Decision Making By Design

Model Eliciting Activities

CollaborativeLearning

PeerTutoring

CooperativeLearning

Model-ElicitingActivities

Problem-BasedLearning

Active Learning

Peer-AssistedLearning

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 2Dear 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:

Fire Wheels

The Fire Wheels

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

Reading Passage 1Fire Wheels Toys31 Sea LaneDetroit, 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

Data Set 1

Letter Template 1Dear Fire Wheels Toy Company,Our team, ______________________________, has determined that you should use ______________. The order from best to worst is1) _________2) _________3) _________Our plan for ranking is ____________________________________________________________________________________________________________________________________.Sincerely,________________________________________________

Data Set 2

Reading Passage 2Fire Wheels Toy Company31 Sea LaneDetroit, 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 2Dear Fire Wheels Toy Company,Our team, ______________________________, has determined that you should use ______________. The order from best to worst is1) _________2) _________3) _________We changed/ did not change our system for ranking the cars because __________________________________________________________________Our plan for ranking is ____________________________________________________________________________________________________________________________________.Sincerely,________________________________________________

Terrific Toy Company

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 1Dear 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. FunPresidentTerrific Toy Company

Data Set 1

Sorting by PropertiesValue Pack 1 Value Pack 2 Value Pack 3

Letter Template 1Dear Terrific Toy Company,

Our team, __________________, has decided the best way to sort the toys is by:

____________________________________________________________________________

The toys in Value Pack 1 are _____________________________________.

The toys in Value Pack 2 are _____________________________________.

The toys in Value Pack 3 are _____________________________________.

Sincerely,

______________________

Reading Passage 2Dear 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. FunPresidentTerrific Toy Company

Data Set 2

Sorting by PropertiesValue Pack 1 Value Pack 2 Value Pack 3

Letter Template 2Dear 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 1 are _____________________________________.

The toys in Value Pack 2 are___________________________________.

The toys in Value Pack 3 are___________________________________.

Sincerely,______________________

Crazy Crayons

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 1Seashore Learning246 Conch RoadGreen Tide, FL 33580Greetings,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 WheelerSeashore Learning Owner

Data Set 1Brand Cost for a

12 PackTransfer 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 1Dear 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 2Seashore Learning246 Conch RoadGreen Tide, FL 33580Greetings,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 2Brand Cost for a

12 PackTransfer 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 2Dear 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):

MEA Lessons

Decision Making By Design

Model Eliciting Activities

CollaborativeLearning

PeerTutoring

CooperativeLearning

Model-ElicitingActivities

Problem-BasedLearning

Active Learning

Peer-AssistedLearning

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.

Molecular Gastronomy

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

Molecular GastronomyReading 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

Preparation

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 GlassA 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 1Dear 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 ReadingDodgeball

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.

Data Set 1

Letter Template 1Dear 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 2Dear 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

Data Set 2

Letter Template 2Dear 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,

The Best Trading Cards Ever!

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 1Texture:

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 2Dear StudentsThanks 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 2Texture: glossy and smooth or dull and slightly roughShiny

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 2Dear 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?

Wire We All Wet?

SC.5.P.11.2: Identify and classify materials that conduct electricity and materials that do not.

Reading Passage 1

Data Set 1 ConductorsMaterial

ConductivitySafetyRating

Durability DefectRate(%)

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 flammableHarmful to skin

Gold 4.10×107 9 9 .01

Aluminum 3.5×107 9 7 .02 Lightweight

Data Set 1 InsulatorsInsulation Types Fire

resistance at high

temperatures

Ability to keep its shape/

resistance to softening

Flexibility Weather resistan

ce

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

Reading Passage 2

Data Set 2 ConductorsMaterial Cost per

ounce ConductivitySafetyRating

Durability DefectRate(%)

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 flammableHarmful to skin

Gold $1350 4.10×107 9 9 .01

Aluminum $0.05 3.5×107 9 7 .02 Lightweight

Data Set 2 InsulatorsInsulation Types Cost per

poundFire

resistance at high

temperatures

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

MEA Lessons