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Find Math 2UU3 web page Click on the link for the online clickers, login, and reply to the
poll questions
Clicker question: You have one big cube, and dip it into yellow paint. Then you cut the cube horizontally, vertically, and sideways to obtain 27 small cubes, as shown. How many small cubes will have exactly two faces painted yellow?
12 8 6
… and one with no faces in yellow
From Tuesday’s lecture:
After class, I will insert clicker questions, your replies, answers, and comments here
From the last time: numeracy in
numeracy in
Correlation between global temperature and sea level changes
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Course material is guided by problem sets …
“Mathematics has no responsibility towards real life”
It is abstract (assumes infinity exists);
however, it appears naturally (think of counting, or symmetry)
it was created to answer real life questions (area, taxes, gambling)
and it turns out to be very useful
“Numeracy is all about real life”
It is always in context (which we either know, or have to learn about)
Math building blocks: DEFINITIONS
A prime number is a positive integer which has exactly two distinct divisors: number 1 and itself
Is 17 a prime number? Is 1002 a prime number? Is 1 a prime number?
Math definition is …
Math building blocks: DEFINITIONS
Math definition is:
Clear Concise Unambiguous independent of time, authority, politics, etc.
Why is this not a pipe?
Real life definitions: We do not usually say “Can you define this for me?” What do we say?
Real life definitions: We do not usually say “Can you define this for me?” What do we say?
• What is it? • Can you explain • What does it mean? • What’s the convention? • What is your understanding? • …
Real life definitions are …
… unclear, often not obvious
sodium free (last lecture) fat free, no fat, low fat
gray zones …
Is tomato a fruit or a vegetable?
gray zones …
Is tomato a fruit or a vegetable?
FRUIT … for botanists
VEGETABLE … for nutritionists
optional reading: http://www.thedailybeast.com/articles/2012/07/26/caster-semenya-and-the-ioc-s-olympics-gender-bender.html
gray zones … we cannot expect clarity of math definitions
prone to interpretations …
Sex (as assigned at birth): F, M, I
Gender: F, M, T (gender identity, gender expression, etc.)
Sexuality: straight, L, G, B, Q
Cis … sex=gender
definitions might not exist…
“species” in biology
… or depend on context
“evidence” in science
Mac Silhouette
optional: https://www.thesil.ca/mcmaster-developing-sexual-assault-policy
https://secretariat.mcmaster.ca/app/uploads/Sexual-Violence-Policy.pdf
definitions!
… misleading
optional reading: http://www.cbc.ca/news/canada/british-columbia/major-pet-insurer-says-dog-injuries-from-jumping-running-slipping-tripping-or-playing-not-covered-1.3781371
Important!
If not …
optional reading: http://www.cbc.ca/news/canada/calgary/cuba-vacation-gone-wrong-tv-1.4270994
definitions change … shyness vs social anxiety disorder
multiple definitions for the same thing … RED is
colour of fire, colour of blood
electromagnetic radiation, in visible light spectrum, wavelength of 620-750 nanometres
hexadecimal: #FF0000
RGB (red, green, blue); (255,0,0)
[in a computer, colours are represented by numbers, and are manipulated using numeric algorithms (e.g., effects in photoshop)]
Photoshop, Illustrator
Web page design
Even “obvious” needs to be defined – what is milk?
optional reading: https://www.theguardian.com/lifeandstyle/shortcuts/2017/jul/23/dairy-milk-court-animal-plant-nut
Real world definitions depend on:
Time (ADHD, SAD, Pluto is no longer a planet)
Authority (freedom fighter, terrorist)
History (young, adult, teenager)
Geography (driving under influence)
Culture (acceptable behaviour, nudity)
Etc.
We must know things … to be aware, to make good decisions
Another example:
Initially, when cell phones came out, their makers strongly denied any effects of cell phone radiation to human health
However …
optional reading: http://www.dailymail.co.uk/health/article-3227648/Mother-kept-phone-bra-day-10-YEARS-convinced-caused-terminal-breast-cancer.html
iPhone:
SAR limits for iPhone 5
Previous page source:
https://www.sportportactive.com/knowledge-base/iphone-safety-guidelines-rf-exposure-information/
Read more about RF exposure, if you wish:
https://www.cancer.org/cancer/cancer-causes/radiation-exposure/cellular-phones.html
Activity:
Hot cocoa: 99.9% caffeine free, in an 8 oz serving
Problem:
Create a mathematically sound argument showing that Starbucks Venti (20 oz) blonde roast cup of coffee (which has 475 mg of caffeine) can be claimed to be 99.9% caffeine free.
extra slides
extra slides
Quantitative reasoning …
Involves numbers, but unlike math, it is not abstract - the numbers always appear within a context
So, we can say that quantitative reasoning involves reasoning with, or about, numbers, and it applies to genuine real-life situations
In this course we will experience … [next page]