SIZING UP SCALESIZING UP SCALE

CREATED BY KRISTINE VESTERCREATED BY KRISTINE VESTER

MATHSCIENCE INNOVATION MATHSCIENCE INNOVATION CENTERCENTER

Where do you want to Where do you want to live?live?

Determining Room SizeDetermining Room Size

“The Cape”

Reflections of West Creek Apartments

How big is this How big is this apartment?apartment?

What are the What are the measurements measurements of the of the bathroom?bathroom?LengthLength WidthWidth

Length

width

What is the length and width of What is the length and width of the bathroom?the bathroom?

0%

0%

0%

0% 1.1. 11 ft by 13 ft11 ft by 13 ft

2.2. 11 ft by about 6 ft11 ft by about 6 ft

3.3. 9.4 ft by 5.8 ft9.4 ft by 5.8 ft

4.4. 11 ft by 5 ft11 ft by 5 ft

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Ba-ila SettlementBa-ila Settlement

Where do I live?Where do I live?

slavesChief

storageanimals

the Chief’ssiblings

Which do you need in order to find Which do you need in order to find the size of the settlement?the size of the settlement?

The

number

of .

..

How m

uch fo

od ...

The

number

of .

..

A m

easu

rem

ent .

..

0% 0%0%0%

1.1. The number of The number of people living there.people living there.

2.2. How much food they How much food they eat.eat.

3.3. The number of The number of animals living in the animals living in the village.village.

4.4. A measurement of A measurement of something within the something within the village.village.

10Seconds

Remaining

0

32

Measure the following lengths in Measure the following lengths in millimetersmillimeters

A. The distance from the Chief’s altar to the Chief’s entrance.

B. Distance from the Chief’s entrance to the settlement’s entrance.

C.Distance from the back hut’s entrance and the settlement’s entrance.

Is there any relationship between the three measurements?

What relationship did you see?What relationship did you see?

Find the following measurements.Find the following measurements.Distance Distance from the from the Chief’s Chief’s

Altar to the Altar to the Chief’s Chief’s

Entrance.Entrance.

Distance Distance from Chief’s from Chief’s Entrance to Entrance to Settlement’s Settlement’s

EntranceEntrance

Distance Distance from Back from Back

Hut’s Hut’s Entrance to Entrance to

the the Settlement’s Settlement’s

EntranceEntrance

3 meters3 meters

2 meters2 meters

1.5 meters1.5 meters

ScaleScale

It is the ratio of the size of the drawing to It is the ratio of the size of the drawing to the actual size of the object.the actual size of the object.

actual

drawing

We can utilize the scale ratio to find the missing measurement.

????

drawing

m

cm

3

25

????

55cm

Why is Scale important?Why is Scale important?

Used by professionals (i.e.: builders, Used by professionals (i.e.: builders, architects and plumbers)architects and plumbers)

Scale Factor: How much an object is Scale Factor: How much an object is increased or decreased by.increased or decreased by.

Scale: gives you an Scale: gives you an idea of how big an idea of how big an

object is.object is.

How tall is Robert How tall is Robert Wadlow?Wadlow?

How about now?How about now?8 ft 11 inches8 ft 11 inches

Ba-ila SettlementBa-ila Settlement

Where do I live?Where do I live?

slavesChief

storageanimals

the Chief’ssiblings

Let’s Test What We Have Learned Let’s Test What We Have Learned About Scale.About Scale.

Where do the Slave’s Living Quarters Begin?

What we do know!!!What we do know!!!The larger huts > 12 meters in width.

The smallest huts < 3 meters wide.

You will have to walk 20 meters into the village before you arrive at any slave’s living areas.

The distance from the entrance of the settlement to

the entrance of the back hut is 60 meters.

But Which Way?

How would you describe this How would you describe this picture?picture?

Sierpinski’s TriangleSierpinski’s Triangle

No matter how much you zoom, you still get the same

picture.

Another Example of Zooming.Another Example of Zooming.

Is this similar?Is this similar?

Scale: Even though you change the Scale: Even though you change the scale, the design stays the same scale, the design stays the same when you zoom in and out.when you zoom in and out.

Village CharacteristicsVillage Characteristics

How would you describe this How would you describe this picture?picture?

Scale: Even though you change the Scale: Even though you change the scale, the design stays the same scale, the design stays the same when you zoom in and out. when you zoom in and out.

Recursion: Repeating the same step.Recursion: Repeating the same step.

Village CharacteristicsVillage Characteristics

What’s the repeating pattern?What’s the repeating pattern?Similarity?

Are they similar?Are they similar?

YES NO

Are they similar? Why or why not?Are they similar? Why or why not?

No, t

hey a

re n

ot the.

..

Yes

, they

are

the

sa..

No, t

hey a

re th

e sa

m...

Yes

, they

are

the

sa..

0% 0%0%0%

1.1. No, they are not the No, they are not the same size.same size.

2.2. Yes, they are the same Yes, they are the same shape, but not the same shape, but not the same size.size.

3.3. No, they are the same No, they are the same shape, but not the same shape, but not the same size.size.

4.4. Yes, they are the same Yes, they are the same color.color.

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Answ

er Now

Is it self-similar?Is it self-similar?

YES NO

Is it self-similar, why or why Is it self-similar, why or why not?not?

Yes

, it i

s m

ad...

No, t

he in

side

...

Yes

, the

insi

d...

No, i

t doe

sn’t.

..

0% 0%0%0%

1.1. Yes, it is made up of Yes, it is made up of shapes.shapes.

2.2. No, the inside shapes No, the inside shapes don’t build the outside don’t build the outside shape.shape.

3.3. Yes, the inside shapes Yes, the inside shapes are similar to the whole are similar to the whole shape.shape.

4.4. No, it doesn’t look the No, it doesn’t look the same.same.

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Similarity?Similarity?Self-Similarity?

Ba-ila Settlement GrowthBa-ila Settlement Growth

Village CharacteristicsVillage Characteristics

Scale: Even though you change the Scale: Even though you change the scale, the design stays the same scale, the design stays the same when you zoom in and out.when you zoom in and out.

Recursion: Repeating the same step.Recursion: Repeating the same step. Self-similar: The parts are the same Self-similar: The parts are the same

as the whole.as the whole.

Charateristics of Fractals

What do they have in common?What do they have in common?

Bamileke SettlementBamileke Settlement

In which order will the settlement In which order will the settlement develop?develop?

A CB

In which order will the settlement In which order will the settlement develop?develop?

A, B

, C

A, C

, B

B, A

, C

B, C

, A

C, A

, B

C, B

, A

0% 0% 0%0%0%0%

1.1. A, B, CA, B, C

2.2. A, C, BA, C, B

3.3. B, A, CB, A, C

4.4. B, C, AB, C, A

5.5. C, A, BC, A, B

6.6. C, B, AC, B, A0of32

A

B

C

Bamileke SettlementBamileke Settlement

Let’s Look at Some Let’s Look at Some FractalsFractals

Which ones are fractals?Which ones are fractals?

A

C

B

Which ones are fractals?Which ones are fractals?

0%

0%

0%

0%

0% 1.1. A, BA, B

2.2. A, CA, C

3.3. B, CB, C

4.4. A, B, CA, B, C

5.5. None of themNone of them

Which ones are fractals?Which ones are fractals?

A

C

B

Which ones are fractals?Which ones are fractals?

14%

14%

14%

14%

14%

14%

14%

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Answer Now

1.1. All of themAll of them

2.2. A, B A, B

3.3. A, CA, C

4.4. AA

5.5. B B

6.6. DD

7.7. None of themNone of them

Why is this important?Why is this important?

Using Fractal Technology, we are able to create more realistic pictures. Which part of this scenery is a fractal?

THANK YOU !!!THANK YOU !!!