Thinking About Modelling... Onsen-Tamago Style Eggs

In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674

Thinking about Modelling… Onsen-tamago style eggs https://www.plagiarismtoday.com/2010/01/12/how-to-correctly- use-creative-commons-works/ Robert Jordan

B.Eng, B.Sc Honours, B.Ed, OCT# 639674

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674

If you don’t know where you’re going, you will probably end up someplace else

---- Yogi Berra

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Overview

▪ IM2C - the need for a Canadian Modeling Contest

▪ What is a Modelling contest

▪ What is a Model / What students need to know

▪ Understanding Problem and Deriving a Plan

▪ Execute/ revise a plan and Validating and Conclusion

▪ How can Contest Supervisors Help

▪ Final Report Tips

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Mission

To provide Ontarian high school students with fun, unique and exciting experience where they construct, explain, justify, predict, and present a model with their mathematical skills and reasoning.

Not (only, just) to win but to have fun while learning!

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Modeling

• There is no unique deﬁnition or structure for Mathematical Modeling.

• We will differentiate modeling questions from real world application of mathematics by focusing on various factors

• Since, different factors must be pointed, we highly encourage groups to be a collection of members with different skills and different views

(interdisciplinary skill set within group)

• Typically Modeling Contest are a multi-day mathematics competition for High School Students and it is to promote students’ mathematical thinking while developing problem solving skills

• Create and early familiarity and practice of skills required for STEM

• Collaboration, Communication, Mathematical Thinking, Reasoning, Logic

"Teaching Mathematics Modelling." 2002. 27 Mar. 2016 This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Two Main Focuses Factual Based Scientiﬁcally Based

• Are all the facts taken • Do calculations make into consideration? sense?

• Does the Model • Is the mathematics represent the situation correct? well? • Would small changes in • Is every characteristic the model results in of the problem different outcomes deﬁned?

• Understand the problem: Determine where you are going?

• Plan a strategy for solving the problem: Decide how to go about solving it

• Execute your strategy and revise it if necessary: Carry it out

• Check and interpret your result: Don’t stop yet.

Does the model “make sense”?

How “sensitive” are the variables to the model’s results?

• Understand the problem, identify the unknowns

• Consider all the aspects, principals, the information, and how unknowns are related… be straight forward

• Find the “essence” of the problem - close to reality

• Introduce your goals in the model

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Deriving a plan

Divide the problem into cases / Carry out a plan

• Analyze each case

• Introduce every case with detail

• Show how data matches every case

• Look Back / Review your work

• Connecting Data to the Mathematics

• Conﬁgure Cases

• Use various methods to present the data

A ramen noodle shop wants to model a method to consistently, cook eggs in the Onsen-tamago style for a top their noodles.

Image Sources:

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Thinking through an Example QUESTIONS : Understanding and Planning The egg is traditionally cooked in hot spring water until the white is soft and the yolk slightly runny, but ﬁrm.

Image Sources: < http://benstarr.com/wp-content/uploads/2014/02/63egg.jpg> In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Thinking through an Example QUESTIONS : Understanding and Planning ###

They wish to use sous-vide water bath cooker with temperature control to achieve the same style egg.

Image Sources: In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Thinking through an Example Clients Requirements.

• Control egg consistency - yolk is runny but ﬁrm

• Meet Health Canada’s food handling and preparations regulations

• Farm Fresh, Free run, certiﬁed organic-unpasteurized

• Eggs need to made and ready to use at an economical price.

• NOTE: Health Canada,”Raw eggs can contain harmful bacteria. Eggs and egg- based foods should be cooked to an internal temperature of at least 74°C (165°F) to ensure they are safe to eat.”(1) Image Sources: References: (1) http://healthycanadians.gc.ca/eating-nutrition/healthy-eating-saine-alimentation/safety-salubrite/meat-viandes/eggs-oeufs- eng.php In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Understand the Problem

• Read the problem carefully! If it helps, read it aloud

• Record the quantities and conditions that are given (often called the data of the problem).

• Identify the knowns and unknowns. Exactly what is to be determined?

• Draw a picture or diagram to help you organize the information and visualize the problem.

• If possible, restate the problem in different ways to clarify or simplify it.

• At what temperature does each part start to solidify?

• What are the regulations regarding handling and cooking eggs?

• Temperature of bath and time at temperature? T_egg, T_bath

• To chill or not…. upon removal from bath?

• How to model heat ﬂow?

• MORE….? http://www.seriouseats.com/images/2013/10/20131004-sous-vide-101-egg-chorizo-corn-crouton-temperature-12.jpg This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Understand the Problem Egg data (1)

• Fresh egg whites coagulate in the range 62° to 65°C

• Egg yolks coagulate in the range 65° to 70°C.

• BUT 65°C is less the 74°C (2)

References • Health regulations ??? (1) http://newton.ex.ac.uk/teaching/CDHW/egg/ Image Source:http://www.scienceworld.ca/sites/ (2) http://healthycanadians.gc.ca/eating-nutrition/healthy-eating-saine-alimentation/ default/ﬁles/eggstrordinary_0.jpg safety-salubrite/meat-viandes/eggs-oeufs-eng.php This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Understand the Problem Food Handling Requirements.

• Store at below 4℃ before cooking (1) A plan is forming! • Use Pasteurized Eggs(2) in Recipes That Call For Raw or Undercooked Eggs

• 2h at 57℃ to pasteurize in the shell.(3)

References: (1) http://healthycanadians.gc.ca/eating-nutrition/healthy-eating-saine-alimentation/safety-salubrite/meat-viandes/eggs-oeufs-eng.php (2) http://www.aeb.org/images/Pasteurization_Manual.pdf (3) http://www.cookingissues.com/uploads/Low_Temp_Charts.pdf This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 State Simpler Cases

How much complexity do we need in the model?

• Include the shell? membrane?

• average diameter of egg?

• mass of egg?

• Assume constant thermal properties of yolk and white?

• Assume no convection within the egg?

• Get down the basics of what is happening…

• What are factors in heat ﬂow? What is the simplest model that has “good” results?

1-D 2-D 3-D

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Understand the Problem Scientific Definitions related to heat flow: Heat: energy flow from a hot body to a cold one Temperature: measure of which way heat will flow Specific Heat: the amount of heat required to raise the temperature of 1 kg of the substance by 1 Degree Celsius Latent Heat: heat added to change the state of a substance that does not change the temperature of the substance Thermal Diffusion: measure of thermal inertia. In a substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its volumetric heat capacity Convection: the transfer of heat by the circulation of the heated parts of a liquid or gas References: (1) http://healthycanadians.gc.ca/eating-nutrition/healthy-eating-saine-alimentation/safety-salubrite/meat-viandes/eggs-oeufs-eng.php (2) http://www.aeb.org/images/Pasteurization_Manual.pdf (3) http://www.cookingissues.com/uploads/Low_Temp_Charts.pdf This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 What Thermal History?

65° to 70°C 65° to 70°C ? mins OR ? mins 57℃ 57℃ serving 2 hrs hold temperature until 4℃ needed 4℃ 4℃ store, Temperature reheat & serve TIME This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 How can Contest Supervisors Help

Help with registration

Check that team follows Contest Rules

Meet submission deadlines

Help team upload solution summary and paper & signed forms

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Final Report Tips

• Don’t forget to write ! Write early, write often.

• Use online collaboration writing tools (Google Docs, SAGEmathcloud, ShareLaTeX)

• Summary that intrigues the reader and is clear and concise.

• Present models in a very logical manner.

• use visualizations ,to clarify the complexity and present ﬁndings.

• Explain assumptions very clearly

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Final Report Tips

• Analyze the model for solutions

• Test the model’s conclusions against test cases they constructed or found in their research

• Perform a sensitivity test to determine how the conclusions change based upon changes in the data thereby identifying the most relevant variables.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. In support of Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 Modelling Contest

• Motivate

• Instil in a sense of discovery and accomplishment in deﬁning and reﬁning their mathematical model

• Designed so there is always more to do!

• Applies mathematical thinking to real life problems.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Thank you!

In support of

Robert Jordan B.Eng, B.Sc Honours, B.Ed, OCT# 639674 This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.