C2.1 · Determine map distances using scale

Ontario Grade 11 Mathematics

Transportation and Travel

MEL3E study topic C2.1: Determine map distances using scale

What you will learn

• Explain what a map scale tells you.
• Use a written scale, a scale bar, or a measured map distance to find the matching real distance.
• Keep units consistent and check whether an answer is reasonable.

1. Read what the scale means

• Map distance and real distance are different lengths.
• A scale tells how the two lengths match.
• Check the map's scale after printing, resizing, or changing a digital map's zoom.

2. Match the map distance to the real distance

• Use the scale as a repeated match: each map unit represents a fixed real distance.
• Multiply by the number of map units when using a statement scale.
• Convert units only when needed, and show which units your answer uses.

3. Use the scale carefully in a practical task

• Decide whether you are measuring directly between points or along a route.
• A calculator or spreadsheet helps with arithmetic, but you must choose the correct scale and units.
• Estimate the size of the answer to catch misplaced digits or incorrect scale readings.

4. Make a final reasonableness check

• Check the measured path, the scale, and the answer units.
• Do not report more precision than the map measurement supports.
• A reasonable estimate should agree with the scale.

Sample scale matches

Worked example

A written scale for a service visit

1. Identify the scale
   The scale gives 3 km for each 1 cm measured on the map. The route measurement and the scale both use centimetres for the map distance.
   $$1\text{ cm}=3\text{ km}$$
2. Count the matching map units
   A route measuring 4.5 cm contains 4.5 groups of 1 cm. Each group represents 3 km, so multiply 4.5 by 3.
   $$4.5× 3=13.5$$
3. State the real distance
   The multiplication gives kilometres because the scale assigns kilometres to each map centimetre. The map measurement is approximate, so the result can be reported as about 13.5 km.
   $$13.5\text{ km}$$

Worked example

Using a scale bar and converting units

1. Compare with the bar
   The trail measurement is 5 cm, while the bar is 2 cm. The trail is 2.5 times the bar length, because 5 divided by 2 is 2.5.
   $$5\div 2=2.5$$
2. Find the matching metres
   Each bar-length represents 800 m. The trail is 2.5 bar-lengths, so multiply 800 m by 2.5.
   $$800× 2.5=2000$$
3. Convert metres to kilometres
   There are 1,000 m in 1 km. Divide 2,000 m by 1,000 to express the trail length in kilometres.
   $$2000\div 1000=2$$

Common mistakes and how to avoid them

Lesson summary

• A map scale matches map distance to real distance.
• Measure the correct line or route, then use the written scale or scale bar.
• Keep units consistent and convert when necessary.
• Estimate and check the result before reporting it.

Check your understanding

Key terms

Map distance

The length measured between places on a map.

Real distance

The matching length between places on the ground.

Scale

A comparison that tells how map distance matches real distance.

Scale bar

A marked line on a map that shows a real distance.

Continue through MEL3E

View the complete Ontario Grade 11 Mathematics learning path

• C1.1 · Interpret driver-licensing procedures, costs, and restrictions
• C1.2 · Describe procedures for buying or leasing a vehicle
• C1.3 · Compare vehicle insurance factors and costs
• C1.4 · Compare costs of buying new, leasing, and buying used
• C1.5 · Explain consequences of irresponsible vehicle operation
• C1.6 · Compare business costs and benefits of using a vehicle

About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation C2.1. It is a study resource, not an official curriculum publication.

Official curriculum reference

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