#### Alison Kimbley

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Subject Area:

Mathematics

Strand:

Patterns and Relationships

Grade Level:

Six

Content (topic)

Exploring Relationships through Equations

WNCP:

 Outcome P6.3: Extend understanding of patterns and relationships by using expressions and equations involving variables. Indicators: Describe and represent geometric patterns and relationships relevant to First Nations and Métis peoples and explain how those patterns or relationships could be represented mathematically. Generalize an expression that describes the relationship between the two columns in a table of values. Write an equation to represent a table of values.

Lesson Preparation

Equipment/materials:

Advanced Preparation:

• Read the background information on the furtrade.

Presentation

Development

• Explain to the students that the fur trade was one of the earliest and most important industries in North America as it played a role in developing the continent.

• The fur trade started shortly after contact in 1500 between First Nations people and Europeans.  First Nations people traded furs for weaponry and other items.

• Show students the PowerPoint presentation, which provides information on the fur trade and the Hudson Bay Company.

• Explain to students that the Hudson Bay Company hired commanders of ships, such as Michael Grimington to bring goods from Europe for the trading posts.

• On an overhead projector or data monitor show the students the official table that was made by Captain Grimington in 1710.

• The associated PowerPoint presentation contains photographs and information on a number of items in the table.

• Display the trading goods table below on an overheadscreen. Have each student complete the activity sheet.

References:

##### Reference

A copy of the invoice of trading goods sent over this year from England by Captain Michael Grimington, commander of the Hudson Bay frigate can be found at

http://www.canadiana.ca/hbc/_popups/PAMalbany1_e.htm

### Trading Goods

 144 pewter spoons 72 pairs stockings 350 brass kettles weighing 1020 lbs 72 pairs shoes 100 lbs thread 144 powder horns 450 guns 580 hatchets 4000 flints 72 egg boxes 24 bayonets 160 shirts 288 fire steels 792 ivory combs 72 files 36 horns 500 worms 216 tobacco boxes 2200 needles 144 pairs of scissors 324 fish hooks 255 blankets 144 alchemy spoons

A copy of some items extracted from the invoice of trading goods sent over from England Captain Michael Grimington, commander of the ship called Hudson Bay.  (lbs is a short form for the weight measure pounds. A pound is approximately 450 grams.)

### Activity Sheet

1. 24 bayonets were counted and recorded by Captain Michael Grimington in 1710, year 1. Assume that the trading post sold 7 bayonets every year for thirteen years.

1. Create a table that shows the number of bayonets available for sale at the beginning of years 1, 2, 3, 4 and 5.

2. In words, describe the pattern in the table of data.

3. Write an expression to represent the pattern in the table.

4. Determine the number of bayonets available for sale at the beginning of the year 1723. Describe the strategy you used to find this.

2. 2200 needles were counted and recorded by Captain Michael Grimington in 1710. Assume that the trading post sold 20 needles every year for ten years.

1. Create a table that shows the number of needles available for sale at the beginning of years 1, 2, 3, 4 and 5.

2. In words, describe the pattern in the table of data.

3. Write an expression to represent the pattern in the table.

4. Use the expression to determine the number of needles available for sale at the beginning of the year 1720.

3. 72 files were counted and recorded by Captain Michael Grimington in 1710. Assume that the trading post sold 4 files every year for seven years.

1. Create a table that shows the number of files available for sale at the beginning of years 1, 2, 3, 4 and 5.

2. In words, describe the pattern in the table of data.

3. Write an equation that represents this table.

4. Determine the number of files available for sale at the beginning of the year 1717. Describe the strategy you used to find this.