Aboriginal Perspectives

 

A many-to-one correspondence

Alison Kimbley

 

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Subject Area:

Mathematics

Strand:

Statistics and Probability

Grade Level:

Four

Content (topic)

Exploring many-to-one correspondence

WNCP:

Outcome SP4.1:

Demonstrate an understanding of many-to-one correspondence by:

  • Comparing correspondences on graphs

  • Justifying the use of many-to-one correspondences

  • Interpreting data shown using a many-to-one correspondence

  • Creating bar graphs and pictographs using many-to-one correspondence.

Indicators:

  1. Compare graphs in which the same data have been displayed using a one-to-one and a many-to-one correspondence, and explain how they are the same and different.

  2. Explain why a many-to-one correspondence is sometimes used rather than a one-to-one correspondence.

  3. Find examples of graphs in which a many-to-one correspondence is used in print and electronic media, such as newspapers, magazines, and the Internet, and describe the correspondence used.

  1. Answer a question using a graph in which data are displayed using a many to one correspondence.

Mathematical Processes:

Communication
Reasoning
Visualization
Logical Thinking

Lesson Preparation  

Equipment/materials:

  • A list of Trading Goods at Albany Fort America, 1706, Appendix A. Each item on the list needs to be cut apart and laminated if possible.

Advanced Preparation:

  • Read the background information on the fur trade.

Presentation  

Set

  • Have the students watch the power point on the fur trade before explaining that the fur trade was one of the earliest and most important industries in North America and it played a role in developing North America. The fur trade started shortly after contact in 1500 between First Nations people and Europeans. Aboriginal people traded furs for implements, cloth, weaponry and other supplies, which aided in the quality of their livelihood.

Development

  • Tell the students that this list (Appendix A) is from Albany, a trading post in the early 1700’s. This list is a one-to-one correspondence as there is one entry list for each good.

  • Review the list with your class as some of the goods may be unknown to them. Ask the class how the items listed can be categorized (weaponry, clothing, household items, etc.).

  • Provide the class with a set of the items cut out and have the class create a many-to-one correspondence chart with the items. Perhaps something like the chart below or perhaps your students can suggest other ways to display the correspondence.
graph
  • Discuss with your students situations where a many-to-one correspondence would be better used than one-to-one correspondence and situations where one-to-one is better than many-to-one. In this example, the owners of the trading post may want a one-to-one correspondence when the goods are delivered to check off that everything has arrived, but may want a many-to-one correspondence to arrange the goods in the store (a row for clothing, a row for household items, etc.).

  • Ask the class if they can think of examples where they would find many-to-one correspondence (e.g., media, newspaper, magazines, websites that chart statistics, etc.)


Appendix A:  


The text below is extracted from the Albany Fort America Journal of 1706. Fort Albany was a fur-trading post in northern Ontario, at the mouth of the Albany River on James Bay. It was founded (before 1682) by the Hudson's Bay Company as one of its earliest forts.

A copy of the invoice of trading goods sent over this year from England by Captain Michael Grimington, commander of the Hudson Bay frigate as her follows viz.

5584 lbs powder
20162 lbs shot
350 brass kettles
60 lbs vermillion
25 lbs black lead
100 lbs thread
450 guns
4000 flints
24 bayonets
288 fire steels
72 files
500 worms
600 net lines
3800 awl blades
2052 skeins twine
2200 needles
324 fish-hooks
6192 knives
600 hatchets
114 ice chisels
146 arrow heads
144 pewter spoons

72 pairs stockings
72 pairs shoes
144 powder horns
580 hatchets
72 egg boxes
160 shirts
792 ivory combs
36 horn combs
3456 pewter buttons
288 rings
305 Turkey reds [brilliant red cloth]
144 pairs scissors
50 plumes Ostrich feathers
3184 yards broadcloth
271 yards baize
320 yards flannel
364 yards duffel
255 blankets
170 edged men’s coats
24 plain men’s coats
66 youth coats