Pizza with LAFS

Pizzanomics: Interdisciplinary Decision Making

Deborah Kozdras USF Stavros CenterAngel Danger, Hillsborough County School District

Thank-you to State Farm for their generous funding of this workshop

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.

Reading Passage 1Dear Pizza Lovers,I am the owner of George’s Pizza Place. I am famous for making unusual and unique pizzas. I am looking for a new pizza topping to add to my menu, and I need your help!I have been working in the kitchen, and I came up with four yummy new toppings, but I can only add one to my menu at this time. I like to keep my pizza prices low, so that they are not too expensive for people to buy. I want to add a pizza that tastes great, doesn’t cost a lot, and is unique.

Can you please look at the data table and come up with a plan to rank my new pizza toppings from best to worst? The number of pizza slices in each category show how that pizza topping rated in each category.Please write back soon to let me know how you ranked the pizzas.Also, please explain the procedure you used, so I can explain it to my employees.Thank you,Mr. Hat, Owner of George’s Pizza Place

• LAFS.K.RI.1.1 With prompting and support, ask and answer questions about key details in a text.• LAFS.K.RI.1.2 With prompting and support, identify the main topic and retell key details of a text.

http://www.cpalms.org/Public/PreviewStandard/Preview/5726


LAFS.K.SL.1.2 Confirm understanding of a text read aloud or information presented orally or through other media by asking and answering questions about key details and requesting clarification . . .LAFS.K.SL.1.1 :Participate in collaborative conversations with diverse partners about kindergarten topics and texts with peers and adults in small and larger groups.

Data Set 1


Letter 1 TemplateDear Mr. Hat,

Our team, __________________________________, thinks that the order of pizzas, from best to worst, is1. ____________________________________2. _____________________________________3. _____________________________________4. _____________________________________The procedure we used to come up with this answer is______________________________________________________________________________________________Sincerely,

LAFS.K.W.2.5• With guidance and support from adults, respond to questions and suggestions from peers and add

details to strengthen writing as needed.



Reading Passage 2Dear Pizza Lovers,

I enjoyed reading your last letters. Thank you for your helpful suggestions. I am writing to you today because I had to make a change to the list I gave you last time. One of my cooks has an allergy to peanuts, so I took the Peanut Butter and Jelly pizza off the menu. I want to keep everyone healthy!

I have been experimenting in the kitchen again, and I came up with a new pizza with lots of fresh vegetables straight from my garden. I think this will make a great, healthy pizza. I added a new category to the data table, so that you can consider how healthy each pizza is.

Now, I need your help. Since the data table has changed, can you please look at it and rank the pizzas again? Be sure to let me know if your procedure had to change. I am excited to get your new letters. I can’t wait to add the newest pizza to my menu!Thank you again,Mr. Hat

Data Set 2

Letter 2 TemplateDear Mr. Hat,

Our team, __________________________________, thinks that the order of pizzas, from best to worst, is1. ____________________________________2. _____________________________________3. _____________________________________4. _____________________________________We _________ did/did not have to change our procedure.The changes we made were_________________________________________________Sincerely,

Reading Passage 1Dear Team,My friend George is having a birthday next week! Since he loves pizza parties so much, I have decided to have a special pizza party for his birthday. Instead of making our own pizza like we did at our friend’s party, I have decided to order pizza for George’s party. (This way he is less likely to get into trouble, like he always seems to do!)I need your help deciding which pizza place to use for George’s party. George loves lots of toppings on his pizza and I want to make sure we order from somewhere reliable and easy to work with. I also want to make sure that I don’t spend too much money on the pizza because I want to buy decorations and favors for the party too. I did some research about the pizza places in our area and made a table for your team to use. Please help me choose the best place by ranking the options from best to worst. Then write me a letter back telling me how you ranked the four pizza places and why you chose those rankings. Thank you so much for your help and I look forward to hearing from you soon!Sincerely,The Man with the Yellow Hat

LAFS.1.RI.1.1 Ask and answer questions about key details in a text.LAFS.1.SL.1.1:Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups.



Data Set 1 Topping

OptionsCrust Options Available

ExtrasCost per

PizzaCustomer

SatisfactionPizza

PalaceChoose frommore than 15

differenttoppings!

Three crustoptions: pancrust, thin &

crispy crust, orclassic hand

tossed

Dipping sauces,wings, cinnamonstreusel dessert

pizza, 2-litersodas

$8.00 each ✰✰

Paul’sPizzeria

Standardtoppings only

(cheese orpepperoni)

Classic handtossed crustonly (secret

family recipefrom Italy)

Breadsticks orcheese sticks

$9.00 each ✰✰✰✰✰

Pizza!Pizza!

Pizza any wayyou want it!

You name thetopping, we will

have it!

Five crustoptions: deep

dish, thin &crispy, hand

tossed, cheesestuffed, or

garlic seasoned

Dipping sauces,wings,

breadsticks,cheese sticks,

cinnamon sticks,pasta, 2-liter

sodas

$12.00 each ✰✰✰✰

PizzaShack

Choose frommore than 30

differenttoppings



tossed

Breadsticks,cheese sticks,

wings, cinnamonstreusel dessert

pizza

$10.00 each ✰✰✰

LAFS.1.SL.1.2: Ask and answer questions about key details in a text read aloud or information presented orally or through other media.


Letter Template 1

Dear Man with the Yellow Hat, Our team, _____________, has decided to rank the pizza places you suggested in the following order: 1.____________________ 2.____________________ 3.____________________ 4.___________________ Here is how we chose these rankings. _______________________________________Your friends, _____________________

LAFS.1.W.1.1 Write opinion pieces in which they introduce the topic or name the book they are writing about, state an opinion, supply a reason for the opinion, and provide some sense of closure.


Reading Passage 2Dear Team, Thank you so much for all of the hard work you did ranking the pizza places for George’s party. The party is getting close and I’ve already sent out the invitations and heard back about who will be attending. Based on the number of guests we are going to have I am going to need to order three pizzas. Planning this party has been more expensive than I thought it would be, so I did a little bit of research about some promotions that each pizza place offers so I can get the best deal. I added this information to the chart and since you did such a great job the first time, I need your help again! Please use the chart to calculate the total cost for three pizzas from each pizza place. Don’t forget to consider the promotions when solving for the price. Then use the new information you have and the information from before to rank the pizza places again and help me choose the best one. You may find that you need to change your original rankings. Write me a letter back telling me the price for three pizzas from each pizza place, and how you ranked them. In your letter make sure you tell me if you needed to change your rankings and why. Thank you so much for your help! Sincerely, The Man with the Yellow Hat

Data Set 2 Topping

OptionsCrust Options Available

ExtrasCost per

Pizza Customer

SatisfactionPizza

PalaceChoose frommore than 15

differenttoppings!



tossed


cinnamonstreusel dessert

pizza, 2-litersodas

$8.00 each Three pizzas

for only$5.00 each!

✰✰

Paul’sPizzeria

Standardtoppings only

(cheese orpepperoni)

Classic handtossed crustonly (secret

family recipefrom Italy)

Breadsticks orcheese sticks

$9.00 each Buy any two

pizzas for$9.00, andget a third

for only$1.00!

✰✰✰✰✰

Pizza!Pizza!

Pizza any wayyou want it!

You name thetopping, we will

have it!

Five crustoptions: deep

dish, thin &crispy, hand

tossed, cheesestuffed, or

garlic seasoned


breadsticks,cheese sticks,

cinnamon sticks,pasta, 2-liter

sodas

$12.00 each Three pizzas

for only$6.00 each!

✰✰✰✰

PizzaShack

Choose frommore than 30

differenttoppings



tossed

Breadsticks,cheese sticks,

wings, cinnamon

streusel dessertpizza

$10.00 each Buy twopizzas, getone free!

✰✰✰

Letter Template 2Date: ___________ Dear Man with the Yellow Hat, Considering the special promotions, this is how we ranked the pizza places along with the cost for three pizzas from each.1.___________ $__.__ 2.___________ $__.__ 3.___________ $__.__ 4.___________ $__.__ Here is how we chose these rankings. _______________________________________Your friends, _____________________

Reading Passage 1

Dear Students,George’s pizza just won an award as Kid’s Choice for the best tasting pizza! We are very happy. We want to celebrate by offering a pizza special to schools. We have decided that we will charge $10.00 per pizza and donate the change to our local zoo to help the monkeys. Can you help me decide which pizza we should offer to schools as this special offer? We want to offer a pizza that the most kids will want and that we can make the raise money by selling. The pizza with fresh sauce tastes better, but costs more to make. Thick crust pizza feeds more people than thin crust pizza. Please see the information in the data table and let me know what we should do.I look forward to your response,Sincerely,LAFS.2.RI.1.1 Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.LAFS.2.SL.1.1 :Participate in collaborative conversations with diverse partners about grade 2 topics and texts with peers and adults in small and larger groups.



Dataset 1

Types of Pizza

Sause Crust Number of slices

Cost Change from $10

A Fresh Thin 8 $7.82

B Fresh Thick 10 $9.45

C Can Thin 8 $6.86

D Can Thick 10 $7.98

LAFS.2.SL.1.2Recount or describe key ideas or details from a text read aloud or information presented orally or through other media.


Letter Template 1Our team, ________________________________, has ranked your pizzas in the followingorder:1. _____________________2. _____________________3. _____________________4. _____________________We ranked your pizzas using the following procedure:____________________________________________________________________________________

LAFS.2.W.1.1 Write opinion pieces in which they introduce the topic or book they are writing about, state an opinion, supply reasons that support the opinion, use linking words (e.g., because, and, also) to connect opinion and reasons, and provide a concluding statement or section.


Reading Passage 2Dear Students,I want to thank you for the great job that you did. You were a big part of our success!I need your help, again! Parents and teachers want to serve kids a healthier pizza. Whole wheat flour ishealthier but more expensive.I have added new information to the next page so you can rank the pizza again. Can you rank the pizzas with the new information and write me back soon? Let me knowif you could rank them the same way you did last time or came up with a new way.Please include your procedure for ranking the pizzas in your letter.Sincerely, Mr. C. George

Data Set 2 Types of

Pizza

Sause Crust Number of slices

Cost with

white flour

Added Cost with

whole wheat flour

Cost of pizza with

whole wheat flour

Change from $10

A Fresh Thin 8 $7.82 + $0.50

B Fresh Thick 10 $9.45 + $0.50

C Can Thin 8 $6.86 + $0.50

D Can Thick 10 $7.98 + $0.50

E Fresh Hand Tossed

9 $8.53 + $0.50

Letter Template 2Our team, ________________________________, has ranked your pizzas in the followingorder:1. _____________________2. _____________________3. _____________________4. _____________________We ranked your pizzas using the following procedure:Here is how we chose these rankings. _______________________________________Your friends, _____________________


I am trying to find the best pizza special for school pizza parties. I want to find the pizza place that offers the best deal, but also has a pizza and toppings that students will love.

I have gathered information from several pizza places that deliver to schools in our area. All of the pizzas listed in this data table cost $10 per pizza. Please discuss this data as a team and let me know which pizza place we should choose. Please explain how your team made this decision.Thank you, Mrs. Azzip

LAFS.3.RI.1.1 :Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.LAFS.3.SL.1.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others ideas and expressing their own clearly.



Data Set 1

Size of pizza

Fraction of pizza each

student receives

Toppings available (pick up to 2)

Taste rating

George’s Pizza Large 2/4 Cheese only *****Pizza, Pizza,

PizzaMedium 2/4 Cheese, sausage,

pepperoni, mushrooms, onions, pineapple, ham

****

Pizza Shack Large 1/4 Cheese, sausage, pepperoni, mushrooms, onions, pineapple, ham,

barbecue chicken

****

Italiano’s Pizza Large 2/4 Cheese, sausage, pepperoni, bacon, bell

peppers, tomatoes

**

Little Brutus Pizza

Medium 1/4 Cheese, sausage, pepperoni, bell peppers, mushrooms, anchovies

****

More *s means better tasting pizza.

LAFS.3.SL.1.2 Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.

Letter Template 1Dear Mrs. Azzip,

Our team, __________________________________, thinks that the order of pizza places, from best to worst, is1. ____________________________________2. _____________________________________3. _____________________________________4. _____________________________________The procedure we used to come up with this answer is__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Sincerely,_______________________________________

LAFS.3.W.1.1 Write opinion pieces on topics or texts, supporting a point of view with reasons. Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons….



Thank you so much for your letters. Remember, I am trying to find the best pizza special for school pizza parties. I want to find the pizza place that offers the best deal, but also has a pizza and toppings that students will love.

Some students and teachers told me that cutting the pizzas into fourths made the slices too big. I have asked for smaller slices and provided you with new data to show what the pizza places have offered.

All of the pizzas listed in this data table cost $10 per pizza. Please discuss this new data as a team and let me know which pizza place we should choose. Please explain how your team made this decision.Thank you, Mrs. Azzip

Data Set 2 Size of pizza Fraction of

pizza per student


Taste rating

George’s Pizza

Large 3/6 Cheese only *****

Pizza, Pizza, Pizza

Medium 3/6 Cheese, sausage, pepperoni, mushrooms, onions,

pineapple, ham

****

Pizza Shack Large 2/8 Cheese, sausage, pepperoni, mushrooms, onions,

pineapple, ham, barbecue chicken

****

Italiano’s Pizza

Large 3/8 Cheese, sausage, pepperoni, bacon, bell peppers, tomatoes

**

Little Brutus Pizza

Medium 3/8 Cheese, sausage, pepperoni, bell peppers, mushrooms,

anchovies

****


Letter Template 2Dear Mrs. Azzip,Our team, __________________________________, thinks that the order of pizzas, from best to worst, is1. ____________________________________2. _____________________________________3. _____________________________________4. _____________________________________We _________ did/did not have to change our procedure.The changes we made were_________________________________________________________________________________________________________________________________________________________________________________________________________________Sincerely,

Formative Assessment questions:

1. Jose ate 2 slices of pizza. Kathy ate 4 slices of pizza. Jose says that he and Kathy ate the same amount of pizza. Using the fraction circles show and explain how Jose could be correct.

2. Dante ate 2 slices from a pizza that was cut into 4 slices. How many slices of a pizza cut into 8 slices would he have to eat to have eaten the same amount of pizza?

Reading Passage 1

Dear Pizza Lovers,I am trying to find the best pizza special for school pizza

parties. I want to find the pizza place that offers the best deal, but also has a pizza that students will love.

I have gathered information from several pizza places in our area that sell pizza by the slice. I have asked them each how much pizza we can buy with $20. Please discuss this data as a team and let me know which pizza place we should choose. Please explain how your team made this decision.Thank you, Mrs. Azzip

LAFS.4.RI.1.1 Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.LAFS.4.SL.1.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others ideas and expressing their own clearly.



Data Set 1 Fraction of pizza

sold for $20Taste rating

George’s Pizza

8/6 *****Pizza, Pizza,

Pizza5/4 ****

Pizza Shack 12/12 ****Italiano’s

Pizza4/3 **

Little Brutus Pizza

10/8 ****


LAFS.4.SL.1.2 Paraphrase portions of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.


Letter Template 1Date ___________________

Dear Mrs. Azzip,

Our team, __________________________________, thinks that the order of pizza places, from best to worst, is1. ____________________________________2. _____________________________________3. _____________________________________4. _____________________________________The procedure we used to come up with this answer is__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Sincerely,

LAFS.4.W.1.1 Write opinion pieces on topics or texts, supporting a point of view with reasons and information.



Thank you so much for your letters. Remember, I am trying to find the best pizza special for school pizza parties. I want to find the pizza place that offers the best deal, but also has a pizza and toppings that students will love, so I have added the available toppings to the data table.

Some students and teachers told me that some of the slices were too big. I have asked for smaller slices and provided you with new data to show what the pizza places have offered.

The data table shows how much pizza can be bought for $20. Please discuss this new data as a team and let me know which pizza place we should choose. Please explain how your team made this decision.Thank you, Mrs. Azzip

Data Set 2 Fraction of

pizza sold for $20


Taste rating

George’s Pizza

16/12 Cheese only *****Pizza, Pizza,

Pizza10/8 Cheese, sausage, peperoni, mushrooms,

onions, pineapple, ham ****Pizza Shack 12/12 Cheese, sausage, peperoni, mushrooms,

onions, pineapple, ham, barbeque chicken

****Italiano’s

Pizza8/6 Cheese, sausage, peperoni, bacon, bell

peppers, tomatoes **

Little Brutus Pizza

20/16 Cheese, sausage, peperoni, bell peppers, mushrooms, anchovies ****

.

More *s means better tasting pizza

Letter Template 2Dear Mrs. Azzip,Our team, __________________________________, thinks that the order of pizzas, from best to worst, is1. ____________________________________2. _____________________________________3. _____________________________________4. _____________________________________We _________ did/did not have to change our procedure.The changes we made were_______________________________________________________________________ Sincerely,

Reading Passage 1 Dear Pizza Lovers,

I am trying to find the best pizza special for school pizza parties. I want to find the pizza place that offers the best deal, but also has a pizza that students will love.

I have gathered information from several pizza places in our area that sell pizza by the slice. I have asked them each how much pizza we can buy with $20. Please discuss this data as a team and let me know which pizza place we should choose. Please explain how your team made this decision.

Thank you, Mrs. Azzip LAFS.5.RI.1.1 Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from

the textLAFS.5.SL.1.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others ideas and expressing their own clearly .



Data set 1 Fraction of

pizza per student


Taste rating

George’s Pizza 8/6 Cheese only *****Pizza, Pizza,

Pizza5/4 Cheese, sausage, pepperoni,

mushrooms, onions, pineapple, ham

****Pizza Shack 12/12 Cheese, sausage, pepperoni,

mushrooms, onions, pineapple, ham, barbeque

chicken

****

Italiano’s Pizza 4/3 Cheese, sausage, pepperoni, bacon, bell peppers,

tomatoes**

Little Brutus Pizza

9/4 Cheese, sausage, pepperoni, bell peppers, mushrooms,

anchovies****

Letter Template 1 Dear Mrs. Azzip,Our team, __________________________, has determined the following procedure for ranking:

The order that we ranked our choices from highest to lowest is:

Sincerely, _________________________________

LAFS.5.W.1.1 Write opinion pieces on topics or texts, supporting a point of view with reasons and information.


Reading Passage 2 Dear Pizza Lovers,

Thank you so much for your recommendations.

The data table shows how much pizza can be bought for $20. We have 20 students and want to give each student at least ¼ of a pizza. What will it cost to provide ¼ or more of each pizza to our students? Please fill in the data table with this information. Please discuss this new data as a team and let me know which pizza place we should choose. Please explain how your team made this decision.

Thank you, Mrs. Azzip

Data Set 2 Amount

of pizza for $20Cost to feed 20 students each ¼ or more of a

pizza.


Taste Rating

George’s Pizza 8/6 Cheese only *****Pizza, Pizza,

Pizza5/4 Cheese, sausage, pepperoni,

mushrooms, onions, pineapple, ham

****Pizza Shack 12/12 Cheese, sausage, pepperoni,

mushrooms, onions, pineapple, ham, barbeque chicken

****

Italiano’s Pizza 4/3 Cheese, sausage, pepperoni, bacon, bell peppers, tomatoes **

Little Brutus Pizza

9/4 Cheese, sausage, pepperoni, bell peppers, mushrooms, anchovies ****

LAFS.5.SL.1.2Summarize a written text read aloud or information presented in diverse media


Letter Template 2

Dear Mrs. Azzip,

Our team, ____________________________________________, has completed the table with the information you requested. The way we figured it out was:

We have determined the following procedure for ranking:

Our procedure for ranking (did / did not) change. (If procedure changed, explain how and why. If procedure did not change, explain why not).

The order that we ranked our choices from highest to lowest is:1. ___________________________2. ___________________________3. ___________________________4. ___________________________5. ___________________________

Sincerely, _________________________________

MEA Lessons

Pizza with LAFS

Education

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