You are buying candy for a class party. The local supermarket is

selling two bags of chocolate bars for $6. You want to buy five bags for the party. How

much will this cost you?

At the drugstore, you see you can by two bags of the same chocolate

bars as in the previous problem for $5. Which offers the better buy: the super market or the

drugstore?

Crystal placed a bucket under a leaky faucet and collected 6 ounces of water in 20 minutes. Joanne placed a bucket

under a second leaky faucet and collected 9 ounces in 25 minutes.

Were the faucets dripping equally fast or was one dripping faster than the

other?

Suppose that you have made a batch of green paint by mixing 2 cans of blue paint

with 7 cans of yellow paint. What are some other combinations of cans of blue paint and cans of yellow paint that you can mix

to make the same shade of green?

On a city center map, 18 centimeters represents an actual distance of 15 miles. What actual distance is represented by 9 cm on the map? Draw a diagram as part of your solution.

1. If the small gear turns clockwise, which direction does the big gear turn?

2. If you turn the small gear a certain number of times, does the large gear turn more revolutions, fewer, or the same amount? How can you tell?

3. Find a way to keep track of how many revolutions the small gear makes. Find a way to keep track of how many revolutions the large gear makes. How can you keep track of both at the same time?

Connected Gears ProblemSay you have a small gear with 8 teeth connected to a big gear with 12 teeth.

Zora sells pasta and sauce and charges $3.00 for a 7-ounce jar or

$16.00 for two jars that hold a total of 37⅓ ounces. Is buying a 7-

ounce jar a better deal that buying two jars that hold 37⅓ ounces?

How do you know?

Notes on Ratio and Rate 1/31

A ratio is a comparison of two quantities with a multiplying relationship, or two quantities joined to make a single unit of measurement.

A ratio answers the questions:• What part of one thing is another thing?• How many times bigger is thing 1 than thing 2?

You can answer the questions by writing a ratio using words, a colon, or a fraction.

Notes on Ratio and Rate (continued) 1/31For example: How many times longer is Worm A than Worm B?

Write a ratio to find out:

As a fraction:Worm A = 6 = 3 = 3⁄2 = 1½ Worm B 4 2

You could say, “Worm A is 1 ½ times bigger than Worm B” or, you could also say ,“Worm B is ⅔ the length of Worm A” and mean the same thing.

Notes on Ratio and Rate (continued) 1/31A rate is a ratio that compares two measurements with different units.

A rate can show change.

Example: Express the following rate as a ratio:My car can travel 75 miles for every three gallons of gas in my tank.

Words: 75 miles to 3 gallons, or 25 miles to 1 gallonColon: 75:3 or 25:1Fraction: 75 or 25 3 1

Notes on Ratio and Rate (continued) 1/31A Unit Rate is rate that tells how much of the first quantity relates to ONE UNIT of the other quantity

For example:

If it costs $3.50 for 2 bags of oranges, how much does one bag cost?

This is a unit rate!