#### Alison Kimbley

pdf

Subject Area:

Mathematics

Strand:

Statistics and Probability

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

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.

• 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