Name:________________________________________________________________________________Date:_____/_____/__________
Fill-in-the-blanks:
Word Bank:
different,
one,
comparison
1. A ratio is a _______________ of two numbers.
2. A rate is special kind of ratio where each number represents a
_________________unit.
3. A unit rate is a special kind of rate, where the comparison is
always out of _______________!
Do the following ratios form a proportion? (Yes or No)
Cross-multiply!
Solve:
6.
3
11
4.
15
5
=
6
2
5.
20
35
=
2
3
Remember: Cross-multiply first, then DIVIDE by coefficient!
=
x
66
7.
10
𝑥
=
4
5
8. The ratio of jelly beans to
chocolate eggs in the Easter basket is
8 : 3. If there are 20 jelly beans in the
basket, then approximately how
many chocolate eggs are there?
Set up PROPORTION and solve:
9. For every 2 dogs at the shelter,
there are 3 cats. If there are 10 dogs
at the shelter, how many TOTAL
dogs AND cats are there?
Set up PROPORTION and solve:
=
=
Today’s Lesson:
What:
scale proportions
Why:
To use proportions to solve problems
involving scale drawings.
Vocabulary:
scale drawing/model — represents
LARGE
something that is too ______________
or too
_______________
to be drawn at actual size.
small
scale factor-- gives the ratio of the paper
real-life
measurement to the________________
measurement (If the scale is 3 cm = 9 mi., then the scale
1
factor is 3 )
How to solve a scale drawing problem using a
proportion:
Step One: Set up given map/ blueprint scale as a
ratio with paper measurement on top and
____________________
measurement on the bottom.
real-life
Step Two: Set up other side of proportion by
placing what you know (as given in problem) in the
correct position (paper on top and real-life on the
bottom). “x” goes in the remaining spot (represents the
unknown
__________________________).
Example:
A certain map has a scale of ½ inch = 20 miles. If two
towns are 50 miles apart, how far apart are they on the
map?
Start with the
SCALE– given
in the
problem!
0.5 𝑖𝑛
20 𝑚𝑖
=
𝒙
𝟓𝟎 𝒎𝒊
25 = 20x
20
20
x = 1.25 in
What else does
the problem
already tell
us??
Video Examples:
Map Example:
1 𝑐𝑚
100 𝑘𝑚
𝑐𝑚
13.5
=
n 𝑘𝑚
Space Shuttle Model:
1𝑚
100 𝑚
𝑚
n
=
37.2 𝑚
1n = 1,350
1
1
37.2 = 100n
100 100
n = 1,350 km
n = 0.372 m
Blueprints or other Scale Drawings:
Together:
A blueprint has the following scale:
2 cm = 5ft
1) On Paper: 20 cm-- What is it in real life?
x = 50 ft
On your own:
A blueprint has the following scale:
𝟏
in = 2 ft
𝟒
2) Real Life: 20 ft-- What is it on paper?
x = 2.5 in
map scenarios:
Together:
A certain map has the following scale:
2cm = 9 km
3) Real Life: 56 km-- What is it on paper?
x ≈ 12.4 cm
On your own:
A certain map has the following scale:
0.75 in = 20 mi
4)
On Paper: 2 in-- What is it in real life?
x ≈ 53.3 miles
homework
IXL: J.13
END OF LESSON
The next slides are student copies of the notes and
handouts for this lesson. These were handed out in
class and filled-in as the lesson progressed.
NAME:____________________________________________________________________________ DATE: ______/_______/_______
Math-7 NOTES
What:
scale proportions
Why:
To use proportions to solve problems involving scale drawings.
Vocabulary:
scale drawing/model — represents something that is too ________________
or too _________________ to be drawn at actual size.
scale factor-- gives the ratio of the paper measurement to the
________________ measurement. (If the scale is 3 cm = 9 mi., then the scale factor is 𝟏𝟑 )
How to solve a scale drawing problem using a proportion:
Step One: Set up given map/ blueprint scale as a ratio with paper
measurement on top and ____________________ measurement on the bottom.
Step Two: Set up other side of proportion by placing what you know (as given
in problem) in the correct position (paper on top and real-life on the bottom).
“x” goes in the remaining spot (represents the __________________________).
Example:
A certain map has a scale of ½ inch = 20 miles. If two towns are 50 miles
apart, how far apart are they on the map?
Start with the
SCALE– given in
the problem!
0.5 𝑖𝑛
20 𝑚
25
20
=
=
𝑥
50 𝑚
20𝑥
20
x = 1.25 inches
What else does
the problem
already tell us??
Video examples:
Map Example:
1 𝑐𝑚
100 𝑘𝑚
Space Shuttle Model:
=
𝑐𝑚
1𝑚
𝑘𝑚
100 𝑚
=
𝑚
𝑚
Blueprints or other Scale Drawings:
Together:
On your own:
A blueprint has the following scale:
2 cm = 5ft
A blueprint has the following scale:
𝟏
in = 2 ft
1)
2)
On Paper: 20 cm– What is it in
real life?
𝟒
Real Life: 20 ft-- What is it on
paper?
Map scenarios:
Together:
On your own:
A certain map has the following
scale: 2cm = 9 km
A certain map has the following
scale: 0.75 in = 20 mi
3)
4)
Real Life: 56 km-- What is it on
paper?
On Paper: 2 in-- What is it in real
life?
IXL: 7th Grade, J.13
(scratch work required)
NAME:___________________________________________________________________________
DATE: ______/_______/_______
For each word problem, you must set up a proportion (label the correct units), and show steps required to
solve. You may stop once you achieve a MINIMUM smart score of 70% (can keep going if desired), or once
you have spent 15 minutes or more. No scratch work will result in a loss of points!
Example:
Answer (showing my work):
𝟑 𝒄𝒎
𝟐𝟏 𝒎
Type answer
in box.
𝟑𝒙
𝟑
=
=
𝟏 𝒄𝒎
𝒙
𝟐𝟏
𝟑
x=7m
Proportion:
Proportion:
=
Proportion:
Proportion:
Proportion:
=
Proportion:
Proportion:
=
=
Proportion:
=
=
=
Proportion:
=
=
Proportion:
Proportion:
=
Proportion:
Proportion:
Proportion:
=
Proportion:
Proportion:
=
Proportion:
=
Proportion:
=
=
Proportion:
=
=
=
Proportion:
Proportion:
=
=
Proportion:
Proportion:
=
=
Proportion:
=
=
NAME:_____________________________________________________________________________
DATE: ______/_______/_______
“Scale drawings”
Use below space to set up the proportions required to complete above table:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Use below space to set up the proportions required to complete above table:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.