Find Math 2UU3 web page Click on the link for the online ... · Clicker question: You have one big...

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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

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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]