ART and MATH Perfect Together

Created by Judith T. Brendelformer K-12 art teacher and K-12 math

teacheredleaderk12@hushmail.com

Jbrendel2012@gmail.com

FEA July 2015

HAVE FUN and LEAVE withIDEAS and RESOURCES!!!

• Experience art activities that will enhance students’ performance in mathematics

• See and solve “friendly” related math examples• Recognize the process strategies that are the

same in math and art • Plan how you could use some activities next year,

or how they can be modified to meet the needs of your students and colleagues.

• Share what you already know and do!

Hdc. Wkbk. p.2, Math examples p. 1-2

Hdc. Wkbk. P.4 (online has variations + answer key)

Math examples p.

Magnetic darts hit only objects not the background

• What is the probability of hitting an apple as compared to hitting a leaf?

• What is the probability of hitting a leaf as compared to hitting a flower?

10/36 =.277 or about 28 % 18/36 = .5 or 50 %

F: about 17% 6/36=1/6

L: about 50 %18/36=1/2

28% compared to100%

Thrown darts hit only objects not the background

• What is the probability of hitting an apple or a leaf?

+

• What is the probability of hitting a leaf and a flower from all the objects?

x `

0.277 + 0.5 = .777about 78%

(.50)(.166)=.083 only about 8.3%

10+18 = 28 36 36 about 78%

Math Standards: ratio & proportion

Grade 6: Understand ratio concepts and use ratio reasoning to solve problems.•Find a percent of a quantity as a rate per 100

Grade 7: Analyze proportional relationships and use them to solve real-world and mathematical problems.•Recognize and represent proportional relationships between quantities.•Use proportional relationships to solve multistep ratio and percent problems

Mondrianart: horizontal and vertical lines

(primary colors, and black and white only)

math: area/perimeter problems

Mondrianhorizontal and vertical lines

warm colors(percent problems)

Mondrianhorizontal and vertical lines

cool colors

GraphPaper Mondrian for math

GraphPaper Modrian for math

Red = 8/48 = 1/6 Blue = 12/48 = ¼ Black = 6/48 = 1/8 Yellow = 4/48 = 1/12PROBABILITY: that a dart thrown will land onred = 17% 1/6 = .1666 about a 17% chance of hitting red blue = 25% ¼ = 25% chance of hitting blueblack = 12 ½% 1/8 = 12 ½ % chance of hitting black yellow = about 8% .083; about 8% chance of hitting a yellow

What fraction of the whole is represented by RED, BLUE, BLACK and YELLOW?What is the PROBABILITY that a dart thrown will land on Red, on Blue, on Black, on Yellow?

TRANSFORMATIONS

The 17 wall paper patterns(4 page handout)

TRANSFORMATIONS/TESSELLATIONS

Resource:QUIZ – 18 question quiz (Let your math teacher help out with an answer key or to borrow protractors to help your students.)

1

2

3

4

5

6

7

1

2

3

4

5

6

7

SIMILAR shapes •Sides in proportion•Angles are equal•Parallel lines (cut by a transversal) corresponding angles are =

a 2-point perspective drawing.

Find the VISUAL MIDDLE in a 2-point perspective drawing.

Geometry and Art

A PERSPECTIVE DRAWING unithttp://www.sde.idaho.gov/site/humanities/docs/curriculum/14%20Perspective%20Drawing.pdf

Linear perspective is a mathematical system for creating the illusion of space and distance on a flat surface. This system originated in Florence, Italy in the early 1400’s. The artist and architect Brunelleschi demonstrated its principles, but another architect and writer, Leon Battista Alberti was first to write down rules of linear perspective for artists to follow.

Ratio/Proportion/Measuring

• Plan/draw a piece of artwork that will be reduced in size by 50% to appear in the school magazine.

• Draw/sketch the artwork that will be enlarged and used as a guide for a 20’ x 40’ school mural. (All wall art must be approved by the district BOE.)

• Help your teacher measure and cut tag-board frames for the spring art show.

FOLDing PAPER and POLYGONS

Are the diagonals of a rectangle congruent?Are the diagonals of a square congruent?

Do diagonals of a rectangle bisect each other?Do diagonals of a square bisect each other?

Is the formula for area of a rectangle the same as the formula for area of a square? How do you know?

FOLDing PAPER and POLYGONS

Are the four angles of a rectangle right angles?Are the four angles of a square right angles?

Show me!Do diagonals of a rectangle bisect each angle?Do diagonals of a square bisect each angle?

Are the diagonals of a rectangle perpendicular?Are the diagonals of a square perpendicular?How do you know?

Math: surface area OR volume

Art: draw & build 3-dimensional forms•Ceramics•Sculpture

What shapes

make up a cylinder?

How many sides (faces) to a cube?

Draw the NET of

this box.

How can you find the volume of liquid in this glass?

NETS and Geometry

How do you find the volume?

CIRCLE FOLD from 2D to 3D

CenterCircumferenceChordsArcsAngleVertexCongruent arcs

CIRCLE FOLD from 2D to 3D

• Triangle• Equilateral

triangle• Sides congruent• Angles equal• Perimeter if one

side = 4 inches• Area?

CIRCLE FOLD from 2D to 3D

• Polygon: 4 sided• Quadrilateral• Trapezoid• Equilateral trapezoid• Sides: opposite

parallel• Angles: Base angles =

Opposite angles 180˚• Area? Perimeter?

Area = base x height

Area = average of the bases

x height

CIRCLE FOLD from 2D to 3D

• 3-dimensional form• Sides/Faces:• Congruent faces• Surface Area• Volume

Art and Math VOCABULARY

should be the same.

CIRCLE FOLD from 2D to 3D

• 3-dimensional form• Sides/Faces:• Congruent faces• Surface Area• Volume

Students need to develop effective ways to

CRITIQUE the work or others

• Math students are required to critique the thinking process, strategies and solutions of others. (CCSS and PARCC) and to explain their conclusions.

• Math teachers often need to learn how to develop a variety of effective critiquing situations, fair rubrics, and to understand the non-math skills students need.

• Art students often critique their own work, other students’ work, and work by professional artists.

• Art teachers design and use a variety of successful critiquing sessions and assess with fair, helpful rubrics.

• Collaboration among math and art teachers would be very helpful here.

Students need to develop effective

Comparing Contrasting SkillsDescribe: 3 ways the same, 2 ways differentMath: A rectangle and a parallelogram

Art: a slab container and a coiled container

Comparing Contrasting SkillsHow did two students solve these problems differently? Explain or model; justify your answer.Math: Find the length of a side of a right triangle-use the Pythagorean Theorem -find the distance between 2 points on a grid-measure with a rulerArt: Create a feeling of excitement-bold, bright colors and black w/jagged shapes-angled thick/thin lines, 3D sparkles, vivid colors

FRACTALS

• History of Fractals (2-pages)• Cut-Out-Fractals activity (4-pages)

Creative Problem-SolvingDesign/decorate this cup: (Select 5 different tasks; create at least 2 thumb-nail sketches for each one).

A)For a 5 year old girlB)For a 5 year old boyC)For a 16 year old girlD)For a 16 year old boyE)To look sturdy and practicalF)To look delicate and expensiveG)To hold a “hot” drinkH)To hold a “cool” refreshing drinkI)Use your own idea (explain use)J) Use your own idea (explain use)

Math Practices Standards K-12

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure8. Look for and express regularity in repeated reasoning

Math Practices Standards K-12

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure8. Look for and express regularity in repeated reasoning

EXIT CARD(last sheet in your workbook package)

Thank you for your participation.