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        6-8, 13+

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        Math + Arts | Circle Designs

        In this lesson, students explore circumference and diameter by creating an abstract design with circles.

        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 discuss the overlap of geometry and visual art. Students will watch a video about formulas for circle area and play an interactive game that teaches how to calculate diameter, radius, and circumference.

        2. Short hands-on activity: students explore circumference and diameter by measuring with string and tracing and cutting out circles.

        3. Project (view and discuss): students use the circles that were cut out in the short activity and others to create an abstract design.

        Time Allotment

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

        2. Short hands-on activity: 1 class period

        3. Project: 2 class periods

        Learning Objectives


        I can identify the parts of a circle including diameter and circumference.

        I can identify pi.

        I can justify that pi can be derived from the diameter and circumference.

        Arts and Humanities

        I can understand the commonalities between geometry and visual art.

        I can discuss works of art in terms of their color schemes and contrast.

        I can work with my peers to create a work of art with specific criteria.

        I can evaluate my own work and the work of my peers in a supportive manner.

        Prep for Teachers

        Information on elements of art, color theory, and contrast as a design principle is included in the PowerPoint.

        Information on the skills students will use is in the document “Basic Skills for 6th-8th Grade Visual Art.”


        String (approximately 2 yards per student group)

        Centimeter rulers or tape measures (one per student)

        Cylindrical shaped objects of various sizes (4 per student group)

        Colored card stock

        Scissors (one pair per student)

        Calculators (one per student)

        Large sheets of black foam core board or cardboard for mounting


        Media Resources

        Cyberchase: Formulas for a Circle

        Cyberchase: Formulas for Circle Area and Circumference: Simple as Pie

        Cyberchase Interactive: Dunk Tank: Circles

        Introductory Activity

        Students should be able to name and identify specific parts of a circle (circumference and diameter).

        Learning Activities

        Frame, Focus, and Reflection

        Ask students what ideas that are important in geometry are also important in art. Allow them to brainstorm and guide them toward identifying shapes.

        Show the Cyberchase video "Formulas for a Circle" and play the Cyberchase interactive "Dunk Tank: Circles."

        Explain that you are going to do an art project related to circles. Show the PowerPoint, pausing to lead discussions about color and contrast. When you get to the last slide, show students the variety of colors of cardstock that you have available. Lead them in developing a rubric for assessing the project.

        Divide the class into groups and allow the groups to select four to six colors of cardstock. Put the sheets away for the next day.

        Short Activity

        Before beginning, be sure to have a variety of cylindrical objects available—at least four per group. You want a variety of sizes, but none should be too small.

        Students will measure the circumferences of a variety of different size cylinders and record the results. Using string to measure the circumference of cylinders and rulers to measure the length of the string, have them record the data on the "Circle Data Chart." It is much easier for students to use the base of the cylinder to measure the circumference of a circle.

        Next, have students trace the circular base of each cylinder, determine the diameter, and record the results. Have students use scrap paper to trace and cut out the circular base of each cylinder. Then, fold the circular template in half to locate diameter. Then have students measure diameter and record data on the "Circle Data Chart."

        Demonstrate how you can trace shapes at the edge of the paper or in the corners and have a larger piece of uncut scrap left over. Tell students to cut their circles by opening their scissors wide, to get a more even cut than with the tips. By rotating the paper toward their scissor hand instead of moving their scissors hand around the circle, they will get a truer circle.

        Then, have students calculate the ratio of circumference to diameter in circles and record data. Have students use their recorded data to discuss the relationships and form a generalization.

        After students have completed the measuring, recording, and ratio activities, have each group store it’s circles and scrap paper for the next day.


        Day One

        Distribute the circles and scrap paper, scissors, cylindrical objects, the black foam board or cardboard, and glue. (See Basic Skills to determine the method of gluing you want to use.)

        Review the rubric you developed as a group. If desired, make any final changes.

        Allow groups to cut additional circles; cut the circles into halves, quarters, or 3⁄4 pieces; experiment with arrangements; and glue their compositions.

        Day Two

        Distribute the rubrics. Allow each group to self-assess and to write a rationale for the score they give themselves. Remind them to use terms like contrast, primary, secondary and tertiary, warm and cool, and shade and tint.

        Then, allow each group to assess another group’s project and write a rationale. Allow the groups that assessed one another’s projects time to compare and discuss their assessments before they finalize the scores. Remind students that an important aspect of discussing and evaluating art is having respect for differing opinions and being supportive of one another.

        Exhibit the projects and the student charts on circumference, diameter and the relationship between the two. Invite other classes, families, school and community leaders, and the media to the exhibit. If possible, have an opening reception for the exhibit and allow your students to present and explain their work.

        Formative Assessment

        What are the indicators of student progress toward or achievement of each learning target?

        Math Assessment Problems

        Completion of "Circle Data Chart."

        Exit slip of calculating circumference of a circle.

        Reflection of relationship of circumference to diameter.

        Arts and Humanities

        Exit slip: what do geometry and visual art have in common?

        Exit slip: what colors did your group select and why? Use terms like contrast, primary, secondary and tertiary, warm and cool, and shade and tint.

        Teacher review of the rationales that students write on their assessment of their own and one another’s art projects. Monitor for correct use of terms.

        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 the lesson plan, PowerPoint, photos of student work, and sample assessments and rationales written by students.

        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 arts curriculum provides for the development of arts literacy in all four arts discipline and also utilizes the Common Core Standards for English/Language Arts?

        c) 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?

        d) 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 appropriate 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: Debbie Jackson Wagers, Cheryl Burchfield, and Judy Sizemore


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