3.8

3.83.8

This logic building problem is a TEAM activity.

Peter bet Bill $10 dollars he would beat him in a 100 yard race. Bill took the bet, they raced, and Peter won by 5 yards. Upset by the loss, Bill asked for a ‘double or nothing’ rematch, but to be fair this time Peter must start 5 yards behind the start line. Should Peter take the bet proposed by Bill? Who would win the race?

Random fact of the day:It takes about 20 seconds for a red blood cell

to circle the whole body.

Rates, Ratios, and PercentsRates, Ratios, and Percents

Rates, Ratios, and PercentsRates, Ratios, and PercentsWhat is a rate?

What is a ratio?

What is a percent?

Rates, Ratios, and PercentsRates, Ratios, and PercentsWhat is a rate?

Relationship between 2 quantities measured in different units.

What is a ratio?Relationship between 2 quantities measured in the same unit.

What is a percent?A ratio where 1 quantity is compared to 100 in the same unit

Rates, Ratios, and PercentsRates, Ratios, and PercentsWhat is a unit rate?

Relationship of one quantity to one unit of another different quantity.

Rates, Ratios, and PercentsRates, Ratios, and Percents

Lets look at some unit rate examples

Rates, Ratios, and PercentsRates, Ratios, and PercentsExample 1: You are with your mother at Big Y and she is comparing Olive Oil. Analyze the prices below and decide which is the best deal. (hint: the work is already done for you)

Rates, Ratios, and PercentsRates, Ratios, and PercentsUnit RateExample 2 (with no work done for you): Now you are in the dairy section of Big Y. Which milk gives you the best deal?Gallon Half-gallon Quart Pint $5.09 $2.79 $1.79 $0.99

Rates, Ratios, and PercentsRates, Ratios, and PercentsUnit RateExample 3: Suppose a farmer has two fields. He recently harvested 10,000 ears of corn in the 4 acre field, and 12,000 ears in the 5 acre field.

Rates, Ratios, and PercentsRates, Ratios, and PercentsUnit RateExample 3: Suppose a farmer has two fields. He recently harvested 10,000 ears of corn in the 4 acre field, and 12,000 ears in the 5 acre field.

To truly compare and analyze his harvesting efficiency, the farmer must look at the unit rate of harvest (the ears per one acre) for each field.

Grocery Store ProblemGrocery Store Problem

You have $5.00 to spend on peanut butter.

Which brand should you choose based on the money?

What are some factors that might influence your decision besides money?

MileageMileageThe table below shows the car mileage and

gasoline use for Mr. Butler’s car. Estimate how far he can drive on a full tank of gas (18 gallons).

MileageMileageThe table below shows the car mileage and

gasoline use for Mr. Butler’s car. Estimate how far he can drive on a full tank of gas (18 gallons).

Miles driven

334 285 240 287 215

Gallons used

12.1 9.8 8.2 9.5 7.8

MileageMileageHow does this rate

compare with the advertised rate?

What type of terrain might I drive on to get these rates?

Exchange Rate ProblemExchange Rate Problem

Exchange Rate ProblemExchange Rate ProblemYou just landed in

Madrid, Spain and are very hungry after your flight.

Exchange Rate ProblemExchange Rate ProblemYou walk past a

pizzeria and notice they have medium pizzas for $16 euros, and a meatball grinder for $7 euros. However you only have a twenty dollar bill from back home.

Exchange Rate ProblemExchange Rate Problem

You go to the nearest money exchange kiosk to exchange $20 USD for euros. Will you have enough for the pizza? Or do you settle for the grinder???

Do workDo work

The CloserThe CloserWhat is the difference

between a rate and a ratio?

Give me an example

(not mentioned in class) of a unit rate in real life.

For a science project, Mike wanted to test the life of a regular incandescent light bulb versus an energy saving light bulb. He determined that he could burn through 8.5 incandescent bulbs in the time it took to use up one energy saving bulb. The energy saving bulb lasted 10,000 hours, so to determine the unit rate for each regular bulb he divided 10,000 into 8.5 to get a unit rate of .00085 hours per incandescent bulb.

4.14.1

This logic building problem is a SOLO activity.

Ron Jon bought a pack of baseball cards and found a rookie card worth $10. He decided to sell it to his friend Tommy Bahama for $10. After the baseball season ended, the card went up in value and Ron Jon bought it back from Tommy Bahama for $15. The following year, Ron Jon sold the card for $8. Did Ron Jon make or lose money on the card?

Random fact of the day:In most watch advertisements the time

displayed on the watch is 10:10 because then the arms frame the brand of the watch

(and make it look like it is smiling).

Coordinate GridCoordinate GridWhat can you tell me

about this type of graph?

Also known as:Coordinate planeCartesian Coordinate

Plane

Coordinate GridCoordinate GridWhat can you tell me

about this type of graph?

Also known as:Coordinate planeCartesian Coordinate

Plane

Coordinate GridCoordinate GridWhere are the

quadrants?


quadrants?Which axis is x? y?


quadrants?Which axis is x? y?Which axis is

dependent? Independent?


quadrants?Which axis is x? y?Which axis is

dependent? Independent?

Coordinate GridCoordinate GridWhat does it mean

when I say something in a graph is dependent? Independent?

Coordinate GridCoordinate GridIn your head think:“Does ___ depend on

____?”

The thing that ‘depends’ is the dependent variable on the y-axis.

Coordinate GridCoordinate GridFor example, which is

dependent/independent?

1. Miles driven and the amount of gas used.

2. Width of a tree and its age.

3. Price of apples and the amount harvested.

How do we say this shot?How do we say this shot?

How do we say this shot?How do we say this shot?

So how do we say this point?So how do we say this point?

So how do we say this point?So how do we say this point?

The ‘x’ value is always said first

How do we write this point?

So how do we write this point?So how do we write this point?

(7,3)

Scatter PlotScatter PlotA scatter plot is a graph

that consists of points.

These points describe a relationship between two distinct quantities.

Scatter PlotScatter PlotLets plot the points below

(70, 55.4) (96, 59.4)(92, 59.2)(80, 56)(82, 57)(84, 57.2)(100, 60)(88, 57.8)(76, 55.5)(78, 56.4)

Scatter PlotScatter PlotLets plot the points below

(70, 55.4) (96, 59.4)(92, 59.2)(80, 56)(82, 57)(84, 57.2)(100, 60)(88, 57.8)(76, 55.5)(78, 56.4)

Scatter PlotScatter Plot

How does the dependent variable appear to change in relation to the independent variable?


Can we estimate a future value given these points?


Can we estimate a future value given these points?

What output (y) might an input (x) of 110 give us?


What could be a possible scenario for this data?



Is this graph still a reliable predictor of a future value? Why or why not?

http://www.youtube.com/watch?v=ROZJmX73FF4

Scatterplots continuedScatterplots continued

If we were to create a scatterplot comparing the sales of CD’s to digital downloads, how do you think they would change over time?


When does the sale of downloads surpass the sale of CD’s?


Has digital downloads helped or hurt music sales according to this graph? Why?


Do workDo work

The CloserThe CloserAssume a scatterplot is made for each scenario

below. Tell me whether or not the correlation would be positive, negative, or none. (it might help to determine the I and D variables, and sketch or think of a quick graph)

Comparing the value of gold per ounce.

Comparing number of leaves that fall each day from a certain tree in the month of September.

Comparing the value of a car over 20 years.

Comparing the height of the sun in the sky over the course of the day.

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