145. Scale Drawings and Real Distances
Learning Intentions
- To understand that scale drawings can be used to depict large or small objects
- convert from a distance on a map or diagram to the actual distance in real life
- convert from the actual distance in real life to a distance on a map or diagram
- Determine the scale factor given a distance on a diagram and the distance in real life
Pre-requisite Summary
- Know that length can be measured in units such as mm, cm, m and km
- Be able to convert between metric units of length
- Understand that a ratio compares two quantities
- Be able to Simplify ratios
- Know that multiplication and division can be used to scale quantities up or down
- Understand that diagrams do not always show real size
- Be able to read labelled lengths on a map or drawing
Worked Examples
Worked Example 1
State what each scale means in words:
a)
b)
c)
Worked Example 2
A map has scale
a)
b)
Worked Example 3
A floor plan has scale
a)
b)
Worked Example 4
A model car is built to scale
a)
b)
Worked Example 5
A map distance of
Worked Example 6
A diagram distance of
Problems
Problem 1
State what each scale means in words:
a)
b)
c)
Problem 2
A map has scale
a)
b)
Problem 3
A floor plan has scale
a)
b)
Problem 4
A model plane is built to scale
a)
b)
Problem 5
A map distance of
Problem 6
A diagram distance of
Exercises
Understanding and Fluency
Exercise 1.
Complete each statement:
a) A scale drawing shows an object at a different ______
b) In the scale
c) To Use a scale correctly, the units must first be made the ______
Exercise 2.
State what each scale means in words:
a)
b)
c)
d)
Exercise 3.
Convert from diagram distance to actual distance:
a) scale
b) scale
c) scale
Exercise 4.
Convert from diagram distance to actual distance:
a) scale
b) scale
c) scale
Exercise 5.
Convert from actual distance to diagram distance:
a) scale
b) scale
c) scale
Exercise 6.
Convert from actual distance to diagram distance:
a) scale
b) scale
c) scale
Exercise 7.
Determine the scale factor in each case:
a)
b)
c)
Exercise 8.
Determine the scale factor in each case:
a)
b)
c)
Reasoning
Exercise 9.
Explain why units must be converted before finding a scale factor.
Exercise 10.
A student says that a scale of
Exercise 11.
Noah says that a scale factor of
Exercise 12.
Explain why a map scale such as
Exercise 13.
A student finds that
Problem-solving
Exercise 14.
A map has scale
Exercise 15.
A classroom plan has scale
Exercise 16.
A real road is
Exercise 17.
A model train is built to scale
Exercise 18.
On a diagram,
Exercise 19.
A map shows two landmarks
Potential Misunderstandings
- Students may think a scale is found by comparing numbers without making the units the same
- Students may reverse the order of drawing distance and real distance in a scale ratio
- Students may multiply when they should divide, or divide when they should multiply
- Students may think a larger number in the scale always means a larger drawing
- Students may confuse enlargement scales such as
with reduction scales such as - Students may forget to convert between cm, m and km when solving scale problems
- Students may write a scale factor that is not simplified
- Students may think map distances are already actual distances