Transcript bringing it all together

Bringing it All Together
HOW DOES THIS ALL CONNECT???
Bringing it All Together
 So, we’ve been talking about
 scale factor,
 scale,
 scale diagrams,
 proportions,
 ratios,
 fractions…………
 Getting a bit mixed up between the concepts? This
PowerPoint will try to link the ideas together so that
you can see how it all comes together.
The beginning
 Let’s say you need to draw a map of a shopping mall.
You want 1 cm on the map to represent 2 meters in
reality. What is the scale???

1cm : 2 meters
 Now, we can take this scale and do a couple of things
with it




We can determine scale factor by creating a fraction
We can set up a proportion to figure out anything we need to
add or draw on the map
We can set up proportions to actually build things in reality
We can set up proportions to figure out missing dimensions
Connecting scale and scale factor
 Lets determine the scale factor first
 We know the scale is 1cm : 2 meters
 First we need all the measurements in the same units so….
1cm : 2 meters = 1cm : 200cm
 Then, we set up the ration as a fraction


1cm : 200 cm =
Yes, it looks like a fraction, but we can actually do some calculating
here because the line represents division!
= 0.005 which is the scale factor!
So, in the creation of the map, they used a scale factor of 0.005 to
reduce all the actual measurements to the correct size to draw on the
map.
Using proportions to reduce
 We can quickly set up a proportion to figure out what
size our drawings need to be on the map in order to
accurately represent the actual mall.
 Let’s say that you need to draw a 13.5 meter long
hallway. How long should the drawing be in order to
accurately represent the hallway?
=
 Using cross multiplication to solve:
2 = 1 x 13.5
= 6.75 cm
Using proportions to reduce
 What about drawing a kiosk that is 3.2 meters long
by 2.6 meters wide?
=
2x = 1 x 3.2
x = 1.6 cm
=
2x = 1 x 2.6
x = 1.3 cm
Using proportions to enlarge
 Now, if you were the master carpenter in charge of building
the actual objects, you could also use proportions to figure
out how large you need to make your objects.
 For example, if you know the blueprints use a scale of 1cm :
2 m , and the blueprint shows a long bench that is 1.7 cm by
2.7 cm , you can set up proportions to figure out the
dimensions of the actual bench that you need to build.
=
=
1x = 2 x 1.7
1x = 2 x 2.7
x = 3.4 m
x = 5.4 m
So your bench needs to be built 3.4 m wide by 5.4 m long.
Using proportions to find missing dimensions
 We can keep up with proportions. What of you built
the bench, and the owner of the mall said it was too
small. They want it to be 6.5 meters long, and
proportionately wider. Use proportions to figure out
the new width.
=
5.4 x = 3.4 x 6.5
5.4 x = 22.1
x = 4.0925925
x = 4.9 m
A final connection
 If you were the architect, and you had to re-draw the
blueprint to show the new bench, use proportions to
figure it out.
=
2x = 1 x 6.5
x = 3.25 cm
=
2x = 1 x 4.1
x = 2.05 cm
And that is how it all connects!
 And there are SO many other ways to use this.......