### Musical Math

```Materials
DE Marker
15 Small White Boards
Reminders
Use similar triangles to find the length of
side x:
6
7.5
10
x
150
Get out your agenda if you see
your name below. You need to
come to my room tomorrow.
Period 4
Period 5
Period 6
4-10 Scale Drawings and
Models
How do I determine scale
and scale factor between
models and reality?
Questions:
What does scale
mean?
Notes:
Scale – the ratio of a length on a drawing or model to the
length of an actual object
Note: a Scale can have different units
Example:
Questions:
What does scale
factor mean?
Notes:
Scale Factor – gives how many TIMES larger or smaller an
object is
Note: a Scale Factor must have the same units and can be
written using a colon (ex. 1:23,000)
Example:
1:16,000,000
1:1,300,000
Questions:
How do I use
proportions
with scale
drawing?
Notes:
Example:
A map shows 2 inches = 6 miles
If we measure a distance of 2.75 inches on a map, how
many miles is this in the real world?
Set up a proportion:
2 ℎ
6
=
2.75 ℎ

Cross multiply and solve for x.
2 = 6 2.75
=
16.5
= 8.25
2
Questions:
How do I
determine scale
factor?
Notes:
Make sure both amounts are using the SAME UNITS.
1 inch on a map = 10 feet in reality
Since there at 12 inches in a foot
1 inch = 10(12) inches
1 inch = 120 inches
1:120
The scale factor from the map to reality is 120.
THIS MEANS THAT IF WE MULTIPLY A MEASURMENT ON
THE MAP BY 120, WE WILL GET THE LENGTH IN THE REAL
WORLD.
Name__________________________
Create a World
1. Think of an imaginary place
a. a mountain range
b. a group of islands
c. Middle Earth
2. Draw a map of your imaginary place
a. (2 POINTS) – made good use of color and put effort into your drawing
b. (2 POINTS) – labeled at least 4 landmarks (towns, mountains, lakes, etc.)
c. (1 POINT) – gave your imaginary place a name
3. (1 POINT) Make an appropriate scale for your map (i.e. 1 inch = 10 miles)
a. (4 POINTS) make a table of distances that includes the distances between 4
landmarks
MAKE SURE YOUR SCALE IS CORRECT (USE A RULER)
BO
ISLAND
Whale
Hangout
8 miles
15 miles
20 miles
Scale: 1 inch = 5 miles
5 miles
YO
ISLAND
Mermaid
Reef
From
To
Distance
(miles)
YO Island
BO Island
15 miles
Whale
Hangout
Mermaid
Reef
20 Miles
Mermaid
Reef
Yo Island
5 Miles
Bo island
Whale
hangout
8 miles
Homework
Create a World Activity
AND Cornell Notes
Summary
```