
You are expanding a patio as shown in the diagram. Which of the following keystroke sequences is better for finding the area that you are adding to the patio? Explain your reasoning.

There are four straightforward ways to find the area of the new portion of the patio.

Subtract the area of the existing patio from the area of the expanded patio.

Add the area of the bottom rectangle to the area of the upper right rectangle.
 Add the area of the lower left rectangle to the area of the right rectangle.

Add the areas of all three rectangles.

This keystroke sequence tells the calculator to multiply 134 by 8. This is not correct.

This keystroke sequence tells the calculator to subtract 48 from 140. This is correct. It agrees with strategy (1) above.
So, the new portion of the expanded patio has an area of 92 square feet.

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You are expanding a patio as shown. You are laying 1foot by 1foot tiles. You estimate that it will take you 1 hour to lay 45 tiles. Estimate how long it will take you to tile the area that you are adding to the patio.
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Population density is the number of people per unit of area.

Use the total area of Canada to estimate the country's population density.

Land area is equal to total area minus water area. Use the land area of Canada to estimate the country's population density.

Do you think population density should be defined in terms of the total area of a country or in terms of the land area? Explain your reasoning.


Because population density is measured in "people per unit of area," you know that you need to divide the population by the area.

The land area of Canada is
So, using the land area instead of the total area, the population density of Canada is

Check the definition of population density on the Internet. In most of the definitions it is unclear whether the denominator is total area or land area. Which one is "correct" is not really the point. More to the point is that when a person talks about population density, the person should specify whether he or she is using total area or land area.
"The world's population is 6.8 billion, and Earth's total area (including land and water) is 510 million square kilometers (197 million square miles). Therefore the worldwide human population density is 6.8 billion · 510 million = 13.3 per km² (34.5 per sq. mile). If only the Earth's land area of 150 million km² (58 million sq. miles) is taken into account, then human population density increases to 45.3 per km² (117.2 per sq. mile). This calculation includes all continental and island land area, including Antarctica. If Antarctica is also excluded, then population density rises to 50 people per km² (129.28 per sq. mile). Considering that over half of the Earth's land mass consists of areas inhospitable to human inhabitation, such as deserts and high mountains, and that population tends to cluster around seaports and fresh water sources, this number by itself does not give any meaningful measurement of human population density." (Source: Wikipedia)

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Excluding Canada's three northern territories, the population of Canada is about 34.0 million people and the land area of Canada is about 5.5 million square kilometers.
 Estimate the population density of Canada, excluding the three northern territories.
 How does excluding the territories change your estimate of the population density? Explain your reasoning
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The population of Toronto is about 2.5 million people and the land area of Toronto is about 630 square kilometers.

Estimate the population density of Toronto.

How does your estimate for Toronto compare to your estimates for Canada?
The Greater Golden Horseshoe is a densely populated region in southern Ontario and is home to over 8.1 million residents. Twothirds of the population of Ontario lives within the horseshoe. Some of the most populous cities in the horseshoe are Toronto, Mississauga, Hamilton, Brampton, Oshawa, Burlington, and St. Catharines (Niagara Falls region).


Because population density is measured in "people per unit of area," you know that you need to divide the population by the area.
The population density of Toronto is about 4000 people per square kilometer.

Using the population density of Canada found in Exercise 3(b), you can conclude that Toronto has roughly 1000 times the population density of Canada.
The city planners in Toronto (and in many other modern cities) have adopted the concept of "build up, not out." This policy promotes high population density within the city and encourages walking and cycling, low energy consumption, and reduced pollution. It is based on an efficient public transport system. Advocates argue that this policy is more sustainable than urban sprawl because it is less dependent on the car.

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Do you think that population density is an accurate measure of a country's population distribution? Explain your reasoning.
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