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.

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)

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 25000 of those same units of measurement on the ground (for example 25 000cm = 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

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: 1 cm to 10 km OR 1 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

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?

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)

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…

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?

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 50 000 of the same units on the Earth’s surface

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 50 000 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.

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 = 100 000 cm

CONVERTING RF TO DIRECT STATEMENTS From RF scale  direct scale: divide the right side of the equation by 100 000, to change centimetres to kilometres convert 1:50 000 RF to direct statement

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

CONVERTING DIRECT STATEMENTS TO RF From direct statement scale  RF scale: multiply the right side of the equation by 100 000 to change kilometres into centimetres convert 1 cm = 2.5 km into a RF

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

IN SUMMARY… Converting R.F to Direct Statements: divide right side by 100 000 to change cm  km Converting Direct Statements to R.F: Multiply right side by 100 000 to change km  cm

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

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

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

QUESTION: In your own words, what does 1:250 000 mean? Answer: One centimeter on ant map represents 250 000 cm on the earth’s surface What does 1:3 000 000 mean? ANSWER: One centimeter on the map represents 250 000 cm on the earth’s surface One centimeter on the map represents 3 000 000 cm on the earth’s surface REMEMBER: in RF the units are always the same

Convert the RF into a DIRECT STATEMENT QUESTION: Convert the RF into a DIRECT STATEMENT 1:250 000 ANSWER: 1 cm = 250 000 1 cm = (250 000/100 000) km 1 cm = 2.5 km OR 1 cm to 2.5 km Answer: 1cm = 2.5km OR 1cm to 2.5km

Convert the RF into a DIRECT STATEMENT QUESTION: Convert the RF into a DIRECT STATEMENT 1:63 000 000 ANSWER: 1 cm = 63 000 000 1 cm = (63 000 000/100 000) km 1 cm = 630 km OR 1 cm to 630 km Answer: 1cm = 630km or 1cm TO 630km

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 100 000) cm 1 cm = 500 000cm 1:500 000 Answer: 1cm = 500 000cm

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 100 000) cm 1 cm = 2 500 000 cm 1:2 500 000 Answer: 1:2 500 000

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 100 000) cm 1 cm = 500 000 cm 1:500 000 Answer: 1:500 000

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 = 33.33333 km 1 cm = (33.33333 x 100 000) cm 1 cm = 3 333 333 cm 1:3 333 333 Answer: 1:3 333 333

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