Math Focus 9

# A Trip to Vancouver Island

## INTRODUCTION

Maps and floor plans can help you visualize your surroundings. Interpreting their scale factors provides useful information for making decisions when planning distances and timing.

Imagine that you are planning a hiking trip on Vancouver Island and a visit to the Royal British Columbia Museum in Victoria, British Columbia.

## THE PROCESS

A Hike on Vancouver Island

1. Look through maps of Vancouver Island Trails. Download and print one of the following trail maps. Plan a hike with a few stops to look at the scenery or have a picnic.
• Bear Hill Regional Park
• Coles Bay Regional Park
• Devonian Regional Park
• Horth Hill Regional Park
• Island View Beach Regional Park
• Matheson Lake Regional Park
• Sooke Potholes Regional Park
• Witty's Lagoon Regional Park
2. Explain how to use the scale on the map to determine the distance between stopping places. Then follow your explanation to determine the distances. Explain whether the contours on a map would affect the distance.
3. Check by comparing your distances with any distances given on the trail map. Are your distances reasonable?

A Visit to the Royal British Columbia Museum

1. Visit Royal British Columbia Museum floor plans. Download and print a floor plan. The length of the outside wall along the left side of room 2 on the second floor (as shown by the thick line in the following diagram) is 33 m long. Mark the length of this wall on your printout as a scale. Use this scale to determine a length and an area on each floor. Explain your strategy.

1. A larger floor plan is needed for a poster. Choose a scale factor and draw an enlargement of the plan for one floor. How did you choose the scale factor?
2. A smaller floor plan is needed for a pamphlet. Choose a scale factor and draw a reduction of the plan for a different floor. How did you choose the scale factor?

2. What did you learn by explaining your thinking to someone else? What did you learn by listening to their response?
3. Why might you want to use a scale factor for a map of a hiking trial or a floor plan?
4. For what other reason might you want to use a scale factor?

## RESOURCES

Websites:

maps of Vancouver Island Trails

Royal British Columbia Museum floor plans

Materials:

a pencil
paper
a ruler
a protractor
a calculator

## ASSESSMENT

 Mathematical Processes Work meets standard of excellence Work meets standard of proficiency Work meets acceptable standard Work does not yet meet acceptable standard Communication Explanations about applying scale factors are clear and well organized, using mathematical language to enhance communication Explanations about applying scale factors are complete and clear, using appropriate mathematical language to support communication Explanations about applying scale factors are complete, using mathematical language to partially support communication Explanations about applying scale factors are incomplete, using mathematical and non-mathematical language and /or inconsistently, which interferes with communication Connections Demonstrates a sophisticated ability to transfer knowledge and skill with similar polygons and scale diagrams to floor plans and maps Demonstrates a consistent ability to transfer knowledge and skill with similar polygons and scale diagrams to floor plans and maps Demonstrates some ability to transfer knowledge and skill with similar polygons and scale diagrams to floor plans and maps Demonstrates a limited ability to transfer knowledge and skill with similar polygons and scale diagrams to floor plans and maps Visualization Uses exceptionally insightful visual reasoning to interpret and draw scale diagrams with exceptional accuracy Uses insightful visual reasoning to interpret and draw scale diagrams quite accurately Uses meaningful visual reasoning to interpret and draw scale diagrams in a workable way Uses unclear visual reasoning that leads to inaccurate interpretations and drawings for scale diagrams