Ratios, Proportions and Probability Explained in 6 Minutes
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A Pecha Kucha (20 slides in 6 minutes) presentation meant to be a useful introduction and overview for a 7th grade middle school mathunit on Ratios, Proportions, and Probability
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Ratios, Proportions and Probability Explained in 6 Minutes
- 1. Ratios, Proportions, and ProbabilityRatios, Proportions, and Probability Through Pecha Kucha: 20 slides In 6 minutes!
- 2. Why Lump All These Together? They are used to easily compare things
- 3. Ratios!
- 4. Visually attractive in art Attractive in architecture Appears in nature: sunflowers and pinecones The GOLDEN Ratio: Ya know, about 1.618 or so
- 6. 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.
- 7. Unit Rates! A rate where the bottom number represents 1 unit
- 8. Solving Proportions! A proportion is an equation setting two ratios equal EXAMPLE: 1 / 3 = ??? / 21
- 9. Scale Drawings and Ratios
- 10. Fractions, Decimals, Percents, Yikes! Ratio → Percent (grades) Decimal → Ratio ($) Percent → Decimal
- 11. Example: Percent Proportion = What percent? Remember: percent means “out of 100”
- 12. What's Your Chance of Learning About Probability?
- 13. 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
- 14. 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
- 15. Another “Simple Event” The pieces of the pie are all the same size, so they all have an equal chance of happening
- 16. 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!
- 17. 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?
- 18. 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
- 19. 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
- 21. intmath.com – Golden Ratio Man www.curly-hair-styles-magazine.com – Marilyn www.contactmusic.com - Lady GaGa library.thinkquest.org – mona lisa www.tvscoop.tv - Clarkson going fast www.scienceblogs.com -pie www.caption-this.com – dice www.pwcphoto.com - dice houseofmashinchi.blogspot.com – spinner www.pokerxclusive.com - poker hand
Editor's Notes
- Describe: Why they are all in one unit? All about comparing things: comparing two things from the same group (like comparing students from my class to students from another teacher's class), comparing two things that are very different (like comparing people to weight), seeing how two things change (how often they change, how drastic they change) and if they change the same over time. Then, we will think about how things change to PREDICT THE FUTURE!
- Ratios: -Ratios are how you compare two things that are the same -Example of ratios: comparing gallons of milk to gallons of OJ -comparing similar stats of different Athletes (like how far certain runners ran in the same period of time) -math history=golden ratio=the idea that all limbs on a human being have a ratio that are the same magic number, and that this was the idea of the “perfect” human being. (note Da Vinci and artwork, statues, sketches) Also, the construction of the Egyptian pyramids are analyzed by math people in terms of the golden ratio
- A special kind of ratio is known as the Golden Ratio. This is an extremely famous ratio discovered in math history by a dude named Fibonacci. It is pretty much determining two numbers whose combined length satssfies the ratio shown. The ratio of the whole length to the long part is equal to the long part to the short part. ---human portraits (Golden square of Mona Lisa's face, ratio of upper torso to bottom torso) ----sunflower seeds spiral out from the center in two directions one direction spirals with 21 seeds, the other spirals with 34. These numbers create the golden ratio as well.
- Rates: a type of ratio that compare two different things. --instead of comparing stats of two athletes, you could compare number of baskets made per minute. (comparing baskets and minutes) --the most common application of rates is in cars...fast cars! MPH, KMH (in europe) --with rates comes something called rate of change:it's like walking on a hill; if the hill is changing very quickily uphill, then it has a large rate of change. If the hill is the same all the way up, then it has a constant rate of change. If the hill is going down, then it has a negative rate of change. like the height of someone changing over time. Rate of change usually looks at a pattern over time. Another example: distance you have traveled on a bike over time. Think about it, you get tired! So your rate of change will get slower over time because your legs get tired
- Rates are all over the world, just like lightning! You can use rates to see how often something happens (like per minute, per hour, per day, per year) According to scientists, lightning strikes on earth about 6002 times every minute! Along with lightning, meteorologists use rates to describe how fast a tornado is moving, which direction it is moving in, and how fast its winds are blowing. Chances are, if the tornado is blowing harder than 50 mph, you will want to seek shelter
- Scale drawings: --can also use ratios to draw things according to a scale. EXAMPLE: Map/globe. Ever wonder how people tell how far a distance is just by looking at a tiny map? The people who make the map draw it to a “scale” (circle scale on the Google Map) The same thing happens for designing models. Architects draw houses to scale, and use that scale to make the actual house. You can draw something really small to represent something really big. Designing boats, houses, basketball courts, tables, even electronics.
- You will most certainly learn about probability, and so you have a 100% chance of learning about probability! Probability covers all sorts of situations, but is seen largely in games. Games of chance like poker and rolling dice are common. In poker, what is the chance that you are randomly given the 4th king if another player already has 2 kings? Also, think of the show The Price is Right. What is the chance you will guess the right price out of 5 possibilities?