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        Math + Arts | Abstract Sculpture & Cubes

        In this lesson, students will form cubes and discuss their attributes including edges, faces, vertices, and angles.

        Lesson Summary

        There are three options for this lesson, depending on class needs and time available:

        1. Frame, Focus, and Reflection (view and discuss): students will view a video on the math in abstract sculptures. They will discuss and identify cubes.

        2. Short hands-on activity: students will form cubes out of cardstock. They will identify the attributes of a cube, including discussion of edges, faces, vertices, and angles.

        3. Project: students will make five cubes varying from one cubic inch to five cubic inches in size. They will then decorate these cubes in a variety of ways. After making the cubes, they will create abstract sculptures.

        Time Allotment

        1. Frame, Focus, and Reflection (view and discuss): 1 class period

        2. Short hands-on activity: 1 class period

        3. Project: 3-4 class periods

        Learning Objectives

        Math

        I can identify how math is used in the real world.

        I can use math tools precisely and accurately.

        I can calculate the surface area and perimeter of flat shapes composed of squares.

        I can understand the concept of volume and calculate the volume of a cube or a structure made of cubes.

        Arts and Humanities

        I can describe artwork using proper terms for at least two elements of art (form and color) and two principles of design (balance and contrast).

        I can make a cube out of cardstock by drawing, cutting and folding.

        I can make a series of cubes using the element s of art and the principles of design.

        I can decorate the cubes using the elements of art and the principles of design.

        I can work independently or with others to create an abstract sculpture.

        I can write a critique of my work.

        Prep for Teachers

        Elements of art

        In this lesson, the emphasis will be on the elements of form and color. In art, a 3-dimensional shape is called a form. Forms have length, width, and height and can be geometric or organic. This lesson emphasizes geometric (geometrically measurable) forms.

        The sculptor sometimes paints her steel and aluminum. The colors seen in the video can be identified as warm (red, yellow, and orange); cool (blue, green, and purple); or neutral (sliver, gray, black, white, and brown). You can add color to your cardstock project either by providing cardstock in different colors or by allowing students to use markers, crayons, or colored pencils. Students should be able to identify the colors they use as warm, cool, or neutral and the values as hues (pure colors), tints (light colors), and shades (dark colors).

        Principles of design

        In this lesson, the emphasis will be on balance (both symmetrical and asymmetrical) and contrast in color. If balance is symmetrical, students should be able to identify the line of symmetry as vertical, horizontal, or diagonal. Contrast in color may be described in terms of warm, cool, and neutral colors or value. Students should understand value as light (tints) and dark (shades) of color.

        Supplies

        Cardstock paper

        Tape

        Scissors

        Markers

        Crayons

        Colored pencils

        "Volume of Cube" Worksheet

        Media Resources

        Sculptor

        Cyberchase: Introduction to Angle Measure

         

        Introductory Activity

        If students are familiar with the attributes of squares and cubes, including measurement and right angles, review quickly. If not, you could use Introduction to Angle Measurement with the two video clips, handouts, and assessments. This will take at least one class period.

        Art Introduction: if needed, show Making a Cube which introduces the elements of art. Ask students to identify shapes and forms in the classroom. Ask them to identify warm, cool, and neutral colors. Ask them to find contrasting colors (warm and cool or dark and light) in the classroom. Quickly review the concepts of symmetrical and asymmetrical balance. A quick exercise is to ask students to stand with their arms at their sides. Explain that their bodies are demonstrating vertical symmetrical balance with the line of symmetry running vertically from the top of their heads to their feet (i.e., one side is the mirror image of the other). Now, have them extend their right arm straight up and their left arm diagonally downward. They are still balanced, but now the balance is asymmetrical because the two sides are no longer mirror images.

        This will take about 15 minutes and can be done in the same class period as watching the video.

        Learning Activities

        Frame, Focus, and Reflection

        Before watching the Sculptor video explain that you will be seeing how a sculptor uses math in creating her art. During the first part of the video, you want students to pay attention to the forms and colors that they see. Pause the video at 46 seconds and ask what forms they have seen. (Some will be easy to describe in geometric terms; others are organic and are more difficult to describe.) Ask students to identify the colors and classify them as warm, cool, or neutral.

        Before resuming, tell students that in the next part of the video you want them to pay attention to the math tools and math procedures that the sculptor uses. After the video, discuss how the sculptor uses math in creating her art.

        Ask students what Ms. Mears does for a living. Do they know anyone who makes their living as an artist? Do they know anyone who creates art for a hobby? Do any of them like to create art? Explain that many people find it personally fulfilling to create art, either as a profession or as a hobby.

        Play the video again and pause on one of the sculptures. Ask students to describe it in terms of form (geometric or organic and size as related to its environment) and color. Ask if they think it is balanced symmetrically or asymmetrically.

        Explain that public art, like Ms. Mears creates, is used to beautify the environment and to make it more interesting. Ask students if they have seen other examples of public art (e.g., statues, murals, stained glass windows, wall hangings or painting in a public building). Ask them to describe a piece they have seen, being sure to use art terms. Ask them if they like the sculpture you are viewing. Allow them to express and explain their opinions, again using art terms. Explain that people will have different responses to art. Ask what idea or emotion they think Ms. Mears might have been trying to communicate in this sculpture. Does it seem playful or does it give a sense of solidity? Again, people will have different responses and interpretations. Explain that they will get to create their own sculptures using cubes as building blocks.

        Ask students to identify the mathematical tools that Ms. Mears uses. Why is it important for her measurements to be precise?

        Short Activity

        Students will construct a 1-inch by 1-inch cube. Show "Making a Cube." Ask students how they will draw the template (geometric net) before cutting out the shape. What tools will they need? When they have their geometric nets drawn, lead them through calculating the length of one edge of one square and the total perimeter and surface area of the flat shape and record the information on the "Cube Calculation Table" worksheet. Have them fold and tape their completed cubes. Lead them through a discussion of volume, explaining that “A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.” Have them record the volume of their cube on the "Cube Calculation Table" worksheet.

        Project

        Days One-Two: Explain that each student will make a series of four more cubes with edges in increments of 2”, 3”, 4” and 5.” Show the slide show again on how to make a cube. If you wish, you can have them explore the different possible geometric nets that result in cubes (there are eleven).

        Have students use rulers and protractors to draw out patterns on cardstock for four different size cubes. Have them record the length of the edge of one square and the perimeter and surface area of their shapes on their "Cube Calculation Table" worksheet.

        Have students cut out cube patterns (geometric nets) and tape them to create cubes. Demonstrate that a cube 2” x 2” can be formed by combining four cubes that are each one cubic inch. Discuss that volume can be seen as the number of cubic units that could be packed into a rectangular solid. Demonstrate how to find the volume of the various sizes of cubes by seeing how many cubic units it would take to fill the larger cube and by multiplying L x W x H.

        Look at the "Cube Calculation Table" worksheets and see what patterns students can identify.

        Day Three: Show the video clip Sculptor again. Explain to students that they will use their cubes to create abstract sculptures. Students can work individually or together and can swap cubes with one another. Students can decorate cubes with markers or colored pencils. Students may bring in things of their own to decorate with, such as glitter and beads. Include in the decoration numbers representing the surface area and volume of each cube.

        When students have an arrangement they like, they can glue or tape it. As a wrap-up, have them calculate the total surface area and volume of their cubist sculpture. For advanced students, have them consider this as a scale model for a large, outdoor sculpture and determine what the size of the final sculpture would be and what the scale of their model is.

        Day Four: Have students give their sculptures titles. If it is a group sculpture, they will have to discuss their various interpretations and come to consensus. Distribute the "Critiquing a Work of Art" and "Critique Rubric" handouts. Review your expectations and have students write a critique of their individual or group sculptures. If they have worked in groups, have them share their critiques with one another. Their descriptions and analyses should be fairly consistent, but their interpretations and evaluations may vary. Explain that people often have different responses to art.

        Extension: If possible, plan an exhibit of students’ work in a public area of the school such as the media center or lobby. Invite other students, families, your site-based council, central office staff and/or community members to a reception for the exhibit. If possible, have your students on hand to explain their artistic and mathematical processes. If not, be sure to have their critiques included in the exhibit.

        Program Review

        Where does this fit in? How should you document it?

        This activity contributes to your school’s overall efforts in art programming in several areas, depending on whether you implement just the Frame, Focus, and Reflection portion or you implement the entire project.

        Document with samples of student work (photos of sculptures and copies of critiques), lesson plan and supplementary materials.

        Curriculum and Instruction: Aligned and Rigorous Curriculum

        a) To what extent does the school ensure that the arts curriculum encompasses creating, performing, and responding and is fully aligned with the Kentucky Core Academic Standards?

        b) To what extent does the school ensure that the school’s curriculum provides opportunities for integration as natural cross-curricular connections are made between the arts and other content areas?

        c) To what extent does the school ensure that the arts curriculum includes the study of representative and exemplary works of dance, music, theater, and visual arts from a variety of artists, cultural traditions, and historical periods?

        Curriculum and Instruction: Instructional Strategies

        a) To what extent do teachers systematically incorporate all three components of arts study: creating, performing, and responding into the arts?

        b) To what extent do teachers provide models of exemplary artistic performances and products to enhance students’ understanding of an arts discipline and to develop their performance/production skills?

        c) To what extent do arts teachers provide for the development of artistic theory, skills, and techniques through the development of student performances or products that are relevant and developmentally ap propriate for students?

        Curriculum and Instruction: Student Performance

        a) To what extent are students actively engaged in creating, performing, and responding to the arts?

        b) To what extent do students identify a purpose and generate original and varied art works or performances that are highly expressive with teacher guidance?

        c) To what extent do students, with teacher guidance, routinely use creative, evaluative, analytical, and problem solving skills in developing and/or reflecting in their artistic performances and products?

        d) To what extent do students use written and verbal communication to objectively reflect on exemplary exhibits and live or technologically provided performances as classroom assignments?

        Formative and Summative Assessment: Assessments

        a) To what extent do teachers utilize formative and summative arts assessments for individual students and performing groups that are clearly aligned with the components of the Kentucky Core Academic Standards; and authentically measure a specific concept, understanding and/or skill and lead to student growth?

        b) To what extent do teachers guide students to use developmentally or grade level appropriate peer review and critique to evaluate each other’s work?

        Formative and Summative Assessment: Expectations for Student Learning

        a) To what extent do teachers utilize exemplar/models to encourage students to demonstrate characteristics of rigorous work in the appropriate art form in most instructional lessons/units.

        b) To what extent do teachers share clearly defined rubrics or scoring guides with students before creating, performing, or responding assignments or other assessments; and students have the opportunity to provide input into the scoring guide?

        Formative and Summative Assessment: Assessment for Teaching

        To what extent do students regularly reflect on, critique, and evaluate the artistic products and performances of others and themselves as is grade level and age appropriate?

         

        Lesson Creators: Lesa Gieringer, Dianne Simpson, Emily Jackson, Dean Cornett, Dawn Hibbard, and Judy Sizemore

        Producer:

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