Ratios, Proportions, and ProbabilityRatios, Proportions, and Probability

Through Pecha Kucha:20 slides

In 6 minutes!

Why Lump All These Together?

They are used to easily compare things

Ratios!

Visually attractive in artAttractive in architectureAppears in nature: sunflowers and pinecones

The GOLDEN Ratio: Ya know, about 1.618 or so

Rates!

Change _______

time

Rates and Lightning

Lightning strikes somewhere on the earth at a rate of 6002 times per minute!

As you watch lightning strike, listen for the thunder! For every 5 seconds between a flash and the sound of thunder, there is 1 mile between you and the strike.

Unit Rates!

A rate where the bottom number represents 1 unit

Solving Proportions!

A proportion is an equation setting two ratios equal

EXAMPLE:

1 / 3 = ??? / 21

Scale Drawings and Ratios

Fractions, Decimals, Percents, Yikes!

Ratio → Percent (grades)

Decimal → Ratio ($)

Percent → Decimal

Example: Percent Proportion

= What percent?

Remember: percent means “out of 100”

What's Your Chance of Learning About Probability?

Sample Spaces

If you roll a die, the sample space is {1, 2, 3, 4, 5, 6}.

(It's a fancy word for 'all possible outcomes'!)

If you roll two dice, the sample space is the whole numbers 2-12

Simple Events: Probability Basics

All outcomes are equally likely to happen

Ex. Rolling an even number using a die.

It is equally likely that you roll any of the 6 numbers

Another “Simple Event”

The pieces of the pie are all the same size, so they all have an equal chance of happening

The Fundamental Counting Principle

What are all the different possible outcomes you can get if you flip a coin and roll two dice?

You just multiply the number of possible outcomes from each Event involved!

The Fundamental Counting Principle

Basically, if you have x ways of doing one thing, and y ways of doing another, then there are x times y ways of doing both things.

Relates to probability: What is the probability of you getting both your dice to land on 3 in the last experiment?

Types of Probability

What should happen?

Ex. How many times should you expect to get heads if you flip a quarter 50 times?

THEORETICAL PROBABILITY

Types of Probability

What actually happens when you perform an experiment?

Ex. How many times do you ACTUALLY get heads if you experiment by flipping the quarter 50 times in class?

Experimental Probability

Ta da!

Ratios

Rates

Probability

AWESOME

intmath.com – Golden Ratio Man

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