Fraction Robots
Lesson by Emilia LeBlanc
Date: November 1, 2011
Lesson Theme / BIG Idea: Integrating Math & Art- World Issues solved by a Fraction Robot!
Grade level: 5th grade
Time: 50 minute periods, 1 class period
Lesson Overview:
In this lesson, students will practice using mixed fractions in order to create a robot that will solve one world problem that students want to solve. This robot will be created using shapes of colored paper consisting of the square, circle, triangle, and rectangle, and students will cut them in either halves, fourths, or eighths to create their robot. The students will be reviewing their knowledge of mixed fractions as well as creating a work of art that will ask them to focus on a problem that is important to them that they would like to solve someday. Artists such as Piet Mondrian, Ellsworth Kelly, and Kenneth Noland will be used to demonstrate how artists simplify images using shapes and color, as well as the use of fractions.
Visual Culture Component/RELEVANCE:
Students are shown how shapes are simplified to create an image everyday, whether it be in street signs, quilts, or even industrial design. These simplifications involve planning whether it is with fractions, scale, or grids. For example, the ultimate shapes of street signs differ to make the meaning behind them more significant. When graphic designers create posters, they consider the shapes they use for the entire design, and use fractions to make an effective design
The students can see how effective this can be when observing these everyday objects, and how important math is when creating these figures. The students are going to be using these shapes and fractions in order to create an icon of a robot that will solve a problem in this world that they would like to change. The students must take note of the process of simplifying shapes and cutting their paper in halves, fourths, and eights to create a design. They will later be asked to calculate the fractions of the cut paper already given to them, and how many times they cut them.
Virginia Standards of Learning:
The student will:
• Select and use art media, subject matter, and symbols for expression and communication;
• Demonstrate understanding of and apply the elements of art and the principles of design and the ways they are used in the visual arts;
• Solve visual arts problems with originality, flexibility, fluency, and imagination;
• Use materials, methods, information, and technology in a safe and ethical manner.
Fine Art
Visual Communication and Production
5.1 The student will synthesize information to produce works of art.
5.5 The student will use the principles of design, including proportion, rhythm, balance, emphasis, variety, contrast, and unity, to express ideas and create images.
5.11 The student will emphasize spatial relationships in works of art.
Cultural Context and Art History
5.20 The student will research artists from a variety of cultures and the works of art they have produced.
Judgment and Criticism
5.24 The student will discuss an artist’s point of view based on evidence from written sources.
Math
The fifth-grade standards place emphasis on number sense with whole numbers, fractions, and decimals. This focus includes concepts of prime and composite numbers, identifying even and odd numbers, and solving problems using order of operations for positive whole numbers. Students will develop proficiency in the use of fractions and decimals to solve problems. Students will collect, display, and analyze data in a variety of ways and solve probability problems, using a sample space or tree diagram. Students also will solve problems involving volume, area, and perimeter. Students will be introduced to variable expressions and open sentences, and will model one-step linear equations in one variable, using addition and subtraction. Students will investigate and recognize the distributive property. All of these skills assist in the development of the algebraic concepts needed for success in the middle grades.
Number and Number Sense Focus: Prime and Composite Numbers and Rounding Decimals
5.2 The student will:
a) recognize and name fractions in their equivalent decimal form and vice versa; and
b) compare and order fractions and decimals in a given set from least to greatest and greatest to least.
Computation and Estimation Focus: Multistep Applications and Order of Operations
5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.
Lesson Objectives:
Students will:
1) Analyze the use of shapes and intentions in the artworks of Piet Mondrian, Ellsworth Kelly, and Kenneth Noland.
2) Decide on a world issue that needs solving and design a robot that will solve this problem
3) Arrange shapes that have been dissected into different fractions in order to assemble the robot the students wish to create
4) Select the fractions students used to create their robot by cutting paper and calculate the mixed fractions used for each shape
Vocabulary Words for Visual Analysis: (in the order they will be introduced)
· Fraction – Part of a whole. In a fraction, the denominator tells us how many parts the whole is divided into, and the numerator tells us how many of those parts we're dealing with.
· Mixed Fraction–a whole number and a proper fraction combined.
· Shape- the quality of a distinct object having an external surface or outline of specific form.
· Simplify- to make less complicated, clearer, or easier
Historical/Cultural/Artist Information:
Piet Mondrian (From Piet Mondrian Website under Resources)
Piet Mondrian was a Dutch painter and an important contributor to the De Stijl art movement. The non-representational paintings for which he is best known, consisting of rectangular forms of red, yellow, blue, or black, separated by thick, black, rectilinear lines, are actually the result of a stylistic evolution that occurred over the course of nearly thirty years, and which continued beyond that point to the end of his life.
Ellsworth Kelly
o Born in Newburgh, New York in 1923
o Real-life observations are the backbone of Kelly's abstraction works, which are replications of the shapes, shadows, and other visual sensations he experiences in the world around him.
o Uses simple shapes and colors to create his art
o Experimented with color-field painting.
o Used a grid system, placing a variety of warm and cool colors against one another to create optical effects on the canvas.
Kenneth Noland
o Known for his brightly colored concentric circles & other color field paintings
o Arrived after Abstract Expressionism and studying the great artists of that time
o “A student of the geometric abstractionists Josef Albers and Ilya Bolotowsky, he found his way toward geometric forms that served as vessels for vibrant washes of color stained into the canvas. In successive series of paintings, he introduced subtle changes into geometric forms that evolved from circles, chevrons, stripes and diamonds and back again to the circle late in his career.” – New York Times
Image Descriptions:
Date: November 1, 2011
Lesson Theme / BIG Idea: Integrating Math & Art- World Issues solved by a Fraction Robot!
Grade level: 5th grade
Time: 50 minute periods, 1 class period
Lesson Overview:
In this lesson, students will practice using mixed fractions in order to create a robot that will solve one world problem that students want to solve. This robot will be created using shapes of colored paper consisting of the square, circle, triangle, and rectangle, and students will cut them in either halves, fourths, or eighths to create their robot. The students will be reviewing their knowledge of mixed fractions as well as creating a work of art that will ask them to focus on a problem that is important to them that they would like to solve someday. Artists such as Piet Mondrian, Ellsworth Kelly, and Kenneth Noland will be used to demonstrate how artists simplify images using shapes and color, as well as the use of fractions.
Visual Culture Component/RELEVANCE:
Students are shown how shapes are simplified to create an image everyday, whether it be in street signs, quilts, or even industrial design. These simplifications involve planning whether it is with fractions, scale, or grids. For example, the ultimate shapes of street signs differ to make the meaning behind them more significant. When graphic designers create posters, they consider the shapes they use for the entire design, and use fractions to make an effective design
The students can see how effective this can be when observing these everyday objects, and how important math is when creating these figures. The students are going to be using these shapes and fractions in order to create an icon of a robot that will solve a problem in this world that they would like to change. The students must take note of the process of simplifying shapes and cutting their paper in halves, fourths, and eights to create a design. They will later be asked to calculate the fractions of the cut paper already given to them, and how many times they cut them.
Virginia Standards of Learning:
The student will:
• Select and use art media, subject matter, and symbols for expression and communication;
• Demonstrate understanding of and apply the elements of art and the principles of design and the ways they are used in the visual arts;
• Solve visual arts problems with originality, flexibility, fluency, and imagination;
• Use materials, methods, information, and technology in a safe and ethical manner.
Fine Art
Visual Communication and Production
5.1 The student will synthesize information to produce works of art.
5.5 The student will use the principles of design, including proportion, rhythm, balance, emphasis, variety, contrast, and unity, to express ideas and create images.
5.11 The student will emphasize spatial relationships in works of art.
Cultural Context and Art History
5.20 The student will research artists from a variety of cultures and the works of art they have produced.
Judgment and Criticism
5.24 The student will discuss an artist’s point of view based on evidence from written sources.
Math
The fifth-grade standards place emphasis on number sense with whole numbers, fractions, and decimals. This focus includes concepts of prime and composite numbers, identifying even and odd numbers, and solving problems using order of operations for positive whole numbers. Students will develop proficiency in the use of fractions and decimals to solve problems. Students will collect, display, and analyze data in a variety of ways and solve probability problems, using a sample space or tree diagram. Students also will solve problems involving volume, area, and perimeter. Students will be introduced to variable expressions and open sentences, and will model one-step linear equations in one variable, using addition and subtraction. Students will investigate and recognize the distributive property. All of these skills assist in the development of the algebraic concepts needed for success in the middle grades.
Number and Number Sense Focus: Prime and Composite Numbers and Rounding Decimals
5.2 The student will:
a) recognize and name fractions in their equivalent decimal form and vice versa; and
b) compare and order fractions and decimals in a given set from least to greatest and greatest to least.
Computation and Estimation Focus: Multistep Applications and Order of Operations
5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.
Lesson Objectives:
Students will:
1) Analyze the use of shapes and intentions in the artworks of Piet Mondrian, Ellsworth Kelly, and Kenneth Noland.
2) Decide on a world issue that needs solving and design a robot that will solve this problem
3) Arrange shapes that have been dissected into different fractions in order to assemble the robot the students wish to create
4) Select the fractions students used to create their robot by cutting paper and calculate the mixed fractions used for each shape
Vocabulary Words for Visual Analysis: (in the order they will be introduced)
· Fraction – Part of a whole. In a fraction, the denominator tells us how many parts the whole is divided into, and the numerator tells us how many of those parts we're dealing with.
· Mixed Fraction–a whole number and a proper fraction combined.
· Shape- the quality of a distinct object having an external surface or outline of specific form.
· Simplify- to make less complicated, clearer, or easier
Historical/Cultural/Artist Information:
Piet Mondrian (From Piet Mondrian Website under Resources)
Piet Mondrian was a Dutch painter and an important contributor to the De Stijl art movement. The non-representational paintings for which he is best known, consisting of rectangular forms of red, yellow, blue, or black, separated by thick, black, rectilinear lines, are actually the result of a stylistic evolution that occurred over the course of nearly thirty years, and which continued beyond that point to the end of his life.
Ellsworth Kelly
o Born in Newburgh, New York in 1923
o Real-life observations are the backbone of Kelly's abstraction works, which are replications of the shapes, shadows, and other visual sensations he experiences in the world around him.
o Uses simple shapes and colors to create his art
o Experimented with color-field painting.
o Used a grid system, placing a variety of warm and cool colors against one another to create optical effects on the canvas.
Kenneth Noland
o Known for his brightly colored concentric circles & other color field paintings
o Arrived after Abstract Expressionism and studying the great artists of that time
o “A student of the geometric abstractionists Josef Albers and Ilya Bolotowsky, he found his way toward geometric forms that served as vessels for vibrant washes of color stained into the canvas. In successive series of paintings, he introduced subtle changes into geometric forms that evolved from circles, chevrons, stripes and diamonds and back again to the circle late in his career.” – New York Times
Image Descriptions:
Piet Mondrian. Broadway Boogie-Woogie. 1942-43. Oil on canvas, 50 x 50"(127x127 cm). The Museum of Modern Art, New York.
Found: http://www.lichtensteiger.de/Images/broadway.jpg
This image shows Mondrian’s use of shapes to simplify an image and represent a subject. You can see his use of squares, rectangles, and color to represent buildings, taxi cabs, and lights. He uses fractions of certain shapes to create depth in his paintings.
Questioning Strategies
1. What do you think is represented in this painting?
2. What shapes does the artist use? Why do you think he used them?
3. How do you think simplifying of shapes relates to street signs? Posters?
4. If you had a very complicated poster/street sign with a lot going on would it be as effective?
Found: http://www.lichtensteiger.de/Images/broadway.jpg
This image shows Mondrian’s use of shapes to simplify an image and represent a subject. You can see his use of squares, rectangles, and color to represent buildings, taxi cabs, and lights. He uses fractions of certain shapes to create depth in his paintings.
Questioning Strategies
1. What do you think is represented in this painting?
2. What shapes does the artist use? Why do you think he used them?
3. How do you think simplifying of shapes relates to street signs? Posters?
4. If you had a very complicated poster/street sign with a lot going on would it be as effective?
Colors for a Large Wall, Ellsworth Kelly, 1951, The Museum of Modern Art, New York. Gift of the artist, 1969
Questioning Strategies
1. There are 64 squares in this piece, how many squares would half of this piece be?
2. Why do you think math relates to this piece?
Questioning Strategies
1. There are 64 squares in this piece, how many squares would half of this piece be?
2. Why do you think math relates to this piece?
MYSTERIES: INFANTA, Kenneth Noland, 2000
Questioning Strategies
1. What shape is being used in this painting?
2. Even though this shape is different than the ones we’ve seen, do you think there are ways to create fractions from it?
3. How do you think you could make different fractions from a circle?
Questioning Strategies:
Beginning Discussion
· When introducing artists- ask image questions above- to be shown on document camera
· After images and artists have been discussed- questioning about creating the robot will begin
Robot Questions:
· How many of you think there are problems in this world that need to be changed? (Wait for raised hands)
· What are some of these problems?
Fraction/Shape Questions
· Just like these artists did, how do you think shapes can represent your robot?
· What shapes could represent different body parts?
· How do you think you can dissect your shapes to create new ones? (For example, a large square can make four smaller ones, or two large triangles)
Closing Discussion Questions:
· Would anyone like to share their robot with the class and what it’s going to solve?
· Why did you choose the shapes that you did?
· How did you plan what shapes to use for your robot’s body parts?
Lesson Procedures:
Day 1:
· Students will begin the class period with daily warmup (provided by cooperating teacher) and calendar activity (5-10 minutes)
· Teacher will put up the three images of artists on the document camera (images should be printed clearly) and will introduce each artist and their backgrounds, as well as ask specific questions for each artist. Then questions should be asked to introduce the project, including questions about what robot the students are going to want to create, and how they can manipulate the shapes(5 minutes)
· Each student will be given a bag consisting of shapes for students to work with made of colored paper. Students will receive five large squares of different colors 3 x 3 inches, and 2 circles to create their shapes. They will also receive one 8.5 x 11 piece of colored construction paper as the background for their robot.
· On the document camera, the teacher will demonstrate that by cutting a square in half, you get a rectangle, and by cutting it into fours, you get four small squares. In order to create triangles, you can cut a diagonal line across the large square, and the circles can be used to create shapes as well. The teacher will let students know that on a piece of paper they should be keeping track of what they cut with their shapes because they will have to add up the fractions later on. (5 minutes)
· Students will be given their bags full of shapes and piece of construction paper. The students can begin cutting their paper, and if they do cut a square in half, they should be recording to keep track of the fractions they used. As soon as a student uses a shape that they have cut, they should be writing the fraction down. The students will be instructed to cut their paper and create the robot for (fifteen minutes), and then glue will be distributed to glue their robots down. They should be gluing their robots for five minutes, and should only be putting small dots on each corner to prevent the over usage of glue.
· During the last ten minutes of class, students should bring all of their pictures to one table, and they will be asked the concluding questions about their robots. The students should take their numbers home, and calculate the mixed fractions for homework. For example, if a student cut a square in half to create two triangles, they should add ½ + 1/2 = 1 square. If a student cut their square into four little squares they should add ¼ + ¼ + ¼ + ¼= 1.
· The students will be asked to bring these calculations back to class for the next time the practicum student is in class, as well as a paragraph about why they created their robot (which world problem) and why they chose the shapes they did. (If I used two large triangles for eyes, it was because I wanted my robot to be able to see really well and find the homeless to feed… etc.)
Materials and Preparation:
Teacher planning:
· Ziploc bags
· Paper cutter to cut colored construction paper into shapes needed for each student’s bag/ Construction paper
· Whole construction paper pieces (8.5 x 11) to use as a background
· Document camera
· Artist images printed to show on document camera
For class time:
· Scissors
· Glue (sticks or bottles)- if using bottles, instruct students on how to use tiny drops on corners to conserve glue
· Piece of loose-leaf paper to record calculation of fractions and write paragraph on about robot
Resources:
Images/Historical Information:
The Art Story: Your Guide to Modern Art. (2011). Ellsworth Kelly: Retrieved from http://www.theartstory.org/artist-kelly-ellsworth.htm
Kenneth Noland. (2010). Kenneth Noland: Retrieved from http://www.kennethnoland.com/
The New York Times: Art. (2010). Kenneth Noland, Abstract Painter of Brilliantly Colored Shapes, Dies at 85: Retrieved from http://www.nytimes.com/2010/01/06/arts/06noland.html
Piet Mondrian. (2005). Piet Mondrian Archive: Retrieved from http://www.pietmondrian.org/piet-mondrian.php
SOLs:
http://www.doe.virginia.gov/testing/sol/standards_docs/index.shtml
Special populations:
· ESL accommodations can be made by rephrasing questions, directions, and explanations. The teacher should make sure that there is understanding within the entire classroom when giving instructions and having discussions.
· The project involves cutting paper and gluing which the teacher will demonstrate so that students can be assisted visually. Students who have trouble understanding will be assisted by the cooperating teacher or practicum student walking around
Evaluation:
Integrating Math & Art- World Issues solved by a Fraction Robot!
Student Name _______________________________________________
Date ____________________________________________
The teacher will rate the student out of 12 points total with each objective being rated 3 points for excellent, 2 for average, and 1 point for a need for improvement. Students will be introduced to these objectives before the project.
1. Analyze the use of shapes and intentions in the artworks of Piet Mondrian, Ellsworth Kelly, and Kenneth Noland.
3*= Student openly participated and added new ideas in discussion of visual culture, artist information and historical information.
2*= Student answered questions, but with no detail or ideas.
1*= Student did not participate at all or show any attention.
_______________________ / 3
2. Decide on a world issue that needs solving and design a robot that will solve this problem and arrange cut paper to create their design solution.
3*= Chose a world issue and created a design using cut paper
2*=Cut paper design was not completely resolved, but does reflect an idea for solving a world issue.
1*= Cut paper design was not resolved and neither was the idea.
________________________ / 3
3. Student completed fraction calculations and paragraph explaining their intentions with their robot design
3*= Student completed all of the requirements
2*=Student did part of the classwork, but did not complete the outside work
1*= Student did not bring in anything to show
________________________ / 3
4. Attitude and Work Effort
3*= The student was focused and worked hard on the project with a positive attitude.
2*=The student did not work hard to complete project on time, and was a disruption.
1*= Project was not completed due to disruptive behaviors.
________________________ / 3
Questioning Strategies
1. What shape is being used in this painting?
2. Even though this shape is different than the ones we’ve seen, do you think there are ways to create fractions from it?
3. How do you think you could make different fractions from a circle?
Questioning Strategies:
Beginning Discussion
· When introducing artists- ask image questions above- to be shown on document camera
· After images and artists have been discussed- questioning about creating the robot will begin
Robot Questions:
· How many of you think there are problems in this world that need to be changed? (Wait for raised hands)
· What are some of these problems?
Fraction/Shape Questions
· Just like these artists did, how do you think shapes can represent your robot?
· What shapes could represent different body parts?
· How do you think you can dissect your shapes to create new ones? (For example, a large square can make four smaller ones, or two large triangles)
Closing Discussion Questions:
· Would anyone like to share their robot with the class and what it’s going to solve?
· Why did you choose the shapes that you did?
· How did you plan what shapes to use for your robot’s body parts?
Lesson Procedures:
Day 1:
· Students will begin the class period with daily warmup (provided by cooperating teacher) and calendar activity (5-10 minutes)
· Teacher will put up the three images of artists on the document camera (images should be printed clearly) and will introduce each artist and their backgrounds, as well as ask specific questions for each artist. Then questions should be asked to introduce the project, including questions about what robot the students are going to want to create, and how they can manipulate the shapes(5 minutes)
· Each student will be given a bag consisting of shapes for students to work with made of colored paper. Students will receive five large squares of different colors 3 x 3 inches, and 2 circles to create their shapes. They will also receive one 8.5 x 11 piece of colored construction paper as the background for their robot.
· On the document camera, the teacher will demonstrate that by cutting a square in half, you get a rectangle, and by cutting it into fours, you get four small squares. In order to create triangles, you can cut a diagonal line across the large square, and the circles can be used to create shapes as well. The teacher will let students know that on a piece of paper they should be keeping track of what they cut with their shapes because they will have to add up the fractions later on. (5 minutes)
· Students will be given their bags full of shapes and piece of construction paper. The students can begin cutting their paper, and if they do cut a square in half, they should be recording to keep track of the fractions they used. As soon as a student uses a shape that they have cut, they should be writing the fraction down. The students will be instructed to cut their paper and create the robot for (fifteen minutes), and then glue will be distributed to glue their robots down. They should be gluing their robots for five minutes, and should only be putting small dots on each corner to prevent the over usage of glue.
· During the last ten minutes of class, students should bring all of their pictures to one table, and they will be asked the concluding questions about their robots. The students should take their numbers home, and calculate the mixed fractions for homework. For example, if a student cut a square in half to create two triangles, they should add ½ + 1/2 = 1 square. If a student cut their square into four little squares they should add ¼ + ¼ + ¼ + ¼= 1.
· The students will be asked to bring these calculations back to class for the next time the practicum student is in class, as well as a paragraph about why they created their robot (which world problem) and why they chose the shapes they did. (If I used two large triangles for eyes, it was because I wanted my robot to be able to see really well and find the homeless to feed… etc.)
Materials and Preparation:
Teacher planning:
· Ziploc bags
· Paper cutter to cut colored construction paper into shapes needed for each student’s bag/ Construction paper
· Whole construction paper pieces (8.5 x 11) to use as a background
· Document camera
· Artist images printed to show on document camera
For class time:
· Scissors
· Glue (sticks or bottles)- if using bottles, instruct students on how to use tiny drops on corners to conserve glue
· Piece of loose-leaf paper to record calculation of fractions and write paragraph on about robot
Resources:
Images/Historical Information:
The Art Story: Your Guide to Modern Art. (2011). Ellsworth Kelly: Retrieved from http://www.theartstory.org/artist-kelly-ellsworth.htm
Kenneth Noland. (2010). Kenneth Noland: Retrieved from http://www.kennethnoland.com/
The New York Times: Art. (2010). Kenneth Noland, Abstract Painter of Brilliantly Colored Shapes, Dies at 85: Retrieved from http://www.nytimes.com/2010/01/06/arts/06noland.html
Piet Mondrian. (2005). Piet Mondrian Archive: Retrieved from http://www.pietmondrian.org/piet-mondrian.php
SOLs:
http://www.doe.virginia.gov/testing/sol/standards_docs/index.shtml
Special populations:
· ESL accommodations can be made by rephrasing questions, directions, and explanations. The teacher should make sure that there is understanding within the entire classroom when giving instructions and having discussions.
· The project involves cutting paper and gluing which the teacher will demonstrate so that students can be assisted visually. Students who have trouble understanding will be assisted by the cooperating teacher or practicum student walking around
Evaluation:
Integrating Math & Art- World Issues solved by a Fraction Robot!
Student Name _______________________________________________
Date ____________________________________________
The teacher will rate the student out of 12 points total with each objective being rated 3 points for excellent, 2 for average, and 1 point for a need for improvement. Students will be introduced to these objectives before the project.
1. Analyze the use of shapes and intentions in the artworks of Piet Mondrian, Ellsworth Kelly, and Kenneth Noland.
3*= Student openly participated and added new ideas in discussion of visual culture, artist information and historical information.
2*= Student answered questions, but with no detail or ideas.
1*= Student did not participate at all or show any attention.
_______________________ / 3
2. Decide on a world issue that needs solving and design a robot that will solve this problem and arrange cut paper to create their design solution.
3*= Chose a world issue and created a design using cut paper
2*=Cut paper design was not completely resolved, but does reflect an idea for solving a world issue.
1*= Cut paper design was not resolved and neither was the idea.
________________________ / 3
3. Student completed fraction calculations and paragraph explaining their intentions with their robot design
3*= Student completed all of the requirements
2*=Student did part of the classwork, but did not complete the outside work
1*= Student did not bring in anything to show
________________________ / 3
4. Attitude and Work Effort
3*= The student was focused and worked hard on the project with a positive attitude.
2*=The student did not work hard to complete project on time, and was a disruption.
1*= Project was not completed due to disruptive behaviors.
________________________ / 3
Student Work Samples:
Lesson shared with permission from the author