1. Map Scale
Looking at the maps on the screen ask the students which one has the largest scale? This will remind the students of what they have already learnt about the basic premise for scale.
Have you ever seen a model car/plane/building etc?
Every part of the model is in true proportion to the life-size object = this is the basic idea of scale.

2. MAP SCALE…
A SCALE shows the relationship between the distance on a map and the ACTUAL distance on the EARTH’s SURFACE
Scale can be represented in 3 ways:
1) direct statement/verbal
2) Line scale
3) Representative Fraction Scale (RF)

3. The scale of a map shows how much you would have to enlarge your map to get the actual size of the piece of land you are looking at. For example, your map has a scale of 1:25000, which means that every 1 cm on the map represents of those same units of measurement on the ground (for example cm = 250 metres).
This image displays examples of all three types of scale that we will be talking about
Verbal or direct statement
Representative fraction
Line scale

4. DIRECT STATEMENT…
Uses words to describe the relationship between a distance on a map and a specific distance on the Earth’s surface
FOR EXAMPLE: cm to 10 km OR cm = 10 km
What does this direct statement mean?
Direct statement scale is also called a verbal statement
1 cm to 10 km means that every 1 cm on the map represents 10 km on earth

5. For example…
If you have measured the distance between Hamilton and Toronto and found it to be 25 cm on the map, and the direct statement reads 1 cm = 2 km, how far would it be in km?
HOW DO WE FIGURE THIS OUT?

6. Solution…
1 cm = 2 km 25 cm X 1 x X = 2 x 25 X = 50 Therefore, the actual distance between Hamilton and Toronto is 50 km
You can also write:
1 cm = 2 km
(1 x 25) cm = (2 x 25) km
25cm = 50 km
(remember: because of the equal sign, what you do to one side you have to do to the other side)

7. 5 STEP PROCESS Write down the statement: 1 cm = 2 km
Add in the information you know: 1 cm = 2 km 25 cm X
Eliminate (the same) units: 1 cm = 2 km 25 cm X
Cross Multiply: 1 x X = 25 x 2
Therefore statement…

8. LINE (Linear) SCALE…
A special kind of ruler on the map that is divided into equal units of distance
Always includes the units of measurement on the Earth’s surface
SO, HOW DOES THIS WORK?

11. REPRESENTATIVE FRACTION SCALE (R.F)…
The scale is written as a ratio
FOR EXAMPLE: 1:50 000
This means: ONE unit on the map represents of the same units on the Earth’s surface

12. 1:50 000 The FIRST term of the ratio: The SECOND term of the ratio:
is always 1
Represents the distance on the map in units
The SECOND term of the ratio:
Represents the distance on the Earth
Same unit of measurement as the first term
In Canada the units would often be in centimeters (in the States it would be inches)
So this means that 1 CM on the map would represent CM on the Earth.
We usually want to know distance in kilometers.
To change centimeters into kilometers we have to CONVERT one unit of measurement into the other.

13. SCALE CONVERSION 1 km = 1 000 m 1 m = 100 cm 1 km = 100 000 cm Since:
1 km = 1000 m, and
1 m = 100 cm,
1 km = (1000 x 100) cm
= cm

14. CONVERTING RF TO DIRECT STATEMENTS
From RF scale  direct scale: divide the right side of the equation by , to change centimetres to kilometres convert 1: RF to direct statement

15. 1:50 000 1 cm = 50 000 cm 1 cm = 50 000 km 100 000 1 cm = 0.5 km or 1 cm = 500 m

16. CONVERTING DIRECT STATEMENTS TO RF
From direct statement scale  RF scale: multiply the right side of the equation by to change kilometres into centimetres convert 1 cm = 2.5 km into a RF

17. 1 cm = 2.5 km 1 cm = (2.5 x 100 000) cm 1 cm = 250 000 cm or 1:250 000

18. IN SUMMARY…
Converting R.F to Direct Statements: divide right side by to change cm  km
Converting Direct Statements to R.F:
Multiply right side by to change km  cm

19. QUESTION: What does 1 cm = 0.5 km mean?
ANSWER: It means 1 cm on the map represents 0.5 km on the earth’s surface
Answer: 1cm on the map represents 0.5 km on the earth’s surface

20. Direct Statement: 1 cm = 35 km
QUESTION:
Direct Statement: 1 cm = 35 km
If the map distance between points A and B is 9 cm, what is the real distance?
ANSWER:
1 cm = 35 km
(9 x 1) cm = (9 x 35) km
9 cm = 315 km
Answer: 9cm = 315km

21. Direct Statement: 1 cm to 250 km
QUESTION:
Direct Statement: 1 cm to 250 km
If two places are 17 cm apart on the map, what is the actual distance between them?
ANSWER:
1 cm = 250 km
(17 x 1) cm = (17 x 250) km
17 cm = 4250 km
Answer: 17cm = 4250km

22. QUESTION: In your own words, what does 1:250 000 mean?
Answer: One centimeter on ant map represents cm on the earth’s surface
What does 1: mean?
ANSWER:
One centimeter on the map represents cm on the earth’s surface
One centimeter on the map represents cm on the earth’s surface
REMEMBER: in RF the units are always the same

23. Convert the RF into a DIRECT STATEMENT
QUESTION:
Convert the RF into a DIRECT STATEMENT 1:
ANSWER:
1 cm =
1 cm = ( / ) km
1 cm = 2.5 km OR 1 cm to 2.5 km
Answer: 1cm = 2.5km OR 1cm to 2.5km

24. Convert the RF into a DIRECT STATEMENT
QUESTION:
Convert the RF into a DIRECT STATEMENT 1:
ANSWER:
1 cm =
1 cm = ( / ) km
1 cm = 630 km OR 1 cm to 630 km
Answer: 1cm = 630km or 1cm TO 630km

25. Convert the direct statements to RF scales
QUESTION:
Convert the direct statements to RF scales
1 cm to 5 km
ANSWER:
1 cm = 5 km
1 cm = (5 x ) cm
1 cm = cm 1:
Answer: 1cm = cm

26. Convert the direct statements to RF scales
QUESTION:
Convert the direct statements to RF scales
1 cm to 25 km
ANSWER:
1 cm = 25 km
1 cm = (25 x ) cm
1 cm = cm 1:
Answer: 1:

27. QUESTION:
The line scale on a map indicates that 4 cm represents 20 km. What is the RF?
ANSWER:
4 cm = 20 km
4 cm/4 = 20 km/4
1 cm = 5 km
1 cm = (5 x ) cm
1 cm = cm 1:
Answer: 1:

28. QUESTION:
The line scale on a map indicates that 1.5 cm represents 50 km. What is the RF?
ANSWER:
1.5 cm = 50 km
1.5 cm/1.5 = 50 km/1.5
1 cm = km
1 cm = ( x ) cm
1 cm = cm 1:
Answer: 1:

29. HAND OUT TO STUDENTS “Map Scale Conversion” Handout
HAND OUT TO STUDENTS “Finding Distances on TOPOGRAPHICAL MAPS”