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The Soda Problem!!

The Soda Problem!!. William Johnson Virtual 8 th grade Math class. On Today’s agenda…. Let’s take a look at the…….(wait for applause)…The Soda Problem!!! Let’s break down the Problem into sizeable chunks Look at some core concepts like rate of change and ratios that fit with today’s lesson!.

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The Soda Problem!!

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  1. The Soda Problem!! William Johnson Virtual 8th grade Math class

  2. On Today’s agenda… • Let’s take a look at the…….(wait for applause)…The Soda Problem!!! • Let’s break down the Problem into sizeable chunks • Look at some core concepts like rate of change and ratios that fit with today’s lesson!

  3. Now, just how are we gonna do this? • We are going to work individually on this. • You can share your answers with others after I say so at specific points during the lesson to check your work. • Feel free to ask questions to me or others anytime during the lesson! We’re here to help each other.

  4. You should probably know this. • I want you guys to get a grip around the basics of ratios and rate of change for today's lesson. • A ratio can be summed up as a relationship between two numbers of the same kind. For Ex.) 1 boy:2 girl ratio in school. Meaning there is 2 girls for every 1 boy in class! • A rate of change can be described as a certain ratio changing over time. For Ex.) The slope of a graph is considered a rate of change as its data is changing over time! • A unit rate is comparing the number of units in the first quanity to the number of units in the second quanity. For Ex.) Miles-per-hour or Cost-per-item.

  5. The Soda Problem: The beginning…duh..duh….DUH • A store is selling sodas in bundles of (1), (2), (3), (4), and (5). The standard cost for one soda is $3.50. This cost per item is a unit rate! • The bundles are priced as so. • (1) = $3.50 • (2) = $6.50 • (3) = $9.50 • (4) = $12.50 • (5) = $15.50

  6. The Soda Problem Continued? • By using simple division, we can see that in the bundle of 2, each soda is technically only $3.25. In the bundle of 3, if we divide the price by 3, each soda technically costs $3.17. How much does each soda cost in the bundle of (4) and (5)? What kind of ratios can we see?

  7. More of The Soda Problem!! • We can also look at the savings for each bundle when comparing it to the standard price of an individual soda. • The bundle of (2) should technically cost $7.00 at the standard price of $3.50 for each soda, but in reality it costs $6.50 producing a savings of $0.50. • We can do this as well for the other bundles! • (1) = $3.50, actual cost=$3.50, savings=$0.00 • (2) = $6.50, actual cost=$7.00, savings=$0.50 • (3) ??? • (4) ??? • (5) ??? • Find the savings in bundles (3), (4) and (5).

  8. The End of the Soda problem! • When looking at the savings, from bundle (1) to bundle (5), what kind of rate of change can we notice?

  9. Almost there guys! • If you guys and gals guessed $0.50 per change in the amount of savings between each bundle, you would be perfectly correct! Astounding job my wee little geniuses! Huzzah!! • Extra Credit: If the Soda Company makes the sodas for $3.00 each, and any money after that is profit. How much profit is made if a bundle of (1) is bought compared to a bundle of (5)? Are these proportional?

  10. Review • Types of ratios we saw! • Types rate of change we saw! • Types of unit rate we saw! • Wasn’t that review just…..magical!

  11. Mission Accomplished! • Congratulations guys and gals!!! You solved the almighty Soda Problem!! Are you okay? Was it really that tough? Will you explode from the brain power you just mustered out? • Now that you’ve had that time to ponder your life. Go think of the amazing and unique ways you can use ratios and rate of change in your everyday life. We’ll look at some of these examples in class tomorrow! Bring your game face chillens!

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