Problem of the Week
Problem of the Week Grade 6 How Dense is This? In honour of Canada 150, let’s explore how much space it has. In terms of its land area, 9156521km2, Canada is the second largest country in the world. Russia, China, and the U.S.A. have greater land area, but Canada’s population is significantly less.
a) Find the area and population∗ of the following countries. Add three of your own choices to the table. Country Canada
Land Area 9156521km2
Population 36.63 million
Persons per km2 ≈4.0 persons/km2
Russia
Japan Ukraine India Finland Brazil Sudan
b) Which countries have the least, and greatest, population density? In each of these two countries, how many square km of land area are there for each person?
c) The city of Mumbai in India has an area of 603.4km2, and a population of 21.69 million. How many square metres of land area are there for each person in Mumbai?
d) How many square metres of classroom space are there for each person in your classroom? ∗ For
populations and areas, try the website http://www.worldometers.info/world-population/population-by-country/ NOTE: Land area
data varies, depending on your chosen source.
Strand Data Management and Probability
Grade 7
A large tent is being set up for a fair. Two poles, QU and RT, are placed perpendicular to the ground and 12 m apart. Pole QU is 4 m in length and pole RT is 7.5 m in length. A tarp is placed over the poles and secured to the ground at P, 3 m from the base of pole QU, and S, 4 m from the base of pole RT. Determine PQ+QR+RS, the length of the tarp.
R Q 7.5 4 P 3 U
12
T 4
S
The Pythagorean Theorem states, “In a right triangle, the square of the length of hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides” In the following right triangle, p2 = r2 +q2.
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Strands Geometry and Spatial Sense, Measurement
a) Find the area and population∗ of the following countries. Add three of your own choices to the table. Country Canada
Land Area 9156521km2
Population 36.63 million
Persons per km2 ≈4.0 persons/km2
Russia
Japan Ukraine India Finland Brazil Sudan
b) Which countries have the least, and greatest, population density? In each of these two countries, how many square km of land area are there for each person?
c) The city of Mumbai in India has an area of 603.4km2, and a population of 21.69 million. How many square metres of land area are there for each person in Mumbai?
d) How many square metres of classroom space are there for each person in your classroom? ∗ For
populations and areas, try the website http://www.worldometers.info/world-population/population-by-country/ NOTE: Land area
data varies, depending on your chosen source.
Strand Data Management and Probability
Grade 7
A large tent is being set up for a fair. Two poles, QU and RT, are placed perpendicular to the ground and 12 m apart. Pole QU is 4 m in length and pole RT is 7.5 m in length. A tarp is placed over the poles and secured to the ground at P, 3 m from the base of pole QU, and S, 4 m from the base of pole RT. Determine PQ+QR+RS, the length of the tarp.
R Q 7.5 4 P 3 U
12
T 4
S
The Pythagorean Theorem states, “In a right triangle, the square of the length of hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides” In the following right triangle, p2 = r2 +q2.
!
# "
Strands Geometry and Spatial Sense, Measurement
