Name: ______Class: ______Date: ______

Partner: ______

It’s how far?!

The world is a HUGE place. It’s circumference at the equator is 24,901.55 miles or 40,075.16 kilometers. In a plane, provided it has enough fuel to make it the whole way and not stop midflight, it would take about 47 hours to fly all the way around.47 hours! That’s almost TWO days! Here in Worcester, we are such a small part of this awesome planet.

These are some places all over the world. Some of them we have been to, most are places we all want to go. London and Sydney are at the top Ms. Mattarazzo’s list personally. But she’s having trouble comprehending how far these places are from Worcester, she doesn’t understand kilometers very well. Everything in her life has been measured in miles, especially long distances. Please help her figure out the relationship between the two units of measurement (miles and kilometers) so she can plan her perfect vacation … and maybe she’ll invite some of you to come along

Consider the following table:

Place / Distance from Worcester (miles) / Distance from Worcester (kilometers)
Reykjavik, Iceland / 2464.6 / 3966.3
Tokyo, Japan / 6731.7 / 10833.7
Moscow, Russia / 4515.4 / 7266.8
Lusaka, Zambia / 7405.7 / 11918.3
Buenos Aires, Argentina / 5341.4 / 8596.1
San Juan, Puerto Rico / 1679.5 / 2702.8
Paris, France / 3464.9 / 5576.2
San Diego, CA, United States / 2563 / 4124.7
Hanoi, Vietnam / 8067.6 / 12983.6
Islamabad, Pakistan / 6753 / 10867.9
Toronto, Canada / 401.6 / 646.3
Cairo, Egypt / 5441.1 / 8756.7
Orlando, Florida, United States / 1102.4 / 1774.1
London, England / 3303.2
Sydney, Australia / 16191.7

Part 1 – Graph (in notebook)

Carefully draw and scale coordinate axes for the data in the table. Let x represent the length in miles and y represent the length in kilometers. Plot points for the first thirteen coordinate pairs.

Part 2 – Patterns (answer on lined paper)

a) What pattern or shape do you see in your graph?

b) Connect the points to illustrate this pattern.

c) Explain how you could use your graph to approximate the missing lengths in the table. (Estimate the missing lengths, as well!)

d) Using the table, split up the data within your group and calculate the ratio of length in kilometers to length in miles to the nearest tenth. (Show the work neatly for your calculations!)

e) Collect your group members’ ratios in this table:

Place / Distance from
Worcester (mi) / Distance from
Worcester (km) / Length in kilometers
Length in miles
Reykjavik,
Iceland / 2464.6 / 3966.3
Tokyo,
Japan / 6731.7 / 10833.7
Moscow,
Russia / 4515.4 / 7266.8
Lusaka,
Zambia / 7405.7 / 11918.3
Buenos Aires,
Argentina / 5341.4 / 8596.1
San Juan,
Puerto Rico / 1679.5 / 2702.8
Paris,
France / 3464.9 / 5576.2
San Diego, CA,
United States / 2563 / 4124.7
Hanoi,
Vietnam / 8067.6 / 12983.6
Islamabad, Pakistan / 6753 / 10867.9
Toronto,
Canada / 401.6 / 646.3
Cairo,
Egypt / 5441.1 / 8756.7
Orlando, FL, United States / 1102.4 / 1774.1
London,
England / 3303.2
Sydney,
Australia / 16191.7

f)Use the rounded ratios you found to calculate the distance from Worcester to London, England in kilometers (to the nearest tenth of a kilometer).

g)How can we use these results to calculate the distance from Worcester to Sydney, Australia in miles?

Part 3 - Rate

The number of kilometers is the same in every mile, so the value you found for the

Length in kilometers is called a CONSTANT.

Length in miles

a)Let X represent miles and Y represent kilometers. Talk with your group members and come up with a way to change X miles to Y kilometers using the constant you calculated. In other words, find a rule for your table.

b)Use the rule you wrote in a) to calculate the distance from Worcester to London in kilometers, and the distance in miles from Worcester to Sydney.

Part 4 - Checking with technology (using a graphing calculator)

To test how accurate your rule is, we’re going to set up a scatter plot in the calculator and then graph your rule to see how closely it models the data.

I. Turn the calculator on and press the WINDOW button. Edit the settings so that your screen shows:

WINDOW

Xmin=0

Xmax=9000

Xscl= 1000

Ymin=0

Ymax=14000

Yscl=1000

Xres=1

II. To create the scatterplot, you’ll need to enter the data into Lists on the calculator.

Press STAT and choose 1: EDIT

Type the data for miles as L1, and the data for kilometers as L2.

III. Press Y= and check that the screen is empty. It should look like this:

IV. Press2ND and then Y= to get the STAT PLOT screen. All the plots should be off.

Turn Plot 1 ON by pressing ENTER and choosing ON.

V. Press GRAPH. Your scatter plot should appear on the screen.

VI. NOW, for the moment of truth. Press Y= and enter your rule. For “X” press the button. Press GRAPH

********

a) Compare the graph on your calculator to the graph in your notebook. Why does this graph go through the origin (0,0)? Explain whether this makes sense in terms of miles and kilometers.

Press 2ND and then GRAPH to see a table of values for your rule. Use the arrow keys to scroll up and down the table and find the missing values on our original table.

b)

The last word….

In this investigation, you used several ways to find missing values- approximating with a graph, calculating with a rate, solving an equation, and searching a table. Briefly summarize what you did with each of these methods and then describe which of these methods you preferred and why.