Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 A B C Homework

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.

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.

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.

 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.

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.

 Problem H6 The three species closest to (220,1000) are the American bison, the water buffalo, and the European bison.

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.

 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.

 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.