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Learning Math Home
Measurement Session 1: Solutions
 
Session 1 Part A Part B Part C Part D Homework
 
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Session 1 Materials:
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A B C 
Homework

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Solutions for Session 1 Homework

See solutions for Problems: H1 | H2 | H3 | H4 | H5 | H6 | H7 | H8 | H9


Problem H1

According to Maria's criterion, here are the values:

 Name (Country/Continent)

Height (cm) + Weight (kg)

 Water Buffalo (Asia)

1,165

 African Buffalo

695

 Yak (Tibet)

750

 Guar (Asia)

1,070

 American Bison (North America)

1,180

 European Bison

1,100

The three largest animals by this criterion are the American bison, the water buffalo, and the European bison.

Note that this method is somewhat problematic since the answers could change drastically if we change the units of measurement. For example, the results would look quite different if we measured weight in tons (1 metric ton = 1,000 kg) instead of in kilograms. Clearly, this can lead to potential errors.

<< back to Problem H1


 

Problem H2

Here are the ranks according to Jacob's criterion:

 Name (Country/Continent)

Height Rank

Weight Rank

Total

 Water Buffalo (Asia)

2

5.5 (tie)

7.5

 African Buffalo

1

2

3

 Yak (Tibet)

4.5 (tie)

1

5.5

 Guar (Asia)

6

3

9

 American Bison (North America)

3

5.5 (tie)

8.5

 European Bison

4.5 (tie)

4

8.5

The three largest animals by this criterion are the guar, the American bison, and the European bison.

<< back to Problem H2


 

Problem H3

Here are the products for each animal:

 Name (Country/Continent)

Height (cm) • Weight (kg)

 Water Buffalo (Asia)

165,000

 African Buffalo

75,600

 Yak (Tibet)

110,000

 Guar (Asia)

187,000

 American Bison (North America)

180,000

 European Bison

180,000

The three largest animals by Quentin's criterion are the guar, the American bison, and the European bison.

<< back to Problem H3


 

Problem H4

These two methods result in the same ordering of the animals, but some may argue that Quentin's method is more capricious than Jacob's, since there is no natural meaning to multiplying height and weight.

<< back to Problem H4


 

Problem H5

a. 

b. 

Using the Pythagorean theorem, we can derive a formula for the distance between two points A (x1,y1) and B (x2,y2) as

Next, we can calculate the distances. So for the Asian water buffalo

Here is the completed table:

 Name (Country/Continent)

Coordinates

Distance from (220,1000)

 Water Buffalo (Asia)

(165,1000)

55

 African Buffalo

(135,560)

448.13

 Yak (Tibet)

(200,550)

450.44

 Guar (Asia)

(220,850)

150

 American Bison (North America)

(180,1000)

40

 European Bison

(200,900)

101.98

To learn more about the Pythagorean theorem and distance formula, go to Learning Math: Geometry, Session 6.

<< back to Problem H5


 

Problem H6

The three species closest to (220,1000) are the American bison, the water buffalo, and the European bison.

<< back to Problem H6


 

Problem H7

Here is the completed table:

 Name (Country/Continent)

Coordinates

Distance from (0,0)

 Water Buffalo (Asia)

(165,1000)

1,013.52

 African Buffalo

(135,560)

576.04

 Yak (Tibet)

(200,550)

585.23

 Guar (Asia)

(220,850)

878.01

 American Bison (North America)

(180,1000)

1,016.07

 European Bison

(200,900)

921.95

According to Marcy's criterion, the three largest animals are the American bison, the water buffalo, and the European bison.

<< back to Problem H7


 

Problem H8

Answers will vary. Another possible method is to use weight as the first determining factor and to use height only in case of a tie.

<< back to Problem H8


 

Problem H9

Answers will vary, but the most likely answer is the African buffalo, which is the shortest and nearly the lightest. It wins easily on Jacob's criterion and is the smallest for many others.

<< back to Problem H9


 

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