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Proportion: Math & Art

Marsh IB-TAP: Hasapis & Alba
by

Michelle Alba

on 16 November 2012

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Transcript of Proportion: Math & Art

Proportion Concepts /Vocabulary Art Ratio a comparison of 2 things
example: the ratio of boys to girls in this class is _____
how to create equivalent ratios Proportion is built from 2 ratios set against each other
example: if there are 100 girls in the school, we can
estimate that there are ____ boys (Concept 3) Unit rates are ratios in which the second quantity is 1 example: $.45 for one lollipop Real-life application Why is
proportion
important? Application
of skills Measure? Examples: Evaluation Knowledge Proportion Other
areas Solve for unknowns? Examples: Solve for various units
of measurement Examples: Nutrition Environment Society Inspiration Larger than life Math Make a plan I will
be able to: Goals Sense Plan Inquire Process Reflect Evaluate Create Personal
Engagement Links / Resources Inspiration Examples I will
understand: I will
be able to: Design / Sketch Examples: Measure dimensions Examples: Scale up in 2-D drawing
or 3-D Construction Examples: Proportion / Scale the relationship between objects, or parts, of a whole Architecture / Planning the art or practice of designing and building structures and especially habitable ones Renaissance the transitional movement 14th-17th century in Italy, humanistic revival of vigorous artistic and intellectual activity and the beginnings of modern science http://www.amazing-planet.net/microscopic-sculptures-by-willard-wigan.php

http://www.smosh.com/smosh-pit/knowledge/giant-sculptures-claes-oldenburg Examples Images that Math is used to describe
ratio a comparison of 2 things
example: the ratio of boys to girls in this class is _____ Proportion is used in Art a comparison of parts to other parts or the whole:
whether in size or number of lines, shapes, color, etc definition: examine, study, look at Infer definition: make an educated guess Observe Examples: Day 1 Close read Describe specifically What are the results of "bad" proportion? What are the results of "good" proportion? What are examples of larger than life? What are examples of "small" that still have wide effect? Music Movies Family Health I will
understand Content Skills Concepts /Vocabulary Content Skills Concepts /Vocabulary Applicable Skills I will
be able to: I will
understand: Names, background, curiosities. "What do we know?" We know more than we think. Introductions Take our time. Observe art image This is how we will
do things today: Observations
Inferences Share & discuss T-charts
Prezi Create T-charts, fill in Sense Reflection - portfolio 1 2 3 4 5 6 Process Documentation - Day 1 MATH: Proportion As we increase the size of the Golden Rectangle,
we keep the proportion the same (roughly). ART: Golden rectangle Golden rectangle has been used in art To create circles & curves Draw with a ruler To create clean, straight lines,
making sure to draw to corners of
the graph paper squares. Draw with a compass Using a calculator and our drawings,
check if the Golden Ratio holds up
through the spiral. Day 3 Golden Rectangle repeated Determine ratios Concepts /Vocabulary Applicable Skills I will do I will learn What's the big deal about the
Golden Ratio? Practice with compass Examples: Review concepts Examples: Create 1.25" Rectangle This is how we will
do things today: Examples: Repeat & check ratios Examples: Setup equations Examples: Reflection - portfolio 1 2 3 4 5 6 Process Documentation - 3 MATH: Math concept a comparison of 2 things
example: the ratio of boys to girls in this class is _____ ART: Artistic proportion
definition Examples: Infer Examples: Observe Examples: Day 4 Start sketches Describe specifically Concepts /Vocabulary Applicable Skills I will
be able to: I will
understand Can "good" or "bad" proportion be both felt and mathematically supported? "What do we know?" Examples: Introductions Examples: Observe art image This is how we will
do things today: Examples: Share & discuss Examples: Create T-charts, fill in Examples: Reflection - portfolio 1 2 3 4 5 6 Process Documentation - 4 MATH: Math concept a comparison of 2 things
example: the ratio of boys to girls in this class is _____ ART: Artistic proportion
definition Examples: Infer Examples: Observe Examples: Day 5 Describe specifically Concepts /Vocabulary Applicable Skills I will
be able to: I will
understand Examples: "What do we know?" Examples: Introductions Examples: Observe art image This is how we will
do things today: Examples: Share & discuss Examples: Create T-charts, fill in Examples: Reflection - portfolio 1 2 3 4 5 6 Process Documentation - 5 MATH: Geometric design Geometry --using measurements & tools can create
work that has smooth & angled shapes. ART: Color is an element The repetition of color & shape creates a pattern. Examples: Carefully color designs Examples: Make thoughtful choices Examples: Day 6 Color, work, & time Time myself on each Concepts /Vocabulary Applicable Skills I will do I will learn The order of things Process Documentation - 6 MATH: the math behind the Golden Ratio The ratio of two parts of a line such that the longer part divided by the smaller part is also equal to the whole length divided by the longer part. ART: Golden Ratio This mathematic ratio can be found in nature (in plants & the human form) and has been used in design: from architecture to paintings to web design. a:b
a/b
a to b Do math behind Golden Ratio A : B = (A+B) : A
A / B = (A+B) / A
A to B = (A+B) to A Express ratio 3 ways Create our own Golden Rectangle.
Apply Golden Ratio to our original square designs. Day 2 the Golden Ratio Draw with a ruler & a compass Concepts /Vocabulary Applicable Skills I will do I will learn Finish discussing Statue of Liberty
Look at Prezi What does 1:1.618 mean?
Let's understand the math behind it! Discuss ratio Can we see how the Golden Ratio applies to nature & can be applied to art? Analyze images The order of things Using: graph paper, pencils, rulers, & compasses. Discuss: the importance of drawing lightly at first. Spiral the Rectangle Continue drawing/increasing the Golden Rectangle, keep notes & make predictions. Draw Golden Rectangle Sense Reflection - portfolio 1 2 3 4 5 6 Process Documentation - Day 2 Scale - work with proportion equations as much as possible

Presenting = real-life (measuring tape + string/yardsticks)

Their own Geometric designs that are enlarged...
-- graph paper

Color - paint (recipe)

23 kids, 10se, 1 hearing disability

Chapter 5
Days 1-4

2:3, 2/3, 2 to 3

Ratio - visual

Simplifying

Days 5-6

Scale drawings
--car drawing 4 inches--what is size of actual car?
--famous buildings from around the world

Days 9-11

Fill in missing side Day 1 - Close Read

Art: look at 1 image, then distribute many....students infer how math is involved...what proportion is to us...examples...does to us....everyday life....(K class)

Day 2: Good proportion? Renaissance etc
Art: Dividing the space in DIFFERENT COLOR - Number it...keep this as a reference/WS ... initial Math will be based on this....
Line & Shape
Drawing practice - light w/ rulers, compasses

Day 3: Composition - symmetry
Art: Design #1 - proportion of shape
challenge: repeat exact shape in diff sizes

Day 4: Composition - asymmetry
Art: Design #2 - attempt diff forms w same start

Day 5: Color Theory - Wheel (color pencil or own wheel w paint?)
Art: Comp 1: Complementary
Comp 2: Analogous
Choose 1 to enlarge

Day 6: Scale up / planning
Art:
multiply by different factors--decide on 1 factor.
ID original dividing lines...largest shapes
measure + scale up on WS [must be congruent]
Make predictions - is it true?

Day 7: Scale up / drawing
Content:
Art: Final day of large drawing

Day 8: Droportions
Content: Collect data on 1 specialized color...
Use eyedropper formulas w R, Y, B, W(ater, Bk
Art: Make recipe cards for color...value scales?
Paint in ALL occurrences of that color...
WORKSHEET: how much is needed to achieve spec color

Day 9: Proportion in paint
Art: Painting w/ recipe for 2nd color...


Day 10
Art: Final day of painting, using last color

Day 11 - Critique + Reflection
Art:

WS: ratios of shapes/color/lines to each other
triangles to squares
Blue-green shapes to green
vertical to diagonal inquiry sense plan reflect evaluate create Good proportion? Renaissance etc
Art: Dividing the space in DIFFERENT COLOR - Number it...keep this as a reference/WS ... initial Math will be based on this....
Line & Shape
Drawing practice - light w/ rulers, compasses http://www.mathsisfun.com/numbers/golden-ratio.html

http://jwilson.coe.uga.edu/emat6680/parveen/gr_in_art.htm Observe Infer Statue of Liberty group inferences

Made out of wood?
Made out of metal/steel
concrete? rock?

air-dry Clay

Scaffolding -
protect?
hold it together?
to stand on when building it?

Made in 1800's?

Size of drawing: 8.5x11
1, 1.5, 2 desks
as big as screen, as big as wall
as big as the playground

Size of statue: ~ 100ft
as big as school? (12x4) + (3x4) inferences:

Bigger than the Bean or Marilyn Monroe downtown
this sculpture is in a park
in California?
Summer or spring?
the sculpture is a bridge
it's in a miniature golf course
it's in a city
Where's the ice cream??
who's going to eat this??
who made it?
made for a famous pie shop
made of metal, clay, plastic? observations:

Sculpture of a cherry on spoon
10x bigger than the 4? people in foreground
there's a jogger behind sculpture
green trees+grass in background
water underneath sclupture
expressway, buildings, wires in background observations

Blueprint of Statue of Liberty

Drawing showed inside

Side + front views

Buildings, crowd people,

Scaffolding around Statue Know Want to know What we want to know about
Proportion, Math & Art: What we know about
Proportion, Math & Art: What we learned about
Proportion, Math & Art: 2 3 Learned 4 What kind of research and analysis did you do today?

How may this help your understanding of the concept of Proportion?

Thoughts & questions you may have: 6 "What do we know?" Observe art image Create T-chart & fill in Share & discuss 5 the Golden Ratio people like art
compare math & art
math & art are unrelated
sometimes related
proportion and size:
clothes, food, class-size
Kool-aid mix!
how big a drawing or painting is
how much paint you need Quiznos - how cheap are they
Where does inspiration come from?
is it real food? how much is "other"
how much fat, calories, cholesterol, fiber? schedules?
are we going to draw, eat, go outside and observe stuff, field trips?
What is too far?? a Ms. Michelle's thoughts after 10/11 on
Ratio in the classroom:

ration of boyx to girls
ratio of raised hands to talking mouths
ratio of number of observations/answers per minute
ratio of nods to confused looks
ratio of serious observations to jokes
ratio of length of time looking at image and questions you have
suggestions??
how much is too far or too much or too loud? how much is not enough? 1st thing:
go through Prezi (add in rates?)

Discuss my thoughts from last time...ask for contributions

play with drawing:
[buy rulers + compasses? + more graph paper + paint]
rulers:
drawing only to corners
....what do smaller increments mean?
discuss polygons possible...

compasses:
practice making curves, circles
discuss stopping...

scaffold to drawing Golden Rectangle 3 2 "We need math to multiply the small measurements to
make the REAL measurements to construct it." - James "Can we measure our school and see if it matches blueprint?" - James or Angel

HOW? Photo compositions: http://photoinf.com/Golden_Mean/Eugene_Ilchenko/GoldenSection.html Finish up Golden Rectangles

Draw 6 squares/rectangles

At least 3" x 3"

Draw 2 lines through each Demonstrate how to expand design
MUST:
use rulers and compasses
draw lines to/from the corners of squares
draw lightly
mark centers of

SUGGESTIONS
Repetition Visual elements vocabulary Demo & reminders Color pencils and risks/limitations View images/discuss Conscientiously choose 3-color design Choose 3 colors each Carefully fill in & complete our designs Time ourselves For each design, mark down
Start time and End time Color, fill, blend Sense Reflection - portfolio 1 2 3 4 5 6 San Marco
tiles stained
glass Visual elements digital prints & painting Write down for each design
Start time
End time Color with pencil strokes
in same direction Reminders Develop design THOUGHTS:

Fashion design
Car design
Product design
Architecture
Sculpture
Painting
Food/cooking
Music
Movies/TV Scale up to back wall measurement,
measurement of a real space...billboard

What went well -- checklist of craftsmanship + endurance + independent thinking...

What would you do differently --with time, resources that Math is used to describe
ratio a comparison of 2 things
example: the ratio of boys to girls in this class is _____ Proportion is used in Art a comparison of parts to other parts or the whole:
whether in size or number of lines, shapes, color, etc definition: examine, study, look at Infer definition: make an educated guess Observe Examples: Day 7 Unit rates Describe specifically Concepts /Vocabulary Applicable Skills I will
be able to: I will
understand: Names, background, curiosities. "What do we know?" We know more than we think. Introductions Take our time. Observe art image This is how we will
do things today: Observations
Inferences Create T-charts, fill in 1 2 3 4 Process Documentation - 7 Worksheet:

Unit Rate that Math is used to describe
ratio a comparison of 2 things
example: the ratio of boys to girls in this class is _____ Proportion is used in Art a comparison of parts to other parts or the whole:
whether in size or number of lines, shapes, color, etc definition: examine, study, look at Infer definition: make an educated guess Observe Examples: Days
8-9 Paint-mixing ratios Describe specifically Concepts /Vocabulary Applicable Skills I will
be able to: I will
understand: Documentation - 8 + 9 that Math is used to describe
ratio a comparison of 2 things
example: the ratio of boys to girls in this class is _____ Proportion is used in Art a comparison of parts to other parts or the whole:
whether in size or number of lines, shapes, color, etc definition: examine, study, look at Infer definition: make an educated guess Observe Examples: Days
10-11 Watercolor Painting Describe specifically Concepts /Vocabulary Applicable Skills I will
be able to: I will
understand: Documentation - 10 + 11 that Math is used to describe
ratio a comparison of 2 things
example: the ratio of boys to girls in this class is _____ Proportion is used in Art a comparison of parts to other parts or the whole:
whether in size or number of lines, shapes, color, etc definition: examine, study, look at Infer definition: make an educated guess Observe Examples: Day 12 Reflection Describe specifically Concepts /Vocabulary Applicable Skills I will
be able to: I will
understand: Documentation - 8 + 9 Names, background, curiosities. "What do we know?" We know more than we think. Introductions Take our time. Observe art image This is how we will
do things today: Observations
Inferences Create T-charts, fill in 1 2 3 4 Names, background, curiosities. "What do we know?" We know more than we think. Introductions Take our time. Observe art image This is how we will
do things today: Observations
Inferences Create T-charts, fill in 1 2 3 4 Names, background, curiosities. "What do we know?" We know more than we think. Introductions Take our time. Observe art image This is how we will
do things today: Observations
Inferences Create T-charts, fill in 1 2 3 4 Posing an actual REAL-WORLD application
- measuring space in the hallway
- logistics

Each make our own tile and find a way to put them all together
- looking for patterns

Something PERMANENT at the school
- archival
- principal ok? small design
scale up! RSA - dan pink
1 day of autonomy throughout process...
PLAY but show us what you've done...

autonomy
mastery
purpose... Research - geometry/pattern in art history
architecture
mexican
islamic
greek
pottery


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