you a data table that shows how many cases of each
topping were ordered. I want to make as much money as possible, the
more orders I get, the more money I make.
Please look at the data again and tell me what your three top
choices are.
Thank you,
Mr. Moose

Letter Template 2
Dear Mr. Moose,
We looked at and discussed your new data set.
Based on the new information we decided that the
the three toppings you should sell are:
1. __________________________________
2. __________________________________
3. __________________________________
We think these are the best three for you to sell
because:

The Fire Wheels
SC.K.P.12.1: Investigate that
things move in different
ways, such as fast, slow, etc.

Reading Passage 1
Fire Wheels Toys
31 Sea Lane
Detroit, MI 48201
Dear Team,
Our company makes toy cars. They are sold in toy stores for less than
five dollars. Kids love racing them on the floor and crashing them into
things. We need you to help us pick which toy car to make for the
holidays.
We made three test cars that we think kids will love. We want to sell
the best car that will not break when crashed into things. We also want
our car to roll on carpet and smooth floors.
Look at the data table and rank the cars in order of worst to best. Be
sure to write back to tell us the rank of the cars and how you chose
them.
Thanks!
Fire Wheels Toys

Letter Template 1
Dear Fire Wheels Toy Company,
Our team, ______________________________, has determined that
you should use ______________. The order from best to worst is
1) _________
2) _________
3) _________
Our plan for ranking is
_________________________________________________________
_________________________________________________________
__________________.
Sincerely,
________________________________________________

Reading Passage 2
Fire Wheels Toy Company
31 Sea Lane
Detroit, MI 48201
Dear Team,
Thank you for creating a plan for ranking our toy cars. Recently, our
company noticed that children want cars that roll in a straight line. We
need you to make sure your plan still works with the new data table.
The new data table includes information about whether the toy cars
rolls in a straight line or turns. We also found one more toy car to add
to the list.
Look at the data table again and see if your plan still works by ranking
the cars in order of worst to best. Be sure to explain your thinking. If
you had to change your plan, tell us what changed and why.
Thank you!
Fire Wheels Toys

Letter Template 2
Dear Fire Wheels Toy Company,
Our team, ______________________________, has determined that you
should use ______________. The order from best to worst is
1) _________
2) _________
3) _________
We changed/ did not change our system for ranking the cars because
_______________________________________________________________
___
Our plan for ranking is
_______________________________________________________________
_______________________________________________________________
______.
Sincerely,
________________________________________________

Terrific Toy Company
SC.1.P.8.1 :Sort objects by
observable properties, such as
size, shape, color, temperature
(hot or cold), weight (heavy or
light), texture, and whether
objects sink or float.

Reading Passage 1
Dear Students,
I am the president of the Terrific Toy Company and I need your help. Our company is
launching a new line of Value Pack Toys. These value packs include several similar
toys. We need your help with deciding which toys go in each pack. We plan to put 3-
4 toys in each pack. We would like you to look at the data table and the pictures of
the toys and develop a plan to sort them into groups using one or more observable
properties. We would like you to create 3 example value packs. You do not have to use
all of the toys in the packs.
In your letter to us please tell us your plan for sorting the toys and attach your three
example packs.
Thank you for your help.
Sincerely,
Mrs. I. M. Fun
President

Sorting by Properties
Value Pack 1 Value Pack 2 Value Pack 3

Letter Template 1
Dear Terrific Toy Company,
Our team, __________________, has decided the best way to sort the toys is by:
______________________________________
______________________________________
The toys in Value Pack 1 are _____________________________________.
Sincerely,
______________________

Reading Passage 2
Dear students,
Thank you for your hard work in figuring out how to sort the toys
for our Value Packs. We need to keep the cost of each pack low. So,
we have added a point value to each toy. We need each pack not to
exceed 10 points. Also, we found some new toys to add to the packs. I
have included pictures with the new toys added. Please look at the
new set of data, the pictures and make any changes needed to your
plan so that we have 3-4 toys in each pack. Remember to explain your
process for sorting the toys and attach your 3 value packs to your
letter. Thank you for your time and we look forward to hearing from
you.
Thank you for your help.
Sincerely,
Mrs. I. M. Fun
President

Letter Template 2
Dear Terrific Toy Company,
Our team, __________________, has decided the best way to sort the toys is by:
______________________________________
______________________________________
______________________________________________________________________
______
The way we sorted the toys (did/ did not) change. (If it changed, explain how and why.
If it did not change, explain why not).
______________________________________________________________________
______
The toys in Value Pack 2 are___________________________________.
The toys in Value Pack 3 are___________________________________.
Sincerely,
______________________

Crazy Crayons!
SC.2.P.8.1 Observe and measure
objects in terms of their
properties, including size, shape,
color, temperature, weight,
texture, sinking or floating in water,
and attraction and repulsion of
magnets.

Reading Passage 1
Seashore Learning
246 Conch Road
Green Tide, FL 33580
Greetings,
I am in the process of purchasing some new crayons for my school supply store for the upcoming school
year. I need your assistance in choosing which brand of crayons I should purchase for the store. I have
researched several brands and have created a data table that includes the factors to consider when
purchasing crayons. I need for your team to come up with a procedure that will help me select the best
brand of crayons for my school supply store.
All of the information your team needs is located on the next page. Please write a letter to me with a list of
your "best to worst" brands in order to assist me with the decision making process. Furthermore, please
advise me as to which brand of crayons would be your "top choice" for my school supply store. Please
explain your team's procedure and include information that tells me how you came up with your decision
and describe your process.
Things to Consider When Buying Crayons:
Texture- Is the writing smooth or bumpy when you write on paper?
Vibrancy of color- Are the crayons bright or dull in color?
Color residue left on hands Does the crayon leave color on your hands?
Hardness/Breakage on scale of 1-3 (3-breaks very easily with normal use, 2-breaks with some normal use 1-
does not break with normal use) How easily are the crayons broken?
I look forward to hearing for you soon! I really appreciate your help.
Thank you,
Ferris Wheeler
Seashore Learning Owner

Data Set 1
Brand Cost for a
12 Pack
Transfer to Paper
(smooth/
bumpy)
Residue left
on hands
(yes/no)
Vibrancy of
color on paper
(bright/dull)
Hardness
Indigo 175¢ smooth No bright 1
Create 125¢ smooth Yes bright 2
Palm 100¢ bumpy Yes Dull 3
Liberty 150¢ bumpy No dull 1
Hardness:
1- does not break with normal use
2- breaks with some normal use
3- breaks very easily with normal use

Letter template 1
Dear Mr. Wheeler,
Our Team, ________________________, has
reviewed all of the data provided by you and
created a list in order from "best to worst" of brand
of crayon for your school supply store to possibly
purchase. The order is as follows:
Additionally, based on the data provided, our team
believes that the "top choice" of crayons for
Seashore Learning to purchase is the
_________________________ brand.
The procedure we used to determine the order
was:

Reading Passage 2
Seashore Learning
246 Conch Road
Green Tide, FL 33580
Greetings,
I want to thank you the terrific job that you did helping me select a brand of
crayons to purchase for my school supply store. The information in your letter was
very helpful. However, it has been brought to my attention by the store owner of
Starfish Education that a new brand of crayons just went on the market that may
just be what I may be looking for. In addition, Create Crayons just got marked down
to 100¢.
I need you to re-rank the brands from "best to worst" again with the new
information that I have given you. You may find that you need to change your
original procedure. When you write me the letter, please let me know your new
"best to worst" list and your "top choice" of crayons, and if your procedure
changed.
I look forward to hearing for you soon! I really appreciate your help.
Thank you,
Ferris Wheeler

Data Set 2
Brand Cost for a
12 Pack
Transfer to Paper
(smooth/
bumpy)
Residue left
on hands
(yes/no)
Vibrancy of
color on paper
(bright/dull)
Hardness
Indigo 175¢ smooth No bright 1
Create 100¢
sale
smooth Yes bright 2
Palm 100¢ bumpy Yes Dull 3
Liberty 150¢ bumpy No dull 1
Adventure 125¢ smooth no bright 2

Letter Template 2
Dear Mr. Wheeler,
Our team, ________________________, has reviewed the second set of
data provided by you and created a new list in order from "best to
worst" of crayon brands for your school supply store to possibly
purchase. The order is as follows:
Additionally, based on the data provided, our team believes that the
"top choice" of crayons for Seashore Learning to purchase is the
_________________________ brand.
Our procedure did/did not change because (please explain your
thinking):
The procedure we used to determine the order was (please explain your
thinking):

Molecular Gastronomy
SC.5.P.9.1 : Investigate
and describe that many
physical and chemical
changes are affected by
temperature.

Molecular Gastronomy
Reading Passage 1
1. What is the problem?
2. Who is the client?
3. What is the client asking your team to do?
4. What things do you need to include in your
solution?
5. How can you determine the cost per serving?.
6. Do you think there is more than one correct
answer to what the client is asking? Why or why
not?

Data Table 1
Menu Item Difficulty
of
Preparati
on
Number
of
servings
per
recipe
Cost per
recipe
Taste and
appeal
Rating (1-5)
5 is the
best score

Letter Template 1
• Dear Chef Chem,
• Our team has come up with a way to choose the
best item for you to enter into a competition.
• Here is an explanation of our procedure:
• We have ranked the choices for contest entries in
order from best to worst as follows:

Reading Passage 2
• Dear Chef Chem,
• We have found evidence that some of your menu items involve chemical
changes and have indicated the two that are physical changes.
• Some signs of chemical change include:
• Some indications of physical change are:
• We marked chemical changes with a C and chemical changes with a P and
listed or marked evidence to explain why.
• We think that you should enter _____________________ into the
competition because________________
• Sincerely,

Data Set 2 - Menu
Edible Flowers in Candy Glass
A mixture of clear fruit juices and liquid sugar reacts when mixed with
Kuzu starch to form thin, glass-like layers. Edible flowers are pressed
between these candy layers for an unusual sweet treat.

Data Set 2
What are some signs of chemical changes?
What are indicators of a physical change?
Where can we find more information about
these?

Letter Template 2
Dear Chef Chem,
We have found evidence that some of your menu
items involve chemical changes and have indicated
the two that are physical changes.
We marked chemical changes with a C and chemical
changes with a P and listed or marked evidence to
explain why.
We think that you should enter
_____________________ into the competition
because________________
Sincerely,

Saving Dodgeball
SC.3.P.8.3 :Compare
materials and objects
according to properties such
as size, shape, color, texture,
and hardness.

Reading Passage 1
Dear Students,
I am a representative of Your Sports Unlimited, a sporting goods superstore!
We sell a lot of sports equipment, including dodge balls. In fact, dodge balls
are our biggest sellers. It has come to our attention that many people think
that dodge ball is too dangerous of a sport, and we are concerned that we
will lose business unless we can market a new type of dodge ball. In order
to continue selling balls to use for dodge ball, we would like to pick a ball
that is already being used for another sport, and market it as a dodge ball as
well.
We have chosen 5 different sports balls, all with different properties.
Complete the properties chart using your scientific knowledge of properties.
Using the properties information, as well as the cost and profit information,
please rank the balls from best choice to worst. Send a letter back to the
company telling us which ball you feel will be most marketable, along with
your other rankings, and give reasons why you made the choice you did.
Please remember that this is a very important task, as our dodge ball market
is quite large. We thank you in advance for all of your hard work.
Regards,
The Dodge Ball Marketing Team at Your Sports Unlimited

Supplemental Reading
Dodgeball
Dodgeball is a game in which players on two teams try to throw balls at
each other while avoiding being hit themselves. There are many variations
of the game, but generally the main objective of each team is to eliminate
all members of the opposing team by hitting them with thrown balls,
catching a ball thrown by a member of the opposing team, or forcing them
to move outside the court boundaries when a ball is thrown at them.
The standard worldwide measurement and material for a dodgeball is a
seven-inch foam ball; however, most dodgeballs are roughly the size of a
volleyball and composed of foam with a thin plastic shell. Some dodgeballs
are made of rubber and some more specialized ones have a padded canvas
surface. Some leagues allow the use of multiple sizes of dodgeballs in a
single match, while others use one standard size for all balls.
Some gym teachers have modified dodgeball to lessen the chances of
injuries or bullying. For example, different types of balls can allow for
softer impacts. Modifying some rules of the game can allow students to
bounce the ball while playing.

Letter Template 1
Dear Your Sports Unlimited,
Our team, _______________________________, has
determined that the ______________________ is the best
replacement for the dodge ball. Below, please find the
ranking for the other balls.
Our procedure for determining the order of our ranking is
below.
__________________________________________________
Sincerely,

Reading Passage 2
Dear Students,
Thank you for determining the ranking of the replacements for
the dodge ball. This has been an extremely helpful first step,
and we have taken it all under advisement. Upon further
discussion, we have decided to add 3 more types of balls to the
choices, as well as share information about the weight of each
ball. We would also like to know how much profit we could
make from the sale of each type of ball.
In a follow up letter, please share any new procedures you used,
as well as the new ranking information that includes all of the
options. Also, please transfer your properties information to
the new data chart, and submit that with your letter.
Again, thank you for all of your help.
Regards,
The Dodge Ball Marketing Team at Your Sports Unlimited

Letter Template 2
Dear Your Sports Unlimited,
Using all of the new information as well as the old, our team,
_______________________________, has determined that
the ______________________ is the best replacement for the
dodge ball. Below, please find the ranking for the other balls.
_________________________
Our procedure for determining the order of our ranking is
below.
Some new information that we considered
was______________________________________________
____________________Sincerely,

Best Trading Cards Ever
SC.4.P.8.1: Measure and compare
objects and materials based on
their physical properties including:
mass, shape, volume, color,
hardness, texture, odor, taste,
attraction to magnets.

Reading Passage 1
Mr. T.R. Cards
Swap-n-Shop
123 Dealer Lane
Trade, Fl. 32111
Dear Students
We sell all kinds of trading cards. Our cards have themes such as cartoons,
sports, movies, animals, famous people, and super heroes. We need to know
which properties kids prefer to have in their trading cards. We would like for
you to consider the following criteria when developing your procedure to test
our products: the cost and value, durability, and the importance of properties
such as color, mass, texture, and size of the cards.
Please write back to us and explain how you decided which trading card is the
best and let us know why. Thank-you in advance for your hard work
Sincerely,
Mr. T.R. Card
President of Swap-n-Shop

Data Set 1
Texture:
glossy and
smooth or
dull and
slightly rough
Shiny
Durability-
How thick and heavy is
the card? (This is
measured by the mass
of the card, the more
mass the more durable
the card)
Measured in grams
Color scheme
and brightness
of cards
(1-5, where 5 is
the brightest or
most colorful)
Size
Cost of the Trading
cards- per package
Glossy,
smooth
4g 3 7cm x 9cm $4.00
Dull, paper
like feel
7g 5 9cm x 12cm $4.00
Glossy and
shiny with foil
7g 4 7cm x 9cm $6.50
Glossy back,
paper like
front
9g 4 6cm x 8cm $8.00
Slightly rough 7g 3 7cm x 9cm $3.00

Letter Template 1
Dear Mr. T.R. Cards
Our team has determined that the best Trading card to use with the criteria you
asked for; the popularity, cost and value, durability, and other connections to the
trading card such as does the trading card have a video game, movie or T.V. show
attached to its product? We ranked the trading cards from best (5) to worst (1) as
follows:
Procedure:
Each team was able to work with each trading card:
Then we ranked each trading card 1-5. (The best score is 5 and the worst score is 1).
The trading card that had the most points on the criteria you asked for and
is our choice for you and your company is;
We hope you are satisfied with the results.
Sincerely,

Reading Passage 2
Dear Students
Thanks for your help with our problem! However, we have
found some new information that we would like you to
consider.
We found a way to scent cards. We are also considering mini
cards. Please consider these two properties of matter and let
us know if they could be important to kids who collect trading
cards.
Sincerely,
Mr. T.R. Card
President Swap-n-Shop

Data Set 2
Texture: glossy
and smooth or
dull and slightly
rough
Shiny
Durability-
How thick and heavy is
the card? (This is
measured by the mass
of the card, the more
mass the more durable
the card)
Measured in grams
Color scheme
and brightness
of cards
(1-5, where 5 is
the brightest or
most colorful)
Size Scented Cost of the Trading
cards- per package
Glossy, smooth 4g 3 7cm x 9cm no $4.00
Dull, paper like
feel
7g 5 9cm x 12cm no $4.00
Glossy and shiny
with foil
7g 4 7cm x 9cm yes $6.50
Glossy back,
paper like front
9g 4 6cm x 8cm yes $8.00
Slightly rough 7g 3 7cm x 9cm no $3.00
Glossy, smooth 4g 3 3.5cm x 4.5cm no $3.00
Glossy and shiny
with foil
7g 4 3.5cm x 4.5cm yes $5.50

Letter Template 2
Dear Mr. T.R. Cards
Our team has determined that the best type of Trading card design based on the properties you
have listed. The properties we find the most important to the least important are:
1.(the most important property) _____________________________
2. ____________________________________________
3. ____________________________________________
4. ____________________________________________
5. (the least important property) ______________________________
We ranked the trading cards from best (1) to worst (5) as follows:
1. _______________________________________
2. _______________________________________
3. _______________________________________
4. _______________________________________
5. _______________________________________
We have listed our procedures for choosing as follows:
We hope you are satisfied with the results.
Sincerely,

Wire We All Wet?
SC.5.P.11.2: Identify and
classify materials that
conduct electricity and
materials that do not.

Data Set 1 Conductors
Material
Conductivity
Safety
Rating
Durability Defect
Rate
(%)
Other Information
Iron 1.00×107 4 2 80 Rusts easily, breaks easily
Copper 5.96×107 9 9 .009
Lead 4.55×106 2 9 .02 toxic
Platinum 9.43×106 10 10 .02 Very durable
Nickel 1.43×107 5 4 .06
Silver 6.30×107 10 3 .008 Corrodes more quickly than
gold
Lithium 1.08×107 1 1 99 Highly flammable
Harmful to skin
Gold 4.10×107 9 9 .01
Aluminum 3.5×107 9 7 .02 Lightweight

Data Set 1 Insulators
Insulation Types Fire
resistance
at high
temperatur
es
Ability to
keep its
shape/
resistance to
softening
Flexibility Weather
resistanc
e
Weight Releases
gases
Silicon Rubber fair good Fair good average poor
ETFE plastic good Fair
Poor at high
temperatures
good good average good
Crosslinked ETFE
plastic
fair excellent poor fair Lightest good
FEP plastic Excellent fair excellent good Very
heavy
good
Polymide plastic excellent excellent good poor Very
light
excellent

Data Set 2 Conductors
Material Cost per
ounce Conductivity
Safety
Rating
Durability Defect
Rate
(%)
Other Information
Iron $0.14 1.00×107 4 2 80 Rusts easily, breaks easily
Copper $0.20 5.96×107 9 9 .009
Lead $1.00 4.55×106 2 9 .02 toxic
Platinum $1460 9.43×106 10 10 .02 Very durable
Nickel $0.40 1.43×107 5 4 .06
Silver $22 6.30×107 10 3 .008 Corrodes more quickly than
gold
Lithium $17 1.08×107 1 1 99 Highly flammable
Harmful to skin
Gold $1350 4.10×107 9 9 .01
Aluminum $0.05 3.5×107 9 7 .02 Lightweight

Data Set 2 Insulators
Insulation Types Cost per
pound
Fire
resistance at
high
temperature
s
ability to keep
its shape/
resistance to
softening
flexibility Weather
resistance
Weight Releases
gases
Silicon Rubber $0.02 fair good Fair good average poor
ETFE plastic $0.05 good Fair
Poor at high
temperatures
good good average good
Crosslinked ETFE
plastic
$0.04 fair excellent poor fair Lightest good
FEP plastic $0.03 Excellent fair excellent good Very
heavy
good
Polymide plastic $0.04 excellent excellent good poor Very light excellent

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